Physics Book - User contributions [en]

Lorentz Force

2016-04-18T02:11:28Z

Awhitacre7:

Claimed by Firas Sheikh- 1 November 2015

'''Improved by Anna Marie Whitacre- Spring 2016'''
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]
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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png|350px]]

==Examples==

===Simple===
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?
[[File:Ldirection.jpg|600px|center|]]
'''Solution: The Lorentz force is 0 N.'''

===Middling===
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.
[[File:LMiddle.jpg|470px|center|]]
'''Solution: Lorentz force = <300,500,700> N'''

===Difficult===
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.
[[File:Lhard.jpg|400px|center|]]
'''Solution: Lorentz force = 4.48e-24 N'''

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]
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.

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.

==History==
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]
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.

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>.

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.

== See also ==
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>.
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]
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!

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

Lorentz Force

2016-04-18T02:05:52Z

Awhitacre7: /* Connectedness */

Claimed by Firas Sheikh- 1 November 2015

'''Improved by Anna Marie Whitacre- Spring 2016'''
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]
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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png|350px]]

==Examples==

===Simple===
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?
[[File:Ldirection.jpg|600px|center|]]
'''Solution: The Lorentz force is 0 N.'''

===Middling===
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.
[[File:LMiddle.jpg|470px|center|]]
'''Solution: Lorentz force = <300,500,700> N'''

===Difficult===
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.
[[File:Lhard.jpg|400px|center|]]
'''Solution: Lorentz force = 4.48e-24 N'''

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|275px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.
[[File:Lorentzrailguns.gif|thumb|right|250px|Railgun use of Lorentz force]]
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 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.

4. The 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.

==History==
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]
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.

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>.

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.

== See also ==
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>.
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]
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!

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

File:Lorentzrailguns.gif

2016-04-18T02:01:09Z

Awhitacre7:

Lorentz Force

2016-04-18T01:44:16Z

Awhitacre7:

Claimed by Firas Sheikh- 1 November 2015

'''Improved by Anna Marie Whitacre- Spring 2016'''
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]
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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png|350px]]

==Examples==

===Simple===
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?
[[File:Ldirection.jpg|600px|center|]]
'''Solution: The Lorentz force is 0 N.'''

===Middling===
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.
[[File:LMiddle.jpg|470px|center|]]
'''Solution: Lorentz force = <300,500,700> N'''

===Difficult===
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.
[[File:Lhard.jpg|400px|center|]]
'''Solution: Lorentz force = 4.48e-24 N'''

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

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 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.

==History==
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]
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.

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>.

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.

== See also ==
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>.
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]
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!

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

Lorentz Force

2016-04-18T01:43:24Z

Awhitacre7:

Claimed by Firas Sheikh- 1 November 2015 (EST)

Improved by Anna Marie Whitacre (SPRING 2016)
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]
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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png|350px]]

==Examples==

===Simple===
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?
[[File:Ldirection.jpg|600px|center|]]
'''Solution: The Lorentz force is 0 N.'''

===Middling===
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.
[[File:LMiddle.jpg|470px|center|]]
'''Solution: Lorentz force = <300,500,700> N'''

===Difficult===
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.
[[File:Lhard.jpg|400px|center|]]
'''Solution: Lorentz force = 4.48e-24 N'''

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

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 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.

==History==
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]
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.

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>.

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.

== See also ==
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>.
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]
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!

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

File:Lhard.jpg

2016-04-18T01:40:34Z

Awhitacre7:

Lorentz Force

2016-04-18T01:37:33Z

Awhitacre7:

Claimed by Firas Sheikh- 1 November 2015 (EST)

Improved by Anna Marie Whitacre (SPRING 2016)
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
[[File:Lheader.jpg|thumb|left|200px|The Lorentz force formula]]
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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
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?
[[File:Ldirection.jpg|600px|center|]]
'''Solution: The Lorentz force is 0 N.'''

===Middling===
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.
[[File:Lmiddle.jpg|600px|center|]]
'''Solution: Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N'''

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

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 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.

==History==
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]
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.

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>.

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.

== See also ==
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>.
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]
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!

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

File:LMiddle.jpg

2016-04-18T01:35:56Z

Awhitacre7:

File:Ldirection.jpg

2016-04-18T01:30:45Z

Awhitacre7:

Lorentz Force

2016-04-18T01:24:02Z

Awhitacre7: /* Examples */

Claimed by Firas Sheikh- 1 November 2015 (EST)

Improved by Anna Marie Whitacre (SPRING 2016)
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==

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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
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?

'''Solution: The Lorentz Force is 0 N.'''

===Middling===
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.

'''Solution:'''

Lorentz Force = Electric Force + Magnetic Force

'''Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N''

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

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 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.

==History==
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]
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.

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>.

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.

== See also ==
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>.
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]
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!

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

File:Lheader.jpg

2016-04-18T01:23:02Z

Awhitacre7:

Lorentz Force

2016-04-18T00:35:18Z

Awhitacre7:

Claimed by Firas Sheikh- 1 November 2015 (EST)

Improved by Anna Marie Whitacre (SPRING 2016)
[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==

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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
If the electric force points in the +x direction and the Magnetic Force points in the –x direction, what direction the Lorentz force point in?

Solution: The Lorentz Force is 0 N.

===Middling===
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.

'''Solution:'''

Lorentz Force = Electric Force + Magnetic Force

Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

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 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.

==History==
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]
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.

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>.

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.

== See also ==
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>.
[[File:Videolorentz.png|thumb|left|175px|The interaction between electricity and magnetism as seen [https://www.youtube.com/watch?v=8QWB8IfNoIs here]]]
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!

