http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Jli639Physics Book - User contributions [en]2026-04-19T14:06:11ZUser contributionsMediaWiki 1.42.7http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=15463Motional Emf2015-12-05T20:58:18Z<p>Jli639: /* Middling */</p>
<hr />
<div>'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, variation of P60''.<br />
<br />
A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?<br />
<br /><br />
<br /><br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.<br />
<br /><br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.<br />
<br /><br />
<br />
===Middling===<br />
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Difficult===<br />
[[File:Middlemotionalemf.png|center|alt=Picture for difficult example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
*[[Motional Emf using Faraday's Law]]: An expansion of this concept<br />
*[[Lorentz Force]]: Combining electric and magnetic forces<br />
*[[Generator]]: Real-world application<br />
*[[Right-Hand Rule]]: How it works and other RHRs<br />
===Further reading===<br />
*''Matter & Interactions, Vol 2''<br />
*''The Feynman Lectures on Physics, Vol 2'', Ch 16<br />
<br />
===External links===<br />
*[http://web.mit.edu/8.02t/www/materials/StudyGuide/guide10.pdf Guide from MIT]<br />
<br />
==References==<br />
<br />
*''Matter & Interactions Vol 2''<br />
*MIT OpenCourseWare<br />
*[http://web.hep.uiuc.edu/home/serrede/P435/Lecture_Notes/A_Brief_History_of_Electromagnetism.pdf A Brief History of The Development of Classical Electrodynamics]<br />
<br />
[[Category:Fields]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13551Motional Emf2015-12-05T05:02:16Z<p>Jli639: </p>
<hr />
<div>'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, variation of P60''.<br />
<br />
A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?<br />
<br /><br />
<br /><br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.<br />
<br /><br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.<br />
<br /><br />
<br />
===Middling===<br />
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Difficult===<br />
[[File:Middlemotionalemf.png|center|alt=Picture for difficult example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
*[[Motional Emf using Faraday's Law]]: An expansion of this concept<br />
*[[Lorentz Force]]: Combining electric and magnetic forces<br />
*[[Generator]]: Real-world application<br />
*[[Right-Hand Rule]]: How it works and other RHRs<br />
===Further reading===<br />
*''Matter & Interactions, Vol 2''<br />
*''The Feynman Lectures on Physics, Vol 2'', Ch 16<br />
<br />
===External links===<br />
*[http://web.mit.edu/8.02t/www/materials/StudyGuide/guide10.pdf Guide from MIT]<br />
<br />
==References==<br />
<br />
*''Matter & Interactions Vol 2''<br />
*MIT OpenCourseWare<br />
*[http://web.hep.uiuc.edu/home/serrede/P435/Lecture_Notes/A_Brief_History_of_Electromagnetism.pdf A Brief History of The Development of Classical Electrodynamics]<br />
<br />
[[Category:Fields]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13439Motional Emf2015-12-05T04:33:24Z<p>Jli639: /* References */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, variation of P60''.<br />
<br />
A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?<br />
<br /><br />
<br /><br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.<br />
<br /><br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.<br />
<br /><br />
<br />
===Middling===<br />
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Difficult===<br />
[[File:Middlemotionalemf.png|center|alt=Picture for difficult example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
*[[Motional Emf using Faraday's Law]]: An expansion of this concept<br />
*[[Lorentz Force]]: Combining electric and magnetic forces<br />
*[[Generator]]: Real-world application<br />
*[[Right-Hand Rule]]: How it works and other RHRs<br />
===Further reading===<br />
*''Matter & Interactions, Vol 2''<br />
*''The Feynman Lectures on Physics, Vol 2'', Ch 16<br />
<br />
===External links===<br />
*[http://web.mit.edu/8.02t/www/materials/StudyGuide/guide10.pdf Guide from MIT]<br />
<br />
==References==<br />
<br />
*''Matter & Interactions Vol 2''<br />
*MIT OpenCourseWare<br />
*[http://web.hep.uiuc.edu/home/serrede/P435/Lecture_Notes/A_Brief_History_of_Electromagnetism.pdf A Brief History of The Development of Classical Electrodynamics]<br />
<br />
[[Category:Fields]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13421Motional Emf2015-12-05T04:30:02Z<p>Jli639: /* Further reading */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, variation of P60''.<br />
<br />
A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?<br />
<br /><br />
<br /><br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.<br />
<br /><br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.<br />
<br /><br />
<br />
===Middling===<br />
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Difficult===<br />
[[File:Middlemotionalemf.png|center|alt=Picture for difficult example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
*[[Motional Emf using Faraday's Law]]: An expansion of this concept<br />
*[[Lorentz Force]]: Combining electric and magnetic forces<br />
*[[Generator]]: Real-world application<br />
*[[Right-Hand Rule]]: How it works and other RHRs<br />
===Further reading===<br />
*''Matter & Interactions, Vol 2''<br />
