http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=ChrismickasPhysics Book - User contributions [en]2026-04-29T13:43:55ZUser contributionsMediaWiki 1.42.7http://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=25862Lorentz Force2016-11-28T01:36:58Z<p>Chrismickas: /* See also */</p>
<hr />
<div>Edited by Chris Mickas Fall 2016<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
<br />
<br />
<br />
1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. <br />
<br />
[[File:Speaker-Diagram-1.png]]<br />
<br />
2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.<br />
<br />
[[File:Electrodynamics papers 70.jpg]]<br />
<br />
3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
<br />
[[File:Eg-magnets copy.jpg]]<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
<br />
The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.<br />
<br />
[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.<br />
<br />
== See also ==<br />
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
<br />
[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.<br />
<br />
===Further reading===<br />
<br />
[[Hall Effect]]<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=25858Lorentz Force2016-11-28T01:36:28Z<p>Chrismickas: </p>
<hr />
<div>Edited by Chris Mickas Fall 2016<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
<br />
<br />
<br />
1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. <br />
<br />
[[File:Speaker-Diagram-1.png]]<br />
<br />
2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.<br />
<br />
[[File:Electrodynamics papers 70.jpg]]<br />
<br />
3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
<br />
[[File:Eg-magnets copy.jpg]]<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
<br />
The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.<br />
<br />
[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.<br />
<br />
== See also ==<br />
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
<br />
[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.<br />
<br />
===Further reading===<br />
<br />
[[Hall Effect]]<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=25856Lorentz Force2016-11-28T01:35:38Z<p>Chrismickas: /* Further reading */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
<br />
<br />
<br />
1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. <br />
<br />
[[File:Speaker-Diagram-1.png]]<br />
<br />
2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.<br />
<br />
[[File:Electrodynamics papers 70.jpg]]<br />
<br />
3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
<br />
[[File:Eg-magnets copy.jpg]]<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
<br />
The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.<br />
<br />
[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.<br />
<br />
== See also ==<br />
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
<br />
[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.<br />
<br />
===Further reading===<br />
<br />
[[Hall Effect]]<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=25850Lorentz Force2016-11-28T01:34:48Z<p>Chrismickas: /* See also */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
<br />
<br />
<br />
1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. <br />
<br />
[[File:Speaker-Diagram-1.png]]<br />
<br />
2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.<br />
<br />
[[File:Electrodynamics papers 70.jpg]]<br />
<br />
3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
<br />
[[File:Eg-magnets copy.jpg]]<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
<br />
The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.<br />
<br />
[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.<br />
<br />
== See also ==<br />
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
<br />
[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=25841Lorentz Force2016-11-28T01:31:48Z<p>Chrismickas: /* History */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
<br />
<br />
<br />
1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. <br />
<br />
[[File:Speaker-Diagram-1.png]]<br />
<br />
2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.<br />
<br />
[[File:Electrodynamics papers 70.jpg]]<br />
<br />
3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
<br />
[[File:Eg-magnets copy.jpg]]<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
<br />
The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.<br />
<br />
[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.<br />
<br />
== See also ==<br />
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=25793Lorentz Force2016-11-28T01:20:42Z<p>Chrismickas: /* Connectedness */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
<br />
<br />
<br />
1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. <br />
<br />
[[File:Speaker-Diagram-1.png]]<br />
<br />
2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.<br />
<br />
[[File:Electrodynamics papers 70.jpg]]<br />
<br />
3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
<br />
[[File:Eg-magnets copy.jpg]]<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=File:Electrodynamics_papers_70.jpg&diff=25789File:Electrodynamics papers 70.jpg2016-11-28T01:20:15Z<p>Chrismickas: </p>
<hr />
<div></div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=25778Lorentz Force2016-11-28T01:17:48Z<p>Chrismickas: /* Connectedness */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
<br />
<br />
<br />
1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. <br />
<br />
[[File:Speaker-Diagram-1.png]]<br />
<br />
2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.<br />
<br />
<br />
<br />
3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
<br />
[[File:Eg-magnets copy.jpg]]<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=File:Speaker-Diagram-1.png&diff=25775File:Speaker-Diagram-1.png2016-11-28T01:17:07Z<p>Chrismickas: </p>
<hr />
<div></div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=25764Lorentz Force2016-11-28T01:15:49Z<p>Chrismickas: /* Connectedness */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. <br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.<br />
[[File:Eg-magnets copy.jpg]]<br />
3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=File:Eg-magnets_copy.jpg&diff=25762File:Eg-magnets copy.jpg2016-11-28T01:15:12Z<p>Chrismickas: </p>
<hr />