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

File:Headerlorentz.png

2016-04-18T00:20:56Z

Awhitacre7:

File:Videolorentz.png

2016-04-18T00:14:44Z

Awhitacre7:

Lorentz Force

2016-04-18T00:11:27Z

Awhitacre7: /* See also */

Claimed by Firas Sheikh- 1 November 2015 (EST)

Improved by Anna Marie Whitacre (SPRING 2016)
==The Main Idea==

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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
If the Electric Force points in the +x direction and the Magnetic Force points in the –x direction, what direction the Lorentz force point in?

Solution: The Lorentz Force is 0 N.

===Middling===
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.

Solution:

Lorentz Force = Electric Force + Magnetic Force

Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

3. In 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 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.

==History==
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]
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.

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 F = (q/2)*v X B.

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.

== See also ==
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>.

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!

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

Lorentz Force

2016-04-17T23:58:59Z

Awhitacre7:

Claimed by Firas Sheikh- 1 November 2015 (EST)

Improved by Anna Marie Whitacre (SPRING 2016)
==The Main Idea==

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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
If the Electric Force points in the +x direction and the Magnetic Force points in the –x direction, what direction the Lorentz force point in?

Solution: The Lorentz Force is 0 N.

===Middling===
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.

Solution:

Lorentz Force = Electric Force + Magnetic Force

Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

3. In 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 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.

==History==
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]
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.

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 F = (q/2)*v X B.

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.

== See also ==
The [[Hall Effect]] explores this concept more in depth because it deals with the Electric Force and Magnetic Force being equal. 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>.

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

Lorentz Force

2016-04-17T23:55:38Z

Awhitacre7: /* The Main Idea */

Claimed by Firas Sheikh- 1 November 2015 (EST)

Improved by Anna Marie Whitacre (SPRING 2016)
==The Main Idea==

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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
If the Electric Force points in the +x direction and the Magnetic Force points in the –x direction, what direction the Lorentz force point in?

Solution: The Lorentz Force is 0 N.

===Middling===
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.

Solution:

Lorentz Force = Electric Force + Magnetic Force

Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

3. In 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 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.

==History==
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]
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.

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 F = (q/2)*v X B.

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.

== See also ==
The [[Hall Effect]] explores this concept more in depth because it deals with the Electric Force and Magnetic Force being equal. Usually, these problems require you to set them equal to each other and solve for B,v, or E.

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

Lorentz Force

2016-04-17T23:39:34Z

Awhitacre7: /* History */

Claimed by Firas Sheikh- 1 November 2015 (EST)

Improved by Anna Marie Whitacre (SPRING 2016)
==The Main Idea==

The 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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
If the Electric Force points in the +x direction and the Magnetic Force points in the –x direction, what direction the Lorentz force point in?

Solution: The Lorentz Force is 0 N.

===Middling===
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.

Solution:

Lorentz Force = Electric Force + Magnetic Force

Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

3. In 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 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.

==History==
[[File:hlorentz.jpg|200px|thumb|right|Hendrik Lorentz]]
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.

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 F = (q/2)*v X B.

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.

== See also ==
The [[Hall Effect]] explores this concept more in depth because it deals with the Electric Force and Magnetic Force being equal. Usually, these problems require you to set them equal to each other and solve for B,v, or E.

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

File:Hlorentz.jpg

2016-04-17T23:34:25Z

Awhitacre7:

Lorentz Force

2016-04-17T23:18:22Z

Awhitacre7:

Claimed by Firas Sheikh- 1 November 2015 (EST)

Improved by Anna Marie Whitacre (SPRING 2016)
==The Main Idea==

The 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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
If the Electric Force points in the +x direction and the Magnetic Force points in the –x direction, what direction the Lorentz force point in?

Solution: The Lorentz Force is 0 N.

===Middling===
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.

Solution:

Lorentz Force = Electric Force + Magnetic Force

Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

3. In 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 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.

==History==
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.

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 F = (q/2)*v X B.

== See also ==
The [[Hall Effect]] explores this concept more in depth because it deals with the Electric Force and Magnetic Force being equal. Usually, these problems require you to set them equal to each other and solve for B,v, or E.

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

Lorentz Force

2016-04-17T23:15:58Z

Awhitacre7: /* History */

Claimed by Firas Sheikh- 1 November 2015 (EST)

Improved by Anna Marie Whitacre (SPRING 2016)
==The Main Idea==

The 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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
If the Electric Force points in the +x direction and the Magnetic Force points in the –x direction, what direction the Lorentz force point in?

Solution: The Lorentz Force is 0 N.

===Middling===
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.

Solution:

Lorentz Force = Electric Force + Magnetic Force

Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

3. In 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 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.

==History==
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-Augustin de Coulomb, using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by H. C. Ørsted that a magnetic needle is acted on by a voltaic current, André-Marie Ampère 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.

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 F = (q/2)*v X B.

== See also ==
The [[Hall Effect]] explores this concept more in depth because it deals with the Electric Force and Magnetic Force being equal. Usually, these problems require you to set them equal to each other and solve for B,v, or E.

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

Lorentz Force

2016-04-17T23:11:42Z

Awhitacre7:

Claimed by Firas Sheikh- 1 November 2015 (EST)

Improved by Anna Marie Whitacre (SPRING 2016)
==The Main Idea==

The 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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
If the Electric Force points in the +x direction and the Magnetic Force points in the –x direction, what direction the Lorentz force point in?

Solution: The Lorentz Force is 0 N.

===Middling===
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.

Solution:

Lorentz Force = Electric Force + Magnetic Force

Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

3. In 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 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.

==History==
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-Augustin de Coulomb, using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by H. C. Ørsted that a magnetic needle is acted on by a voltaic current, André-Marie Ampère 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.