*''The Feynman Lectures on Physics, Vol 2'', Ch 16<br />
<br />
===External links===<br />
*[http://web.mit.edu/8.02t/www/materials/StudyGuide/guide10.pdf Guide from MIT]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13417Motional Emf2015-12-05T04:29:48Z<p>Jli639: /* See also */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, variation of P60''.<br />
<br />
A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?<br />
<br /><br />
<br /><br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.<br />
<br /><br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.<br />
<br /><br />
<br />
===Middling===<br />
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Difficult===<br />
[[File:Middlemotionalemf.png|center|alt=Picture for difficult example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
*[[Motional Emf using Faraday's Law]]: An expansion of this concept<br />
*[[Lorentz Force]]: Combining electric and magnetic forces<br />
*[[Generator]]: Real-world application<br />
*[[Right-Hand Rule]]: How it works and other RHRs<br />
===Further reading===<br />
*''Matter & Interactions, Vol 2''<br />
*''The Feynman Lectures on Physics, Vol 2", Ch 16<br />
===External links===<br />
*[http://web.mit.edu/8.02t/www/materials/StudyGuide/guide10.pdf Guide from MIT]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13413Motional Emf2015-12-05T04:29:25Z<p>Jli639: /* See also */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, variation of P60''.<br />
<br />
A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?<br />
<br /><br />
<br /><br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.<br />
<br /><br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.<br />
<br /><br />
<br />
===Middling===<br />
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Difficult===<br />
[[File:Middlemotionalemf.png|center|alt=Picture for difficult example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
*[[Motional Emf using Faraday's Law]]: An expansion of this concept<br />
*[[Lorentz Force]]: Combining electric and magnetic forces<br />
*[[Generator]]: Real-world application<br />
*[[Right-Hand Rule]]: How it works and other RHRs<br />
<br />
===Further reading===<br />
<br />
*''Matter & Interactions, Vol 2''<br />
*''The Feynman Lectures on Physics, Vol 2", Ch 16<br />
<br />
<br />
===External links===<br />
<br />
*[http://web.mit.edu/8.02t/www/materials/StudyGuide/guide10.pdf Guide from MIT]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13333Motional Emf2015-12-05T03:58:13Z<p>Jli639: /* Difficult */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, variation of P60''.<br />
<br />
A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?<br />
<br /><br />
<br /><br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.<br />
<br /><br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.<br />
<br /><br />
<br />
===Middling===<br />
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Difficult===<br />
[[File:Middlemotionalemf.png|center|alt=Picture for difficult example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13331Motional Emf2015-12-05T03:58:00Z<p>Jli639: /* Simple */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, variation of P60''.<br />
<br />
A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?<br />
<br /><br />
<br /><br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.<br />
<br /><br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.<br />
<br /><br />
<br />
===Middling===<br />
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Difficult===<br />
[[File:Middlemotionalemf.png|center|alt=Picture for difficult example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13329Motional Emf2015-12-05T03:57:10Z<p>Jli639: /* Difficult */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]<br />
<br />
A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?<br />
<br /><br />
<br /><br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.<br />
<br /><br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.<br />
<br /><br />
<br />
===Middling===<br />
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Difficult===<br />
[[File:Middlemotionalemf.png|center|alt=Picture for difficult example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13328Motional Emf2015-12-05T03:56:55Z<p>Jli639: /* Middling */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]<br />
<br />
A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?<br />
<br /><br />
<br /><br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.<br />
<br /><br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.<br />
<br /><br />
<br />
===Middling===<br />
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Difficult===<br />
[[File:Middlemotionalemf.png|thumb|center|alt=Picture for difficult example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13326Motional Emf2015-12-05T03:56:29Z<p>Jli639: /* Simple */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]<br />
<br />
A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?<br />
<br /><br />
<br /><br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.<br />
<br /><br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.<br />
<br /><br />
<br />
===Middling===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for middle example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Difficult===<br />