<div></div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=25748Lorentz Force2016-11-28T01:12:12Z<p>Chrismickas: /* The Main Idea */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. <br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.<br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24841Lorentz Force2016-11-27T18:13:58Z<p>Chrismickas: /* See also */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. <br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.<br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24840Lorentz Force2016-11-27T18:10:53Z<p>Chrismickas: /* Connectedness */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. <br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.<br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24837Lorentz Force2016-11-27T17:54:53Z<p>Chrismickas: /* Connectedness */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. <br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24673Lorentz Force2016-11-27T05:38:07Z<p>Chrismickas: /* The Main Idea */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24671Lorentz Force2016-11-27T05:33:24Z<p>Chrismickas: /* Difficult */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
<br />
[[File:Hardlorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24670Lorentz Force2016-11-27T05:33:11Z<p>Chrismickas: /* Difficult */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
[[File:Hardlorentz.JPG]]<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=File:Hardlorentz.JPG&diff=24669File:Hardlorentz.JPG2016-11-27T05:32:45Z<p>Chrismickas: </p>
<hr />
<div></div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24667Lorentz Force2016-11-27T05:31:22Z<p>Chrismickas: /* Difficult */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?<br />
[[File:Lhard.jpg|400px|center|]]<br />
'''Solution: Lorentz force = 122.5 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24658Lorentz Force2016-11-27T05:26:28Z<p>Chrismickas: /* Middling */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz1.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The speed of the proton is 5e3 m/s. The magnitude of the electric field on the proton is 8e-6 N/C and the magnitude of the magnetic field at that same proton is 4e-9 T. Find the Lorentz force on this proton.<br />
[[File:Lhard.jpg|400px|center|]]<br />
'''Solution: Lorentz force = 4.48e-24 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=File:Middlelorentz1.JPG&diff=24656File:Middlelorentz1.JPG2016-11-27T05:26:09Z<p>Chrismickas: </p>
<hr />
<div></div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24655Lorentz Force2016-11-27T05:25:25Z<p>Chrismickas: /* Middling */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:Middlelorentz.JPG]]<br />
<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The speed of the proton is 5e3 m/s. The magnitude of the electric field on the proton is 8e-6 N/C and the magnitude of the magnetic field at that same proton is 4e-9 T. Find the Lorentz force on this proton.<br />
[[File:Lhard.jpg|400px|center|]]<br />
'''Solution: Lorentz force = 4.48e-24 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=File:Middlelorentz.JPG&diff=24654File:Middlelorentz.JPG2016-11-27T05:24:47Z<p>Chrismickas: </p>
<hr />
<div></div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24651Lorentz Force2016-11-27T05:23:37Z<p>Chrismickas: /* Middling */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.<br />
[[File:LMiddle.jpg|470px|center|]]<br />
'''Solution: Lorentz force = <-500,-200,300> N'''<br />
<br />
===Difficult===<br />
The speed of the proton is 5e3 m/s. The magnitude of the electric field on the proton is 8e-6 N/C and the magnitude of the magnetic field at that same proton is 4e-9 T. Find the Lorentz force on this proton.<br />
[[File:Lhard.jpg|400px|center|]]<br />
'''Solution: Lorentz force = 4.48e-24 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24645Lorentz Force2016-11-27T05:18:55Z<p>Chrismickas: /* Simple */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
<br />
'''Solution: More information is needed to know the direction of the force.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <500,-200,300> N and the magnetic force is <-200,700,400> N. Find the Lorentz force.<br />
[[File:LMiddle.jpg|470px|center|]]<br />
'''Solution: Lorentz force = <300,500,700> N'''<br />
<br />
===Difficult===<br />
The speed of the proton is 5e3 m/s. The magnitude of the electric field on the proton is 8e-6 N/C and the magnitude of the magnetic field at that same proton is 4e-9 T. Find the Lorentz force on this proton.<br />
[[File:Lhard.jpg|400px|center|]]<br />
'''Solution: Lorentz force = 4.48e-24 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24644Lorentz Force2016-11-27T05:18:23Z<p>Chrismickas: /* Simple */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz2.JPG]]<br />
'''Solution: The Lorentz force is 0 N.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <500,-200,300> N and the magnetic force is <-200,700,400> N. Find the Lorentz force.<br />
[[File:LMiddle.jpg|470px|center|]]<br />
'''Solution: Lorentz force = <300,500,700> N'''<br />
<br />
===Difficult===<br />
The speed of the proton is 5e3 m/s. The magnitude of the electric field on the proton is 8e-6 N/C and the magnitude of the magnetic field at that same proton is 4e-9 T. Find the Lorentz force on this proton.<br />
[[File:Lhard.jpg|400px|center|]]<br />
'''Solution: Lorentz force = 4.48e-24 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=File:Easylorentz2.JPG&diff=24643File:Easylorentz2.JPG2016-11-27T05:17:58Z<p>Chrismickas: </p>
<hr />
<div></div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24641Lorentz Force2016-11-27T05:16:51Z<p>Chrismickas: /* Simple */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz1.JPG]]<br />
'''Solution: The Lorentz force is 0 N.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <500,-200,300> N and the magnetic force is <-200,700,400> N. Find the Lorentz force.<br />
[[File:LMiddle.jpg|470px|center|]]<br />
'''Solution: Lorentz force = <300,500,700> N'''<br />
<br />
===Difficult===<br />
The speed of the proton is 5e3 m/s. The magnitude of the electric field on the proton is 8e-6 N/C and the magnitude of the magnetic field at that same proton is 4e-9 T. Find the Lorentz force on this proton.<br />
[[File:Lhard.jpg|400px|center|]]<br />
'''Solution: Lorentz force = 4.48e-24 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=File:Easylorentz1.JPG&diff=24640File:Easylorentz1.JPG2016-11-27T05:16:02Z<p>Chrismickas: </p>
<hr />
<div></div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24638Lorentz Force2016-11-27T05:15:30Z<p>Chrismickas: /* Examples */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Easylorentz.JPG]]<br />
'''Solution: The Lorentz force is 0 N.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <500,-200,300> N and the magnetic force is <-200,700,400> N. Find the Lorentz force.<br />
[[File:LMiddle.jpg|470px|center|]]<br />
'''Solution: Lorentz force = <300,500,700> N'''<br />
<br />