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 Lord Kelvin and James Clerk 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 F = (q/2)*v X B.
== See also ==
The [[Hall Effect]] explores this concept more in depth because it deals with the Electric Force and Magnetic Force being equal. Usually, these problems require you to set them equal to each other and solve for B,v, or E.

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

Lorentz Force

2016-04-17T23:07:13Z

Awhitacre7: /* Connectedness */

Claimed by Firas Sheikh- 1 November 2015 (EST)
Improved by Anna Marie Whitacre (SPRING 2016)
==The Main Idea==

The 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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
If the Electric Force points in the +x direction and the Magnetic Force points in the –x direction, what direction the Lorentz Force point in?

Solution: The Lorentz Force is 0 N.

===Middling===
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.

Solution:

Lorentz Force = Electric Force + Magnetic Force

Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
[[File:Hoverspacecraft.jpg|thumb|right|250px|Hovering spacecraft]]
#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.
[[File:RotLFV.png|thumb|left|200px|Simplified sketch of the LFF]]
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.

3. In 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 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.

==History==
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-Augustin de Coulomb, using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by H. C. Ørsted that a magnetic needle is acted on by a voltaic current, André-Marie Ampère 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.

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 Lord Kelvin and James Clerk 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 F = (q/2)*v X B.
== See also ==
The Hall Effect explores this concept more in depth because it deals with the Electric Force and Magnetic Force being equal. Usually, these problems require you to set them equal to each other and solve for B,v, or E.

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

File:RotLFV.png

2016-04-17T23:03:00Z

Awhitacre7:

File:Metallurgy.jpg

2016-04-17T22:56:08Z

Awhitacre7:

File:Hoverspacecraft.jpg

2016-04-17T22:50:26Z

Awhitacre7:

Lorentz Force

2016-04-17T22:42:48Z

Awhitacre7: /* A Mathematical Model */

Claimed by Firas Sheikh- 1 November 2015 (EST)
Improved by Anna Marie Whitacre (SPRING 2016)
==The Main Idea==

The 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.

===A Mathematical Model===

<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.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
If the Electric Force points in the +x direction and the Magnetic Force points in the –x direction, what direction the Lorentz Force point in?

Solution: The Lorentz Force is 0 N.

===Middling===
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.

Solution:

Lorentz Force = Electric Force + Magnetic Force

Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
#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 propellantless hovering and the corresponding required specific charge of a Lorentz spacecraft.
#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 propellantless method for orbital maneuvers.
#In 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 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.

==History==
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-Augustin de Coulomb, using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by H. C. Ørsted that a magnetic needle is acted on by a voltaic current, André-Marie Ampère 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.

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 Lord Kelvin and James Clerk 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 F = (q/2)*v X B.
== See also ==
The Hall Effect explores this concept more in depth because it deals with the Electric Force and Magnetic Force being equal. Usually, these problems require you to set them equal to each other and solve for B,v, or E.

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

Bar Magnet

2016-04-17T22:38:55Z

Awhitacre7:

A bar magnet creates a magnetic field, just like many other devices (i.e. a current carrying wire), however, it has a different pattern of magnetic field which we will explore.

__TOC__

== '''The Main Idea''' ==
----
The main idea for this topic is to explore how a bar magnet works and the effects that it has on its surroundings.

== '''A Mathematical Model''' ==
----
Due to the fact that an observation location can either be on the axis of the magnet, or off the axis of the magnet, we have to different equations. For an observation location that is on the same axis as the magnet, assuming that the distance from the observation location to the magnet is much greater than the the separation distance of the two poles we find that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{2\mu }{r^{3}}</math>

If the observation location is not on the axis of the bar magnet, and assuming that the distance from the observation location to the magnet is much greater than the the separation distance of the two poles we conclude that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{\mu }{r^{3}}</math>

== '''A Computational Model''' ==
----
[[File:VFPt cylindrical magnet thumb.svg|thumb|left|The curly magnetic field of a bar magnet.]]

As you can see in this picture, the magnetic field of a bar magnet takes the exact same form as an electric field of a dipole. The magnetic lines flow out of the north pole to the magnet, and into the south pole of the magnet, in a curling fashion. However, the 'poles' are merely just conventions. They do not represent anything, and are terms just assigned to each end, but it is true that the magnetic field will always flow out of the 'north end'. Like a bar magnet, the Earth itself can also be represented by the computational model of a bar magnet, however, there are a few misconceptions about this. For starters, the magnetic North Pole is actually located at the geographic South Pole, and the magnetic South Pole is located at the geographic North Pole. Furthermore, the magnetic poles are off axis, meaning the are not directly at the top and bottom of the Earth. There is a difference of almost 1.5 degrees!
It is also interesting to note that just because this illustration depicts the bar magnet as having two distinct ends, if you were to cut the magnet down the middle, you would assume that you would end up with a south end and a north end. However, this is not the case. If a magnet were to be cut in half, it would polarize in such a way that you would end up with two bar magnets, not a single south pole and a single north pole.

== '''Examples''' ==
----
'''Example 1''': If a bar magnet is located at the origin aligned with its North end aligned with the positive X-axis, what are the directions of the magnetic field at the following observation locations: above, below, to the left, to the right, and in a plane that is above the magnet?

Well, we already know that the field of a bar magnet flows out of the north end and into the south end in a curling fashion. So, using the diagram above, it is easy to see that to the right of the magnet, the direction of the magnetic field points in the +X direction. At a position to the left of the magnet, the field is flowing back into the south end of the magnet, so the direction of the magnetic field at this location is ALSO in the +X direction.