[[File:Middlemotionalemf.png|thumb|center|alt=Picture for difficult example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13314Motional Emf2015-12-05T03:52:07Z<p>Jli639: /* Examples */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
[[File:Motionalemfsimple.png|thumb|center|alt=Diagram for simple example]]<br />
<br />
===Middling===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for middle example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Difficult===<br />
[[File:Middlemotionalemf.png|thumb|center|alt=Picture for difficult example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=File:Motionalemfsimple.png&diff=13309File:Motionalemfsimple.png2015-12-05T03:50:49Z<p>Jli639: Source: Matter & Interactions textbook vol 2</p>
<hr />
<div>Source: Matter & Interactions textbook vol 2</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13252Motional Emf2015-12-05T03:28:55Z<p>Jli639: /* Middling */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for simple example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Middling===<br />
[[File:Middlemotionalemf.png|thumb|center|alt=Picture for middle level example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br /><br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.<br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13230Motional Emf2015-12-05T03:18:59Z<p>Jli639: /* Middling */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for simple example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Middling===<br />
[[File:Middlemotionalemf.png|thumb|center|alt=Picture for middle level example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br /><br />
<br /><br />
<br />
A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar.<br />
<br /><br />
<br /><br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.<br />
<br /><br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.<br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13187Motional Emf2015-12-05T03:05:34Z<p>Jli639: /* Middling */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for simple example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Middling===<br />
[[File:Middlemotionalemf.png|thumb|center|alt=Picture for middle level example]]<br />
<br />
''Taken from the'' Matter & Interactions ''textbook, P64''.<br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13185Motional Emf2015-12-05T03:05:13Z<p>Jli639: /* Middling */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for simple example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Middling===<br />
[[File:Middlemotionalemf.png|thumb|center|alt=Picture for middle level example]]<br />
<br />
''Taken from'' Matter & Interactions ''P64''.<br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=File:Middlemotionalemf.png&diff=13180File:Middlemotionalemf.png2015-12-05T03:03:51Z<p>Jli639: Source: Matter & Interactions textbook vol 2</p>
<hr />
<div>Source: Matter & Interactions textbook vol 2</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13158Motional Emf2015-12-05T02:49:25Z<p>Jli639: /* Simple */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for simple example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13156Motional Emf2015-12-05T02:49:04Z<p>Jli639: /* Simple */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for simple example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br /><br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.<br />
<br /><br />
'''(f)''' No force is needed. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.<br />
<br /><br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13146Motional Emf2015-12-05T02:45:15Z<p>Jli639: /* Simple */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for simple example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13138Motional Emf2015-12-05T02:42:47Z<p>Jli639: /* Simple */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for simple example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.<br />
<br /><br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.<br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13115Motional Emf2015-12-05T02:31:00Z<p>Jli639: /* Simple */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for simple example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0</math> because after the initial transient the electric force balances out the magnetic force.<br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13109Motional Emf2015-12-05T02:28:04Z<p>Jli639: /* A Mathematical Model */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for simple example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)'''<br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13108Motional Emf2015-12-05T02:27:44Z<p>Jli639: /* Simple */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for simple example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br /><br />
<br /><br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.<br />
<br /><br />
'''(b)'''<br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13104Motional Emf2015-12-05T02:24:54Z<p>Jli639: /* Simple */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
[[File:21.X.091-moving-bar01.gif|thumb|center|alt=Diagram for simple example]]<br />
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''<br />
<br />
A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?<br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=File:21.X.091-moving-bar01.gif&diff=13088File:21.X.091-moving-bar01.gif2015-12-05T02:15:35Z<p>Jli639: Source: Matter & Interactions Textbook Vol 2</p>
<hr />