===Difficult===<br />
The speed of the proton is 5e3 m/s. The magnitude of the electric field on the proton is 8e-6 N/C and the magnitude of the magnetic field at that same proton is 4e-9 T. Find the Lorentz force on this proton.<br />
[[File:Lhard.jpg|400px|center|]]<br />
'''Solution: Lorentz force = 4.48e-24 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24588Lorentz Force2016-11-27T04:41:14Z<p>Chrismickas: /* Connectedness */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:easylorentz.jpg|600px|center|]]<br />
'''Solution: The Lorentz force is 0 N.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <500,-200,300> N and the magnetic force is <-200,700,400> N. Find the Lorentz force.<br />
[[File:LMiddle.jpg|470px|center|]]<br />
'''Solution: Lorentz force = <300,500,700> N'''<br />
<br />
===Difficult===<br />
The speed of the proton is 5e3 m/s. The magnitude of the electric field on the proton is 8e-6 N/C and the magnitude of the magnetic field at that same proton is 4e-9 T. Find the Lorentz force on this proton.<br />
[[File:Lhard.jpg|400px|center|]]<br />
'''Solution: Lorentz force = 4.48e-24 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. <br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=24560Lorentz Force2016-11-27T03:08:54Z<p>Chrismickas: /* Simple */</p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:easylorentz.jpg|600px|center|]]<br />
'''Solution: The Lorentz force is 0 N.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <500,-200,300> N and the magnetic force is <-200,700,400> N. Find the Lorentz force.<br />
[[File:LMiddle.jpg|470px|center|]]<br />
'''Solution: Lorentz force = <300,500,700> N'''<br />
<br />
===Difficult===<br />
The speed of the proton is 5e3 m/s. The magnitude of the electric field on the proton is 8e-6 N/C and the magnitude of the magnetic field at that same proton is 4e-9 T. Find the Lorentz force on this proton.<br />
[[File:Lhard.jpg|400px|center|]]<br />
'''Solution: Lorentz force = 4.48e-24 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I am interested in hovering spacecrafts and the Lorentz force can be useful for this topic. Assuming that the Earth's magnetic field is a dipole that rotates with the Earth, a dynamical model that characterizes the relative motion of Lorentz spacecraft is derived to analyze the required open-loop control acceleration for hovering. What must be understood first is the hovering configurations that could achieve hovering without a propellor and the corresponding required specific charge of a Lorentz spacecraft.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. As an aerospace engineering major, I can investigate the feasibility of using the induced Lorentz force as an auxiliary means of propulsion for spacecraft hovering. To achieve hovering, a spacecraft thrusts continuously to induce an equilibrium state at a desired position. Due to the constraints on the quantity of propellant onboard, long-time hovering around low-Earth orbits (LEO) is hardly achievable using traditional chemical propulsion. The Lorentz force, acting on an electrostatically charged spacecraft as it moves through a planetary magnetic field, provides a new method for orbital maneuvers without propellant.<br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
4. The [https://www.carroll.edu/library/thesisArchive/HarmonSFinal_2011.pdf railgun], a 21st-century weapon, uses the Lorentz force to propel an electrically conductive projectile. A magnetic field is generated in the rails and armature by the current flowing through the rails. Consequently, (with an exerted force) the armature is pushed out of the magnetic field of the rails, accelerating the projectile. Railguns and other electromagnetic weapons are crucial to the United States Armed Forces because they have the potential to replace conventional artillery in the near future.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=File:Easylorentz.JPG&diff=24558File:Easylorentz.JPG2016-11-27T03:08:03Z<p>Chrismickas: </p>
<hr />
<div></div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Lorentz_Force&diff=23580Lorentz Force2016-11-15T22:02:35Z<p>Chrismickas: </p>
<hr />
<div>Claimed by Chris Mickas 11/15/16<br />
<br />
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]<br />
==The Main Idea==<br />
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]<br />
Electric and magnetic forces can be combined into a single force called the "Lorentz force." This combination of the two forces is useful in applications where a magnetic field and electric field act on a specific particle or series of particles. Common variations of the [[#A Mathematical Model|Lorentz force formula]] can be applied to various scenarios where a moving particle is subject to both a magnetic and electric field. For example, the Lorentz force can be used to describe the magnetic force on a current-carrying wire and the electromotive force (emf) in a wire loop moving through a magnetic field.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''<math>q\vec{E}</math>''' is the electric force and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force.<br />
<br />
===A Computational Model===<br />
[[File:Lorentz Force.png|350px]]<br />
<br />
==Examples==<br />
<br />
===Simple===<br />
If the electric force points in the +x direction and the magnetic force points in the –x direction, what direction does the Lorentz force point in?<br />
[[File:Ldirection.jpg|600px|center|]]<br />
'''Solution: The Lorentz force is 0 N.'''<br />
<br />
===Middling===<br />
The electric force on a certain particle is <500,-200,300> N and the magnetic force is <-200,700,400> N. Find the Lorentz force.<br />
[[File:LMiddle.jpg|470px|center|]]<br />
'''Solution: Lorentz force = <300,500,700> N'''<br />
<br />
===Difficult===<br />
The speed of the proton is 5e3 m/s. The magnitude of the electric field on the proton is 8e-6 N/C and the magnitude of the magnetic field at that same proton is 4e-9 T. Find the Lorentz force on this proton.<br />
[[File:Lhard.jpg|400px|center|]]<br />
'''Solution: Lorentz force = 4.48e-24 N'''<br />
<br />
==Connectedness==<br />
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]<br />
#I am interested in hovering spacecrafts and the Lorentz force can be useful for this topic. Assuming that the Earth's magnetic field is a dipole that rotates with the Earth, a dynamical model that characterizes the relative motion of Lorentz spacecraft is derived to analyze the required open-loop control acceleration for hovering. What must be understood first is the hovering configurations that could achieve hovering without a propellor and the corresponding required specific charge of a Lorentz spacecraft.<br />