The field above and below the magnet is flowing from the right to the left at both locations, so the direction of the magnetic field above and below the magnet is in the -X direction.

At a different plane (z doesn't = 0), there is no magnetic field, because we can assume that bar magnet acts as a 2-D dipole.

'''Example 2:''' A bar magnet with magnetic dipole moment 0.58 lies on the negative x axis, as shown in the figure below. A compass is located at the origin. Magnetic north is in the negative z direction. Between the bar magnet and the compass is a coil of wire of radius 3.5 cm, connected to batteries not shown. The distance from the center of the coil to the center of the compass is 9.6 cm. The distance from the center of the bar magnet to the center of the compass is 23.0 cm. A steady current of 0.96 A runs through the coil. Conventional current runs clockwise in the coil when viewed from the location of the compass. Despite the presence of the magnet and coil the compass still points north.

'''(a)''' Which end of the bar magnet is closest to the compass?
'''(b)''' How many turns of wire are in the coil?

'''Part A:''' Because the conventional current runs clockwise in the coil, you can use right hand rule to determine what direction the magnetic field is due to the coil. This tells us that the magnetic field due to the coil is in the -X direction. In order for the compass to stay still, the magnet needs to directly oppose the magnetic field of the coil, meaning its magnetic field has to point in the +X direction, meaning the '''NORTH end''' would have to be nearest the compass (because the field flows out of the north end into the positive end).

'''Part B:''' Because the field created by the coil equals the field created by the magnet, we can set their two fields equal to each other:
<math> \frac{\mu _{0}}{4 \pi } \cdot \frac{2\mu }{r^{3}} = \frac{\mu _{0}}{4 \pi } \cdot \frac{2NI\pi R^{2}}{(z^{2}+R^{2})^{3/2}} </math>

Rearranging to solve this equation for N, we get: <math> N = \frac{\mu (z^{2}+R^{2})^{3/2}}{I\pi R^{2} d^{3}} </math>

Plugging in .58 the magnetic dipole moment (mu), .096 meters for z, .035 meters for R, .96 Amps for I, and .23 meters for d, we get that the number of loops in the coil is '''14.'''

== '''Connectedness''' ==
----
[[File:Series L0.JPG|thumb|left|An experimental MAGLEV train created by Japanese engineers.]]
One very interesting applications of magnets is their ability to levitate objects. This is the main driving force in the case of MAGLEV trains. Magnetic levitation, or MAGLEV trains, hover above a long series of magnets where the magnets on the bottom of the train repel the magnets on the tracks below it. Sending an electric current through the coils on the bottom of the track allows the train to levitate a few inches off the ground, and propelling the current through the guided coils on the bottom of the track propels the train forward at unbelievable speeds (up to 250 MPH!).

Making the train levitate is a useful tool because it reduces the amount of friction between the wheels and the track, and it allows for less fossil fuels to be used in order to make the train propel forwards.

== '''History''' ==
----
[[File:James Clerk Maxwell.png|thumb|right|James Clerk Maxwell]]
The first magnets were not invented, but rather discovered. The ancient Greeks and ancient Chinese peoples stumbled upon a naturally occurring material, called magnetite, by mistake. People were so astounded by it that tales were told of magical islands where magnetic nature was everywhere. The Chinese actually developed a compass around 4500 years using this magnetite!

Despite not being the first people to study magnetism, Hans Christian Oersted did prove that electricity and magnetism were related by bringing a current carrying wire close to a compass needle. However, it wasn't until Maxwell published his findings in 1862 that led to the relationships between electricity and magnetism (Maxwell's Equations; see other Wikipedia page).

== '''External links''' ==
----
# MAGLEV Trains: http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Magnetism-Real-life-applications.html
# More information on Bar Magnets: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html

== '''References''' ==
----
# http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html
# https://en.wikipedia.org/wiki/Magnet#/media/File:VFPt_cylindrical_magnet_thumb.svg
# http://www.howmagnetswork.com/history.html
# https://en.wikipedia.org/wiki/Maglev#/media/File:Series_L0.JPG
# https://en.wikipedia.org/wiki/James_Clerk_Maxwell#/media/File:James_Clerk_Maxwell.png
Category: '''Fields'''

'''Created by: John Joyce'''

__FORCETOC__

Lorentz Force

2016-04-17T17:20:41Z

Awhitacre7:

Claimed by Firas Sheikh- 1 November 2015 (EST)
Improved by Anna Marie Whitacre (SPRING 2016)
==The Main Idea==

The 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.

===A Mathematical Model===

<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math> where '''qE''' is the electric force and '''qv x B''' is the magnetic force.

===A Computational Model===
[[File:Lorentz Force.png]]

==Examples==

===Simple===
If the Electric Force points in the +x direction and the Magnetic Force points in the –x direction, what direction the Lorentz Force point in?

Solution: The Lorentz Force is 0 N.

===Middling===
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.

Solution:

Lorentz Force = Electric Force + Magnetic Force

Lorentz Force = <500,-200,300> + <-200,700,400> = <300,500,700> N

===Difficult===
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.

Solution:

Electric Force = qE = (1.6e-19)*(8e-6) = 1.28e-24 N

Magnetic Force = q*B*v = (1.6e-19)*(4e-9)*(5e3) = 3.2e-24 N

Lorentz Force = Force Electric + Force Magnetic = 4.48e-24 N

==Connectedness==
#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 propellantless hovering and the corresponding required specific charge of a Lorentz spacecraft.
#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 propellantless method for orbital maneuvers.
#In 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 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.

==History==
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-Augustin de Coulomb, using a torsion balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by H. C. Ørsted that a magnetic needle is acted on by a voltaic current, André-Marie Ampère 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.