<div>Source: Matter & Interactions Textbook Vol 2</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=13069Motional Emf2015-12-05T02:05:11Z<p>Jli639: /* Driving Current */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=File:Circuitmotionalemf.png&diff=13067File:Circuitmotionalemf.png2015-12-05T02:02:06Z<p>Jli639: Source: http://www.kshitij-iitjee.com/motional-emf</p>
<hr />
<div>Source: http://www.kshitij-iitjee.com/motional-emf</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=12996Motional Emf2015-12-05T00:57:06Z<p>Jli639: /* Polarization and Steady State */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=12995Motional Emf2015-12-05T00:56:40Z<p>Jli639: /* Polarization and Steady State */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.4 for a right-hand rule applicable to the scenario]]<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=File:Polarizationmotionalemf.png&diff=12992File:Polarizationmotionalemf.png2015-12-05T00:52:28Z<p>Jli639: Source: http://www.kshitij-iitjee.com/motional-emf</p>
<hr />
<div>Source: http://www.kshitij-iitjee.com/motional-emf</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=12980Motional Emf2015-12-05T00:46:55Z<p>Jli639: /* A Mathematical Model */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]<br />
<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=File:RHRmotionalemf.JPG&diff=12956File:RHRmotionalemf.JPG2015-12-05T00:36:19Z<p>Jli639: Source: http://physicsed.buffalostate.edu/SeatExpts/resource/rhr/rhr.htm</p>
<hr />
<div>Source: http://physicsed.buffalostate.edu/SeatExpts/resource/rhr/rhr.htm</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=12794Motional Emf2015-12-04T22:46:10Z<p>Jli639: /* A Mathematical Model */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \phi_ {mag}}{\mathrm{d} t} \right |</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=12793Motional Emf2015-12-04T22:45:44Z<p>Jli639: /* A Mathematical Model */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br /><br />
<br /><br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \phi_ {mag}}{\mathrm{d} t} \right |</math><br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=12742Motional Emf2015-12-04T22:21:58Z<p>Jli639: /* History */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=12739Motional Emf2015-12-04T22:21:14Z<p>Jli639: /* History */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
[[File:Hendrik Antoon Lorentz.jpg|thumb|left|alt=Picture of Hendrik Lorentz|Hendrik Lorentz]] At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=12726Motional Emf2015-12-04T22:10:26Z<p>Jli639: /* History */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and Maxwell's equations. <br />
<br /><br />
<br /><br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=12659Motional Emf2015-12-04T21:45:02Z<p>Jli639: </p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
'''Motional emf''' is emf caused by motion in a magnetic field, leading to polarization. This is in contrast to how emf is generated in nature, namely through fluctuation of a magnetic field through a surface. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=10744Motional Emf2015-12-03T21:10:59Z<p>Jli639: /* Connectedness */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
Motional emf is emf caused by motion in a magnetic field, leading to polarization. It is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=10743Motional Emf2015-12-03T21:10:47Z<p>Jli639: /* Power */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
Motional emf is emf caused by motion in a magnetic field, leading to polarization. It is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=10726Motional Emf2015-12-03T21:00:50Z<p>Jli639: /* A Computational Model */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
Motional emf is emf caused by motion in a magnetic field, leading to polarization. It is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===Power===<br />
Power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br />
===A Computational Model===<br />
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=10695Motional Emf2015-12-03T20:49:27Z<p>Jli639: </p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
Motional emf is emf caused by motion in a magnetic field, leading to polarization. It is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===Power===<br />
Power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=10684Motional Emf2015-12-03T20:47:06Z<p>Jli639: </p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
Motional emf is emf caused by motion in a magnetic field, leading to polarization. It is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (qvB = qE). Consequently, in the steady state, E = vB and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===Power===<br />
Power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br /><br />
<br /><br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=10675Motional Emf2015-12-03T20:42:40Z<p>Jli639: </p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
Motional emf is emf caused by motion in a magnetic field, leading to polarization. It is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (qvB = qE). Consequently, in the steady state, E = vB and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===Power===<br />
Power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.<br />
<br />