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]<br />
2. As an aerospace engineering major, I can investigate the feasibility of using the induced Lorentz force as an auxiliary means of propulsion for spacecraft hovering. To achieve hovering, a spacecraft thrusts continuously to induce an equilibrium state at a desired position. Due to the constraints on the quantity of propellant onboard, long-time hovering around low-Earth orbits (LEO) is hardly achievable using traditional chemical propulsion. The Lorentz force, acting on an electrostatically charged spacecraft as it moves through a planetary magnetic field, provides a new method for orbital maneuvers without propellant.<br />
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]<br />
3. In the metallurgic industry the in-situ measurement of the flow rate of metal melts is still an unsolved problem. Due to the chemical aggressiveness of high-temperature melts, classical measurement techniques such as fly-wheel, Pitot tube, and hotwire probes cannot be used as these methods require mechanical contact with the melt. This is where the calibration of a non-contact electromagnetic flow rate measurement device called [https://www.tu-ilmenau.de/fileadmin/media/tfd/Mitarbeiter/Andre/Publication/Thess-54-PRL-2006.pdf Lorentz force flow meter (LFF)] comes in handy. To use this Lorentz force flow meter in industrial applications with a determined accuracy, a proper calibration of the flow meter has to be performed beforehand. To this aim, a two-step calibration method consisting of a dry and a wet technique must be performed.<br />
<br />
4. The [https://www.carroll.edu/library/thesisArchive/HarmonSFinal_2011.pdf railgun], a 21st-century weapon, uses the Lorentz force to propel an electrically conductive projectile. A magnetic field is generated in the rails and armature by the current flowing through the rails. Consequently, (with an exerted force) the armature is pushed out of the magnetic field of the rails, accelerating the projectile. Railguns and other electromagnetic weapons are crucial to the United States Armed Forces because they have the potential to replace conventional artillery in the near future.<br />
<br />
==History==<br />
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]<br />
Early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, and electrically charged objects, by [[Henry Cavendish]] in 1762, obeyed an inverse-square law. However, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by [[Hans Christian Ørsted]] that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] that same year was able to devise through experimentation the formula for the angular dependence of the force between two current elements. In all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields.<br />
<br />
The modern concept of electric and magnetic fields first arose in the theories of [[Michael Faraday]], particularly his idea of lines of force, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, in the time of Maxwell it was not evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>.<br />
<br />
Although some historians suggest that the Lorentz force originated in the works of Maxwell, the first derivation is generally attributed to [[Oliver Heaviside]] in 1889. The Lorentz force's namesake is attributed to [[Hendrik Lorentz]], who derived it a few years after Heaviside.<br />
<br />
== See also ==<br />
The [[Hall Effect]] explores this concept more in depth because it deals with the electric force and magnetic force being equal given (zero net force). Usually, these problems require you to set them equal to each other and solve for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.<br />
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]<br />
If you wish to further explore how electricity and magnetism interact via the Lorentz force, watch [https://www.youtube.com/watch?v=8QWB8IfNoIs this video] that provides interesting real-life examples!<br />
<br />
===Further reading===<br />
<br />
*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html<br />
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf<br />
<br />
===External links===<br />
<br />
*http://jnaudin.free.fr/lifters/lorentz/<br />
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force<br />
<br />
==References==<br />
<br />
*Feynman, Richard Phillips; Leighton, Robert B.; Sands, Matthew L. (2006). The Feynman lectures on physics (3 vol.). Pearson / Addison-Wesley. ISBN 0-8053-9047-2.: volume 2.<br />
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.<br />
*Serway, Raymond A.; Jewett, John W., Jr. (2004). Physics for scientists and engineers, with modern physics. Belmont, [CA.]: Thomson Brooks/Cole. ISBN 0-534-40846-X.<br />
<br />
<br />
[[Category:Which Category did you place this in?]]</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Work_Done_By_A_Nonconstant_Force&diff=22615Work Done By A Nonconstant Force2016-04-17T23:18:26Z<p>Chrismickas: </p>
<hr />
<div>This page explains the significance and fundamental calculations work done by non-constant forces.<br />
<br />
==The Main Idea==<br />
<br />
Basic calculations of work can be solved with a simple formula: force times displacement. However, this formula only works when work is constant. Calculus is essential for the calculation of work in many cases because force is not always a constant. In cases such as springs and gravity, for example, the force applied varies depending on location. By integrating, or finding the area under the curve of force by displacement, we can calculate work without having to use inaccurate approximations.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math><br />
<br />
This means that the work is equal to the integral of the function of the force with respect to the change in the objects position. This is also the same as the summation of the force on an object multiplied by the change in position.<br />
<br />
===A Computational Model===<br />
<br />
<https://trinket.io/glowscript/49f7c0f35f><br />
<br />
This model shows both the total work and the work done by a spring on a ball attached to a vertical spring. The work done by the spring oscillates because the work is negative when the ball is moving away from the resting state and is positive when the ball moves towards it.<br />
<br />
Because gravity causes the ball’s minimum position to be further from the spring’s resting length than its maximum position could be, the work is more negative when the ball approaches its minimum height.<br />
<br />
The code works by using small time steps of 0.01 seconds and finding the work done in each time step. Work is the summation of all of the work done in each time step, so another step makes sure the value for work is cumulative.<br />