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 Lord Kelvin and James Clerk 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 F = (q/2)*v X B.
== See also ==
The Hall Effect explores this concept more in depth because it deals with the Electric Force and Magnetic Force being equal. Usually, these problems require you to set them equal to each other and solve for B,v, or E.

===Further reading===

*http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html
*http://www.ittc.ku.edu/~jstiles/220/handouts/section%203_6%20The%20Lorentz%20Force%20Law%20package.pdf

===External links===

*http://jnaudin.free.fr/lifters/lorentz/
*https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

==References==

*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.
*Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York, [NY.]: Wiley. ISBN 0-471-30932-X.
*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.

[[Category:Which Category did you place this in?]]

Bar Magnet

2016-04-17T17:16:33Z

Awhitacre7:

**CLAIMED BY ANNA MARIE WHITACRE (SPRING 2016)

A bar magnet creates a magnetic field, just like many other devices (i.e. a current carrying wire), however, it has a different pattern of magnetic field which we will explore.

__TOC__

== '''The Main Idea''' ==
----
The main idea for this topic is to explore how a bar magnet works and the effects that it has on its surroundings.

== '''A Mathematical Model''' ==
----
Due to the fact that an observation location can either be on the axis of the magnet, or off the axis of the magnet, we have to different equations. For an observation location that is on the same axis as the magnet, assuming that the distance from the observation location to the magnet is much greater than the the separation distance of the two poles we find that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{2\mu }{r^{3}}</math>

If the observation location is not on the axis of the bar magnet, and assuming that the distance from the observation location to the magnet is much greater than the the separation distance of the two poles we conclude that:
<math> B = \frac{\mu _{0}}{4\pi }\cdot \frac{\mu }{r^{3}}</math>

== '''A Computational Model''' ==
----
[[File:VFPt cylindrical magnet thumb.svg|thumb|left|The curly magnetic field of a bar magnet.]]

As you can see in this picture, the magnetic field of a bar magnet takes the exact same form as an electric field of a dipole. The magnetic lines flow out of the north pole to the magnet, and into the south pole of the magnet, in a curling fashion. However, the 'poles' are merely just conventions. They do not represent anything, and are terms just assigned to each end, but it is true that the magnetic field will always flow out of the 'north end'. Like a bar magnet, the Earth itself can also be represented by the computational model of a bar magnet, however, there are a few misconceptions about this. For starters, the magnetic North Pole is actually located at the geographic South Pole, and the magnetic South Pole is located at the geographic North Pole. Furthermore, the magnetic poles are off axis, meaning the are not directly at the top and bottom of the Earth. There is a difference of almost 1.5 degrees!
It is also interesting to note that just because this illustration depicts the bar magnet as having two distinct ends, if you were to cut the magnet down the middle, you would assume that you would end up with a south end and a north end. However, this is not the case. If a magnet were to be cut in half, it would polarize in such a way that you would end up with two bar magnets, not a single south pole and a single north pole.

== '''Examples''' ==
----
'''Example 1''': If a bar magnet is located at the origin aligned with its North end aligned with the positive X-axis, what are the directions of the magnetic field at the following observation locations: above, below, to the left, to the right, and in a plane that is above the magnet?

Well, we already know that the field of a bar magnet flows out of the north end and into the south end in a curling fashion. So, using the diagram above, it is easy to see that to the right of the magnet, the direction of the magnetic field points in the +X direction. At a position to the left of the magnet, the field is flowing back into the south end of the magnet, so the direction of the magnetic field at this location is ALSO in the +X direction.

The field above and below the magnet is flowing from the right to the left at both locations, so the direction of the magnetic field above and below the magnet is in the -X direction.

At a different plane (z doesn't = 0), there is no magnetic field, because we can assume that bar magnet acts as a 2-D dipole.

'''Example 2:''' A bar magnet with magnetic dipole moment 0.58 lies on the negative x axis, as shown in the figure below. A compass is located at the origin. Magnetic north is in the negative z direction. Between the bar magnet and the compass is a coil of wire of radius 3.5 cm, connected to batteries not shown. The distance from the center of the coil to the center of the compass is 9.6 cm. The distance from the center of the bar magnet to the center of the compass is 23.0 cm. A steady current of 0.96 A runs through the coil. Conventional current runs clockwise in the coil when viewed from the location of the compass. Despite the presence of the magnet and coil the compass still points north.

'''(a)''' Which end of the bar magnet is closest to the compass?
'''(b)''' How many turns of wire are in the coil?

'''Part A:''' Because the conventional current runs clockwise in the coil, you can use right hand rule to determine what direction the magnetic field is due to the coil. This tells us that the magnetic field due to the coil is in the -X direction. In order for the compass to stay still, the magnet needs to directly oppose the magnetic field of the coil, meaning its magnetic field has to point in the +X direction, meaning the '''NORTH end''' would have to be nearest the compass (because the field flows out of the north end into the positive end).

'''Part B:''' Because the field created by the coil equals the field created by the magnet, we can set their two fields equal to each other:
<math> \frac{\mu _{0}}{4 \pi } \cdot \frac{2\mu }{r^{3}} = \frac{\mu _{0}}{4 \pi } \cdot \frac{2NI\pi R^{2}}{(z^{2}+R^{2})^{3/2}} </math>

Rearranging to solve this equation for N, we get: <math> N = \frac{\mu (z^{2}+R^{2})^{3/2}}{I\pi R^{2} d^{3}} </math>

Plugging in .58 the magnetic dipole moment (mu), .096 meters for z, .035 meters for R, .96 Amps for I, and .23 meters for d, we get that the number of loops in the coil is '''14.'''