When the bar in the circuit, in steady state, moves a distance delta_x over a time delta_t, the work done is F*delta_x and the power supplied is F*delta_x/delta_t, or F*v_bar. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is ILBv_bar = I*emf = (emf/R)*emf = emf^2/R = R*I^2.<br />
<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. <br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=10674Motional Emf2015-12-03T20:41:54Z<p>Jli639: </p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
Motional emf is emf caused by motion in a magnetic field, leading to polarization. It is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (qvB = qE). Consequently, in the steady state, E = vB and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.<br />
<br />
===Driving Current===<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip is zero.<br />
<br />
===Power===<br />
Power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
===A Mathematical Model===<br />
The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then delta_V = emf - r_int*I.<br />
<br />
When the bar in the circuit, in steady state, moves a distance delta_x over a time delta_t, the work done is F*delta_x and the power supplied is F*delta_x/delta_t, or F*v_bar. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is ILBv_bar = I*emf = (emf/R)*emf = emf^2/R = R*I^2.<br />
<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. <br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=10650Motional Emf2015-12-03T20:31:11Z<p>Jli639: </p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
Motional emf is emf caused by motion in a magnetic field, leading to polarization. It is difficult to observe visually using batteries, light bulbs, and compasses because it is so small. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (qvB = qE). Consequently, in the steady state, E = vB and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar, or vBL.<br />
<br />
===Driving Current===<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance, and the potential difference is then emf - r_int*I. In the circuit, the potential difference round-trip is zero.<br />
<br />
===Power===<br />
When the bar in the circuit, in steady state, moves a distance delta_x over a time delta_t, the work done is F*delta_x and the power supplied is F*delta_x/delta_t, or F*v_bar. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is ILBv_bar = I*emf = (emf/R)*emf = emf^2/R = R*I^2.<br />
<br /><br />
<br /><br />
This concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.<br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. <br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=10635Motional Emf2015-12-03T20:15:31Z<p>Jli639: </p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
Motional emf is emf caused by motion in a magnetic field, leading to polarization. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (qvB = qE). Consequently, in the steady state, E = vB and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar, or vBL.<br />
<br />
===Driving Current===<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. The mobile electrons will be affected by both this magnetic force and the force being applied on the bar. Eventually, over time, the net force on the bar decreases to zero, and the bar moves at a constant speed, with a balance between the force pulling the bar and the component of magnetic force on the mobile electrons in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.<br />
<br /><br />
<br /><br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance, and the potential difference is then emf - r_int*I.<br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. <br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639http://www.physicsbook.gatech.edu/index.php?title=Motional_Emf&diff=10594Motional Emf2015-12-03T19:56:34Z<p>Jli639: /* The Main Idea */</p>
<hr />
<div>Claimed --[[User:Jli639|Jli639]] ([[User talk:Jli639|talk]]) 14:50, 5 November 2015 (EST)<br />
<br /><br />
<br /><br />
Motional emf is emf caused by motion in a magnetic field, leading to polarization. <br />
<br />
==The Main Idea==<br />
<br />
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current in a circuit. <br />
<br /><br />
<br /><br />
Additionally, as a result of the polarization, an electric field is also generated.<br />
<br />
===Polarization and Steady State===<br />
<br />
Polarization occurs due to the shift of the mobile electron sea in one direction. Eventually, the shifting will stop; enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (qvB = qE). Consequently, in the steady state, E = vB and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity. <br />
<br /><br />
<br /><br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar, or vBL.<br />
<br />
===Driving Current===<br />
<br />
If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the charge separation in the bar mimics a battery and can drive a current. <br />
<br /><br />
<br /><br />
When the bar, in the described configuration, has a force applied to it and initially begins to move from rest, the entire lattice of positive ions is pulled in the direction of the bar's velocity. The mobile electrons are left behind for a brief moment, causing a near-instantaneous polarization in the bar, but are then pulled along with the positive ions due to the electric interaction between the charges. <br />
<br /><br />
<br /><br />
Now that the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. <br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Jli639