<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
A box is pushed to the East, 5 meters by a force of 40 N, then it is pushed to the north 7 meters by a force of 60 N. Calculate the work done on the box.<br />
<br />
<math> W = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math><br />
<br />
<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math><br />
<br />
<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math><br />
<br />
<math> W = 620 J </math><br />
<br />
===Example 2===<br />
We know that the formula for force is <math> F=ks </math>, where <math> s </math> is the distance the spring is stretched. If we integrate this with respect to <math> s </math>, we find that <math> W=.5ks^2 </math> is the formula for work.<br />
<br />
<math> W=\int\limits_{i}^{f}\overrightarrow{k}\bullet\overrightarrow{ds} = .5ks^2 </math><br />
<br />
Say that we want to find the work done by a horizontal spring with spring constant k=100 N/m as it moves an object 15 cm. Using the formula W=.5ks2 that we derived from F=ks, we can calculate that the work done by the spring is 1.125 J.<br />
<br />
<math> W=\int\limits_{0}^{15}100\bullet\overrightarrow{ds}=.5ks^2=.5(100)(0.15^2)=1.125 J </math><br />
<br />
===Example 3===<br />
The earth does work on an asteroid approaching from an initial distance r. How much work is done on the asteroid by gravity before it hits the earth’s surface?<br />
<br />
First, we must recall the formula for gravitational force.<br />
<br />
Because <math> G </math>, <math> M </math>, and <math> m </math> are constants, we can remove them from the integral. We also know that the integral of <math> -1\over r^2 </math> is <math> 1\over r </math>. We then must calculate the integral of <math> –GMm\over r^2 </math> from the initial radius of the asteroid, <math> R </math>, to the radius of the earth, <math> r </math>. <br />
<br />
<math> W=-GMm\bullet\int\limits_{R}^{r}{-1\over r^2}\bullet dr </math><br />
<br />
<math> W=-GMm\bullet({1\over r}-{1\over R}) </math><br />
<br />
Our answer will be positive because the force done by the earth on the asteroid and the direction of the asteroid's displacement are the same.<br />
<br />
==Connectedness==<br />
I am most interested in the types of physics problems that accurately model real world situations. Some forces, like gravity near the surface of the earth and some machine-applied forces, are constant. However, most forces in the real world are not. <br />
<br />
Because of this, calculating work for non-constant forces is essential to mechanical engineering. For example, when calculating work done by an engine over a distance, the force applied by the engine can vary depending on factors such as user controls.<br />
<br />
On an industrial level, the work needed to fill and empty tanks depends on the weight of the liquid, which varies as the tanks fill and empty. Energy conversion in hydroelectric dams depends on the work done by water against turbines, which depends on the flow of water. Windmills work in the same way.<br />
<br />
<br />
==History==<br />
<br />
Gaspard-Gustave de Coriolis, famous for discoveries such as the Coriolis effect, is credited with naming the term “work” to define force applied over a distance. Later physicists combined this concept with Newtonian calculus to find work for non-constant forces.<br />
<br />
== See also ==<br />
<br />
[[Work]]<br />
<br />
==References==<br />
<br />
[http://www.britannica.com/biography/Gustave-Gaspard-Coriolis]<br />
[http://www.math.northwestern.edu]<br />
<br />
[[Category:Energy]]<br />
<br />
Created by Justin Vuong<br />
Edited by Chris Mickas</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Work_Done_By_A_Nonconstant_Force&diff=22611Work Done By A Nonconstant Force2016-04-17T23:17:03Z<p>Chrismickas: </p>
<hr />
<div>This page explains the significance and fundamental calculations work done by non-constant forces.<br />
<br />
==The Main Idea==<br />
<br />
Basic calculations of work can be solved with a simple formula: force times displacement. However, this formula only works when work is constant. Calculus is essential for the calculation of work in many cases because force is not always a constant. In cases such as springs and gravity, for example, the force applied varies depending on location. By integrating, or finding the area under the curve of force by displacement, we can calculate work without having to use inaccurate approximations.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math><br />
<br />
This means that the work is equal to the integral of the function of the force with respect to the change in the objects position. This is also the same as the summation of the force on an object multiplied by the change in position.<br />
<br />
===A Computational Model===<br />
<br />
<https://trinket.io/glowscript/49f7c0f35f><br />
<br />
This model shows both the total work and the work done by a spring on a ball attached to a vertical spring. The work done by the spring oscillates because the work is negative when the ball is moving away from the resting state and is positive when the ball moves towards it.<br />
<br />
Because gravity causes the ball’s minimum position to be further from the spring’s resting length than its maximum position could be, the work is more negative when the ball approaches its minimum height.<br />
<br />
The code works by using small time steps of 0.01 seconds and finding the work done in each time step. Work is the summation of all of the work done in each time step, so another step makes sure the value for work is cumulative.<br />
<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
A box is pushed to the East, 5 meters by a force of 40 N, then it is pushed to the north 7 meters by a force of 60 N. Calculate the work done on the box.<br />
<br />
<math> W = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math><br />
<br />
<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math><br />
<br />
<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math><br />
<br />
<math> W = 620 J </math><br />
<br />
===Example 2===<br />
We know that the formula for force is <math> F=ks </math>, where <math> s </math> is the distance the spring is stretched. If we integrate this with respect to <math> s </math>, we find that <math> W=.5ks^2 </math> is the formula for work.<br />
<br />
<math> W=\int\limits_{i}^{f}\overrightarrow{k}\bullet\overrightarrow{ds} = .5ks^2 </math><br />
<br />
Say that we want to find the work done by a horizontal spring with spring constant k=100 N/m as it moves an object 15 cm. Using the formula W=.5ks2 that we derived from F=ks, we can calculate that the work done by the spring is 1.125 J.<br />