== '''Connectedness''' ==
----
[[File:Series L0.JPG|thumb|left|An experimental MAGLEV train created by Japanese engineers.]]
One very interesting applications of magnets is their ability to levitate objects. This is the main driving force in the case of MAGLEV trains. Magnetic levitation, or MAGLEV trains, hover above a long series of magnets where the magnets on the bottom of the train repel the magnets on the tracks below it. Sending an electric current through the coils on the bottom of the track allows the train to levitate a few inches off the ground, and propelling the current through the guided coils on the bottom of the track propels the train forward at unbelievable speeds (up to 250 MPH!).

Making the train levitate is a useful tool because it reduces the amount of friction between the wheels and the track, and it allows for less fossil fuels to be used in order to make the train propel forwards.

== '''History''' ==
----
[[File:James Clerk Maxwell.png|thumb|right|James Clerk Maxwell]]
The first magnets were not invented, but rather discovered. The ancient Greeks and ancient Chinese peoples stumbled upon a naturally occurring material, called magnetite, by mistake. People were so astounded by it that tales were told of magical islands where magnetic nature was everywhere. The Chinese actually developed a compass around 4500 years using this magnetite!

Despite not being the first people to study magnetism, Hans Christian Oersted did prove that electricity and magnetism were related by bringing a current carrying wire close to a compass needle. However, it wasn't until Maxwell published his findings in 1862 that led to the relationships between electricity and magnetism (Maxwell's Equations; see other Wikipedia page).

== '''External links''' ==
----
# MAGLEV Trains: http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-3-Biology-Vol-1/Magnetism-Real-life-applications.html
# More information on Bar Magnets: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html

== '''References''' ==
----
# http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html
# https://en.wikipedia.org/wiki/Magnet#/media/File:VFPt_cylindrical_magnet_thumb.svg
# http://www.howmagnetswork.com/history.html
# https://en.wikipedia.org/wiki/Maglev#/media/File:Series_L0.JPG
# https://en.wikipedia.org/wiki/James_Clerk_Maxwell#/media/File:James_Clerk_Maxwell.png
Category: '''Fields'''

'''Created by: John Joyce'''

__FORCETOC__

Predicting the Position of a Rotating System

2015-12-06T03:52:52Z

Awhitacre7:

[[File:Rotating_Sphere.gif|thumb|right|300px|Visual of a rotating system.]]
In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of a rotating system.

==The Main Idea==
The position of a rotating system can be predicted by predicting the angle over which the object will rotate through out time. Basically, the key to finding out how much a rotating object has moved (over a specific time interval) is the angle through which it moves.

===A Mathematical Model===

Given that the system in question is indeed rotating, the update form of [[The Angular Momentum Principle]] is always applied about the the center of mass in our calculations.

The update form of the Angular Momentum Principle is as follows: <math>\vec{L}_{rot,f}=\vec{L}_{rot,i}+\vec{\tau}_{net}\Delta t</math> where <math>{L}</math> is rotational angular momentum and <math>\tau</math> is net torque from the surroundings.

In basic situations, the update form of the Angular Momentum Principle can further be simplified to account for [[The Moments of Inertia]], <math>I</math>, and the [[Angular Velocity]], <math>\omega</math> of the rotating system. This simplification of the update form of the Angular Momentum Principle yields the following mathematical equation: <math>I\omega _{f}=I\omega _{i}+RF\Delta t</math> where net torque, <math>\vec{\tau}_{net}</math> is simplified to the product of all the forces acting on the system and the locations to which these forces are applied, <math>RF</math>.

As mentioned before, the key to solving these types of problems is figuring out the angle, [math]\theta[/math], which the object rotates through. Given that the angle will always change at an instantaneous rate of [math]\omega=d\theta / dt[/math], the change in the angle [math]\theta[/math] is: [math]\Delta \theta=\omega_{avg} \Delta t[/math].

We will limit the complexity of this topic to situations where the angular speed [math]\omega[/math] changes at a constant rate [math]RF / I[/math]. Therefore, the average speed is said to be: [math]\omega_{avg}=\frac{\omega_{i} + \omega_{f} }{2}[/math]

===A Computational Model===
The position of a rotating system can be predicted using the following vPython code below. [https://trinket.io/python/22d3018e32 Try out the code here with different values!]. Take note that the default values in the code computationally calculate the answers to [[#Middling|this physics problem]].
[[File:Pythonscreenshot.png|center|550px|vPython code for solving rotational position.]]

==Examples==

===Simple===
A wheel of radius <math>R</math> and a moment of inertia <math>I</math> is mounted on a low-friction axle. A string is wrapped around the edge, and you pull on it with a force <math>F</math>, At a certain time the angular speed is <math>\omega_{i}</math>.

'''(a)''' After a time interval <math>\Delta t</math>, what is the angular speed <math>\omega_{f}</math>?
[[File:Simplea.jpg|400px|center|]]

'''(b)''' How far did your hand move during this time interval?
[[File:Easbi.jpg|400px|center|]]

[[File:Easbii.jpg|400px|center|]]
===Middling===
A uniform-density wheel of mass 6 kg and radius 0.3 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15 N for 0.6 s.

'''(a)''' What is the final angular speed?
[[File:Mida.jpg|400px|center|]]
'''(b)''' What is the average angular speed?
[[File:Midb.jpg|400px|center|]]
'''(c)''' Through how big an angle did the wheel turn?
[[File:Midc.jpg|400px|center|]]
'''(d)''' How much string came off the wheel?
[[File:Midd.jpg|400px|center|]]

==Connectedness==

===Industrial Application===
[[File:World_of_Color_overview.jpg|thumb|left|200px|Mickey's Fun Wheel.]]
[[File:Stlouisflags.jpg|thumb|right|200px|Colossus at Six Flags]]
In the theme and amusement park industry (e.g. Six Flags and Disney World), the aforementioned method of predicting the position of a rotating system can be applied to determine how far a certain rider has moved on either Mickey's Fun Wheel or Colossus. This prediction of a rider's position after a certain amount of time could be applied by economists to determine the ideal speed ''and'' time interval to run their respective ferris wheels to yield an optimal economic profit with respect to the cost of admission tickets.