<br />
<math> W=\int\limits_{0}^{15}100\bullet\overrightarrow{ds}=.5ks^2=.5(100)(0.15^2)=1.125 J </math><br />
<br />
===Example 3===<br />
The earth does work on an asteroid approaching from an initial distance r. How much work is done on the asteroid by gravity before it hits the earth’s surface?<br />
<br />
First, we must recall the formula for gravitational force.<br />
<br />
Because <math> G </math>, <math> M </math>, and <math> m </math> are constants, we can remove them from the integral. We also know that the integral of <math> -1\over r^2 </math> is <math> 1\over r </math>. We then must calculate the integral of <math> –GMm\over r^2 </math> from the initial radius of the asteroid, <math> R </math>, to the radius of the earth, <math> r </math>. <br />
<br />
<math> W=-GMm\bullet\int\limits_{R}^{r}{-1\over r^2}\bullet dr </math><br />
<br />
<math> W=-GMm\bullet({1\over r}-{1\over R}) </math><br />
<br />
Our answer will be positive because the force done by the earth on the asteroid and the direction of the asteroid's displacement are the same.<br />
<br />
==Connectedness==<br />
I am most interested in the types of physics problems that accurately model real world situations. Some forces, like gravity near the surface of the earth and some machine-applied forces, are constant. However, most forces in the real world are not. <br />
<br />
Because of this, calculating work for non-constant forces is essential to mechanical engineering. For example, when calculating work done by an engine over a distance, the force applied by the engine can vary depending on factors such as user controls.<br />
<br />
On an industrial level, the work needed to fill and empty tanks depends on the weight of the liquid, which varies as the tanks fill and empty. Energy conversion in hydroelectric dams depends on the work done by water against turbines, which depends on the flow of water. Windmills work in the same way.<br />
<br />
<br />
==History==<br />
<br />
Gaspard-Gustave de Coriolis, famous for discoveries such as the Coriolis effect, is credited with naming the term “work” to define force applied over a distance. Later physicists combined this concept with Newtonian calculus to find work for non-constant forces.<br />
<br />
== See also ==<br />
<br />
[[Work]]<br />
<br />
==References==<br />
<br />
[http://www.britannica.com/biography/Gustave-Gaspard-Coriolis]<br />
[http://www.math.northwestern.edu]<br />
<br />
[[Category:Energy]]<br />
<br />
Created by Chris Mickas</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Work_Done_By_A_Nonconstant_Force&diff=22113Work Done By A Nonconstant Force2016-04-17T16:11:56Z<p>Chrismickas: /* Examples */</p>
<hr />
<div>'''Claimed by Chris Mickas'''<br />
<br />
This page will help students understand how to calculate the work done by a non constant force.<br />
<br />
==The Main Idea==<br />
<br />
Basic calculations of work can be solved with a simple formula: force times displacement. However, this formula only works when work is constant. Calculus is essential for the calculation of work in many cases because force is not always a constant. In cases such as springs and gravity, for example, the force applied varies depending on location. By integrating, or finding the area under the curve of force by displacement, we can calculate work without having to use inaccurate approximations.<br />
<br />
===A Mathematical Model===<br />
<br />
<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math><br />
<br />
This means that the work is equal to the integral of the function of the force with respect to the change in the objects position. This is also the same as the summation of the force on an object multiplied by the change in position.<br />
<br />
===A Computational Model===<br />
<br />
<https://trinket.io/glowscript/49f7c0f35f><br />
<br />
This model shows both the total work and the work done by a spring on a ball attached to a vertical spring. The work done by the spring oscillates because the work is negative when the ball is moving away from the resting state and is positive when the ball moves towards it.<br />
<br />
Because gravity causes the ball’s minimum position to be further from the spring’s resting length than its maximum position could be, the work is more negative when the ball approaches its minimum height.<br />
<br />
The code works by using small time steps of 0.01 seconds and finding the work done in each time step. Work is the summation of all of the work done in each time step, so another step makes sure the value for work is cumulative.<br />
<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
A box is pushed to the East, 5 meters by a force of 40 N, then it is pushed to the north 7 meters by a force of 60 N. Calculate the work done on the box.<br />
<br />
<math> W = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math><br />
<br />
<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math><br />
<br />
<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math><br />
<br />
<math> W = 620 J </math><br />
<br />
===Example 2===<br />
We know that the formula for force is <math> F=ks </math>, where <math> s </math> is the distance the spring is stretched. If we integrate this with respect to <math> s </math>, we find that <math> W=.5ks^2 </math> is the formula for work.<br />
<br />
<math> W=\int\limits_{i}^{f}\overrightarrow{k}\bullet\overrightarrow{ds} = .5ks^2 </math><br />
<br />
Say that we want to find the work done by a horizontal spring with spring constant k=100 N/m as it moves an object 15 cm. Using the formula W=.5ks2 that we derived from F=ks, we can calculate that the work done by the spring is 1.125 J.<br />
<br />
<math> W=\int\limits_{0}^{15}100\bullet\overrightarrow{ds}=.5ks^2=.5(100)(0.15^2)=1.125 J </math><br />
<br />
===Example 3===<br />
The earth does work on an asteroid approaching from an initial distance r. How much work is done on the asteroid by gravity before it hits the earth’s surface?<br />
<br />
First, we must recall the formula for gravitational force.<br />
<br />
Because <math> G </math>, <math> M </math>, and <math> m </math> are constants, we can remove them from the integral. We also know that the integral of <math> -1\over r^2 </math> is <math> 1\over r </math>. We then must calculate the integral of <math> –GMm\over r^2 </math> from the initial radius of the asteroid, <math> R </math>, to the radius of the earth, <math> r </math>. <br />
<br />
<math> W=-GMm\bullet\int\limits_{R}^{r}{-1\over r^2}\bullet dr </math><br />
<br />
<math> W=-GMm\bullet({1\over r}-{1\over R}) </math><br />
<br />
Our answer will be positive because the force done by the earth on the asteroid and the direction of the asteroid's displacement are the same.<br />
<br />
==Connectedness==<br />
I am most interested in the types of physics problems that accurately model real world situations. Some forces, like gravity near the surface of the earth and some machine-applied forces, are constant. However, most forces in the real world are not. <br />
<br />
Because of this, calculating work for non-constant forces is essential to mechanical engineering. For example, when calculating work done by an engine over a distance, the force applied by the engine can vary depending on factors such as user controls.<br />
<br />
On an industrial level, the work needed to fill and empty tanks depends on the weight of the liquid, which varies as the tanks fill and empty. Energy conversion in hydroelectric dams depends on the work done by water against turbines, which depends on the flow of water. Windmills work in the same way.<br />
<br />
<br />
==History==<br />
<br />
Gaspard-Gustave de Coriolis, famous for discoveries such as the Coriolis effect, is credited with naming the term “work” to define force applied over a distance. Later physicists combined this concept with Newtonian calculus to find work for non-constant forces.<br />
<br />
== See also ==<br />
<br />
[[Work]]<br />
<br />
==References==<br />
<br />
[http://www.britannica.com/biography/Gustave-Gaspard-Coriolis]<br />
[https://en.wikibooks.org/wiki/FHSST_Physics/Work_and_Energy/Work]<br />
[https://trinket.io/glowscript/31d0f9ad9e]<br />
<br />
[[Category:Energy]]<br />
<br />
Created by Justin Vuong</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Work_Done_By_A_Nonconstant_Force&diff=21452Work Done By A Nonconstant Force2016-04-15T16:42:39Z<p>Chrismickas: </p>
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<div>'''Claimed by Chris Mickas'''<br />
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This page will help students understand how to calculate the work done by a non constant force.<br />
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==The Main Idea==<br />
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Basic calculations of work can be solved with a simple formula: force times displacement. However, this formula only works when work is constant. Calculus is essential for the calculation of work in many cases because force is not always a constant. In cases such as springs and gravity, for example, the force applied varies depending on location. By integrating, or finding the area under the curve of force by displacement, we can calculate work without having to use inaccurate approximations.<br />
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===A Mathematical Model===<br />
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<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math><br />
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This means that the work is equal to the integral of the function of the force with respect to the change in the objects position. This is also the same as the summation of the force on an object multiplied by the change in position.<br />
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===A Computational Model===<br />
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<https://trinket.io/glowscript/49f7c0f35f><br />
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This model shows both the total work and the work done by a spring on a ball attached to a vertical spring. The work done by the spring oscillates because the work is negative when the ball is moving away from the resting state and is positive when the ball moves towards it.<br />
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Because gravity causes the ball’s minimum position to be further from the spring’s resting length than its maximum position could be, the work is more negative when the ball approaches its minimum height.<br />
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The code works by using small time steps of 0.01 seconds and finding the work done in each time step. Work is the summation of all of the work done in each time step, so another step makes sure the value for work is cumulative.<br />
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==Examples==<br />
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===Example 1===<br />
A box is pushed to the East, 5 meters by a force of 40 N, then it is pushed to the north 7 meters by a force of 60 N. Calculate the work done on the box.<br />
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<math> W = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math><br />
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<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math><br />
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<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math><br />
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<math> W = 620 J </math><br />
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===Example 2===<br />
As a ball is attached to a spring and moves to the right. The ball moves 5 meters to the right and the spring constant of the spring is 5 N/m. How much work is done by the spring?<br />
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<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} </math><br />
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<math> F = -k \bullet\ r </math><br />
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<math> W=\int\limits_{0}^{5m} -k \bullet\ dr </math><br />
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<math> W=\int\limits_{0}^{5m} -5 \bullet\ dr </math><br />
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<math> W=\int\limits_{0}^{5m} -5 \bullet\ dr </math><br />
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<math> W=-5 ((5m^2)/2 - 0) </math><br />
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<math> W= 62.5 J </math><br />
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===Example 3===<br />
The earth does work on an asteroid approaching from an initial distance r. How much work is done on the asteroid by gravity before it hits the earth’s surface?<br />
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First, we must recall the formula for gravitational force.<br />
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Because G, M, and m are constants, we can remove them from the integral. We also know that the integral of 1/r2 is -1/r. We then must calculate the integral of –GMm/r from the initial radius of the asteroid, rasteroid, to the radius of the earth, rearth. <br />