===Scientific Application===
[[File:fig3-11.jpg|150px|thumb|right|Magnetic field produced by current]]
[[File:29_22_Magnetic_dipole_moment.JPG|150px|thumb|left|Orbiting electron]]
Predicting the position of a rotating system can also pioneer revelations in scientific research fields (esp. biochemistry and chemistry). Given that the position of an electron in relation to the nucleus of a hydrogen atom can be predicted based upon the angular momentum of the electron, this technique can be applied to determining the magnetism exhibited by the electron with respect to some defined axis. Therefore, the relationship between the position of an electron at a certain time (at some distance from a defined axis) could be related to the electric current produced by a magnetic field at that same time.

==History==

The key mathematical equation to predicting the position of a rotating system, the update form of the Angular Momentum Principle, has historical roots in the Laws of Motion of [[Sir Isaac Newton]]. The conservation of angular momentum was further described and put into terms by [[Johannes Kepler]].

== See also ==
[[The Angular Momentum Principle]]

[[The Moments of Inertia]]

[[Angular Velocity]]

[[Systems with Zero Torque]]

[[Systems with Nonzero Torque]]

===Further reading===
Judd, Brian R. ''Angular Momentum Theory for Diatomic Molecules''. Academic Press, 1975. Print.

===External links===
[https://www.youtube.com/watch?v=0k276y9kuQQ Angular Momentum - Science Theater Video ]

[http://chaos.utexas.edu/wp-uploads/2012/03/Lecture_24_post.pdf A Guide to the Angular Momentum Principle]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. ''Matter & Interactions''. Hoboken, NJ: Wiley, 2015. 443-45. Print.

[http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_3.html Angular Momentum of an Electron in an H Atom]

[[Category:Momentum]]

Predicting the Position of a Rotating System

2015-12-05T22:39:44Z

Awhitacre7: /* External links */

[[File:Rotating_Sphere.gif|thumb|right|300px|Visual of a rotating system.]]
In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of a rotating system.

==The Main Idea==
The position of a rotating system can be predicted by predicting the angle over which the object will rotate though out time. Basically, the key to finding out how much a rotating object has moved (over a specific time interval) is the angle through which it moves.

===A Mathematical Model===

Given that the system in question is indeed rotating, the update form of [[The Angular Momentum Principle]] is always applied about the the center of mass in our calculations.

The update form of the Angular Momentum Principle is as follows: <math>\vec{L}_{rot,f}=\vec{L}_{rot,i}+\vec{\tau}_{net}\Delta t</math> where <math>{L}</math> is rotational angular momentum and <math>\tau</math> is net torque from the surroundings.

In basic situations, the update form of the Angular Momentum Principle can further be simplified to account for [[The Moments of Inertia]], <math>I</math>, and the [[Angular Velocity]], <math>\omega</math> of the rotating system. This simplification of the update form of the Angular Momentum Principle yields the following mathematical equation: <math>I\omega _{f}=I\omega _{i}+RF\Delta t</math> where net torque, <math>\vec{\tau}_{net}</math> is simplified to the product of all the forces acting on the system and the locations to which these forces are applied, <math>RF</math>.

As mentioned before, the key to solving these types of problems is figuring out the angle, [math]\theta[/math], which the object rotates through. Given that the angle will always change at an instantaneous rate of [math]\omega=d\theta / dt[/math], the change in the angle [math]\theta[/math] is: [math]\Delta \theta=\omega_{avg} \Delta t[/math].

We will limit the complexity of this topic to situations where the angular speed [math]\omega[/math] changes at a constant rate [math]RF / I[/math]. Therefore, the average speed is said to be: [math]\omega_{avg}=\frac{\omega_{i} + \omega_{f} }{2}[/math]

===A Computational Model===
The position of a rotating system can be predicted using the following vPython code below. [https://trinket.io/python/22d3018e32 Try out the code here with different values!]. Take note that the default values in the code computationally calculate the answers to [[#Middling|this physics problem]].
[[File:Pythonscreenshot.png|center|550px|vPython code for solving rotational position.]]

==Examples==

===Simple===
A wheel of radius <math>R</math> and a moment of inertia <math>I</math> is mounted on a low-friction axle. A string is wrapped around the edge, and you pull on it with a force <math>F</math>, At a certain time the angular speed is <math>\omega_{i}</math>.

'''(a)''' After a time interval <math>\Delta t</math>, what is the angular speed <math>\omega_{f}</math>?
[[File:Simplea.jpg|400px|center|]]

'''(b)''' How far did your hand move during this time interval?
[[File:Easbi.jpg|400px|center|]]

[[File:Easbii.jpg|400px|center|]]
===Middling===
A uniform-density wheel of mass 6 kg and radius 0.3 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15 N for 0.6 s.