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Although the integral is negative, because the final radius is less than the initial radius, our answer will be positive. This is because the force done by the earth on the asteroid and the direction of motion of the asteroid are the same.<br />
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==Connectedness==<br />
I am most interested in the types of physics problems that accurately model real world situations. Some forces, like gravity near the surface of the earth and some machine-applied forces, are constant. However, most forces in the real world are not. <br />
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Because of this, calculating work for non-constant forces is essential to mechanical engineering. For example, when calculating work done by an engine over a distance, the force applied by the engine can vary depending on factors such as user controls.<br />
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On an industrial level, the work needed to fill and empty tanks depends on the weight of the liquid, which varies as the tanks fill and empty. Energy conversion in hydroelectric dams depends on the work done by water against turbines, which depends on the flow of water. Windmills work in the same way.<br />
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==History==<br />
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Gaspard-Gustave de Coriolis, famous for discoveries such as the Coriolis effect, is credited with naming the term “work” to define force applied over a distance. Later physicists combined this concept with Newtonian calculus to find work for non-constant forces.<br />
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== See also ==<br />
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[[Work]]<br />
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==References==<br />
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[http://www.britannica.com/biography/Gustave-Gaspard-Coriolis]<br />
[https://en.wikibooks.org/wiki/FHSST_Physics/Work_and_Energy/Work]<br />
[https://trinket.io/glowscript/31d0f9ad9e]<br />
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[[Category:Energy]]<br />
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Created by Justin Vuong</div>Chrismickashttp://www.physicsbook.gatech.edu/index.php?title=Work_Done_By_A_Nonconstant_Force&diff=20942Work Done By A Nonconstant Force2016-04-12T01:55:46Z<p>Chrismickas: </p>
<hr />
<div>'''Claimed by Chris Mickas'''<br />
<br />
This page will help students understand how to calculate the work done by a non constant force.<br />
<br />
==The Main Idea==<br />
<br />
When calculating the force, if the magnitude of the force or direction of the force changes, it is not possible to calculate the work done by multiplying force by the displacement. Instead the non constant force is split into a path with small increments. <br />
<br />
<br />
===A Mathematical Model===<br />
<br />
<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math><br />
<br />
This means that the work is equal to the integral of the function of the force with respect to the change in the objects position. This is also the same as the summation of the force on an object multiplied by the change in position.<br />
<br />
===A Computational Model===<br />
<br />
[[File:Screen Shot 2015-12-05 at 5.23.32 PM.png]]<br />
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This python code creates a ball with a force acting on it that changes with respect to time and it prints the total work at the end of the the loop that lasts while t is less than 10.<br />
This uses the concept that work is equal to the summation of the force multiplied by the change in distance over that interval, which is an estimate for the integral of the force function over this distance.<br />
<br />
==Examples==<br />
<br />
===Example 1===<br />
A box is pushed to the East, 5 meters by a force of 40 N, then it is pushed to the north 7 meters by a force of 60 N. Calculate the work done on the box.<br />
<br />
<math> W = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math><br />
<br />
<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math><br />
<br />
<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math><br />
<br />
<math> W = 620 J </math><br />
<br />
===Example 2===<br />
As a ball is attached to a spring and moves to the right. The ball moves 5 meters to the right and the spring constant of the spring is 5 N/m. How much work is done by the spring?<br />
<br />
<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} </math><br />
<br />
<math> F = -k \bullet\ r </math><br />
<br />
<math> W=\int\limits_{0}^{5m} -k \bullet\ dr </math><br />
<br />
<math> W=\int\limits_{0}^{5m} -5 \bullet\ dr </math><br />
<br />
<math> W=\int\limits_{0}^{5m} -5 \bullet\ dr </math><br />
<br />
<math> W=-5 ((5m^2)/2 - 0) </math><br />
<br />
<math> W= 62.5 J </math><br />
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==Connectedness==<br />
How is this topic connected to something that you are interested in?<br />
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Even though I'm an ECE major, I have an interest in aviation, and the force of a jet engine is not always a constant force, so you would need to use this method to calculate the work done instead of the simple method.<br />
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How is it connected to your major?<br />
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As an ECE major, this could be connected by my major when working with an electric motor and calculating the amount of power needed to power the motor.<br />
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Is there an interesting industrial application?<br />
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Since many forces in the real world are not constant, this method of calculating work is needed for most situations.<br />
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==History==<br />
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The concept of work was introduced by a French mathematician named Gaspard-Gustave Coriolis in 1826. The concept was established as a "weight lifted through a height".<br />
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== See also ==<br />
<br />
[[Work]]<br />
<br />
==References==<br />
<br />
[http://www.britannica.com/biography/Gustave-Gaspard-Coriolis]<br />
[https://en.wikibooks.org/wiki/FHSST_Physics/Work_and_Energy/Work]<br />
[https://trinket.io/glowscript/31d0f9ad9e]<br />
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[[Category:Energy]]<br />
<br />
Created by Justin Vuong</div>Chrismickas