'''(a)''' What is the final angular speed?
[[File:Mida.jpg|400px|center|]]
'''(b)''' What is the average angular speed?
[[File:Midb.jpg|400px|center|]]
'''(c)''' Through how big an angle did the wheel turn?
[[File:Midc.jpg|400px|center|]]
'''(d)''' How much string came off the wheel?
[[File:Midd.jpg|400px|center|]]

==Connectedness==

===Industrial Application===
[[File:World_of_Color_overview.jpg|thumb|left|200px|Mickey's Fun Wheel.]]
[[File:Stlouisflags.jpg|thumb|right|200px|Colossus at Six Flags]]
In the theme and amusement park industry (e.g. Six Flags and Disney World), the aforementioned method of predicting the position of a rotating system can be applied to determine how far a certain rider has moved on either Mickey's Fun Wheel or Colossus. This prediction of a rider's position after a certain amount of time could be applied by economists to determine the ideal speed ''and'' time interval to run their respective ferris wheels to yield an optimal economic profit with respect to the cost of admission tickets.

===Scientific Application===
[[File:fig3-11.jpg|150px|thumb|right|Magnetic field produced by current]]
[[File:29_22_Magnetic_dipole_moment.JPG|150px|thumb|left|Orbiting electron]]
Predicting the position of a rotating system can also pioneer revelations in scientific research fields (esp. biochemistry and chemistry). Given that the position of an electron in relation to the nucleus of a hydrogen atom can be predicted based upon the angular momentum of the electron, this technique can be applied to determining the magnetism exhibited by the electron with respect to some defined axis. Therefore, the relationship between the position of an electron at a certain time (at some distance from a defined axis) could be related to the electric current produced by a magnetic field at that same time.

==History==

The key mathematical equation to predicting the position of a rotating system, the update form of the Angular Momentum Principle, has historical roots in the Laws of Motion of [[Sir Isaac Newton]]. The conservation of angular momentum was further described and put into terms by [[Johannes Kepler]].

== See also ==
[[The Angular Momentum Principle]]

[[The Moments of Inertia]]

[[Angular Velocity]]

[[Systems with Zero Torque]]

[[Systems with Nonzero Torque]]

===Further reading===
Judd, Brian R. ''Angular Momentum Theory for Diatomic Molecules''. Academic Press, 1975. Print.

===External links===
[https://www.youtube.com/watch?v=0k276y9kuQQ Angular Momentum - Science Theater Video ]

[http://chaos.utexas.edu/wp-uploads/2012/03/Lecture_24_post.pdf A Guide to the Angular Momentum Principle]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. ''Matter & Interactions''. Hoboken, NJ: Wiley, 2015. 443-45. Print.

[http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_3.html Angular Momentum of an Electron in an H Atom]

[[Category:Momentum]]

Predicting the Position of a Rotating System

2015-12-05T22:39:24Z

Awhitacre7: /* External links */

[[File:Rotating_Sphere.gif|thumb|right|300px|Visual of a rotating system.]]
In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of a rotating system.

==The Main Idea==
The position of a rotating system can be predicted by predicting the angle over which the object will rotate though out time. Basically, the key to finding out how much a rotating object has moved (over a specific time interval) is the angle through which it moves.

===A Mathematical Model===

Given that the system in question is indeed rotating, the update form of [[The Angular Momentum Principle]] is always applied about the the center of mass in our calculations.

The update form of the Angular Momentum Principle is as follows: <math>\vec{L}_{rot,f}=\vec{L}_{rot,i}+\vec{\tau}_{net}\Delta t</math> where <math>{L}</math> is rotational angular momentum and <math>\tau</math> is net torque from the surroundings.

In basic situations, the update form of the Angular Momentum Principle can further be simplified to account for [[The Moments of Inertia]], <math>I</math>, and the [[Angular Velocity]], <math>\omega</math> of the rotating system. This simplification of the update form of the Angular Momentum Principle yields the following mathematical equation: <math>I\omega _{f}=I\omega _{i}+RF\Delta t</math> where net torque, <math>\vec{\tau}_{net}</math> is simplified to the product of all the forces acting on the system and the locations to which these forces are applied, <math>RF</math>.

As mentioned before, the key to solving these types of problems is figuring out the angle, [math]\theta[/math], which the object rotates through. Given that the angle will always change at an instantaneous rate of [math]\omega=d\theta / dt[/math], the change in the angle [math]\theta[/math] is: [math]\Delta \theta=\omega_{avg} \Delta t[/math].

We will limit the complexity of this topic to situations where the angular speed [math]\omega[/math] changes at a constant rate [math]RF / I[/math]. Therefore, the average speed is said to be: [math]\omega_{avg}=\frac{\omega_{i} + \omega_{f} }{2}[/math]

===A Computational Model===
The position of a rotating system can be predicted using the following vPython code below. [https://trinket.io/python/22d3018e32 Try out the code here with different values!]. Take note that the default values in the code computationally calculate the answers to [[#Middling|this physics problem]].
[[File:Pythonscreenshot.png|center|550px|vPython code for solving rotational position.]]

==Examples==

===Simple===
A wheel of radius <math>R</math> and a moment of inertia <math>I</math> is mounted on a low-friction axle. A string is wrapped around the edge, and you pull on it with a force <math>F</math>, At a certain time the angular speed is <math>\omega_{i}</math>.

'''(a)''' After a time interval <math>\Delta t</math>, what is the angular speed <math>\omega_{f}</math>?
[[File:Simplea.jpg|400px|center|]]

'''(b)''' How far did your hand move during this time interval?
[[File:Easbi.jpg|400px|center|]]

[[File:Easbii.jpg|400px|center|]]
===Middling===
A uniform-density wheel of mass 6 kg and radius 0.3 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15 N for 0.6 s.

'''(a)''' What is the final angular speed?
[[File:Mida.jpg|400px|center|]]
'''(b)''' What is the average angular speed?
[[File:Midb.jpg|400px|center|]]
'''(c)''' Through how big an angle did the wheel turn?
[[File:Midc.jpg|400px|center|]]
'''(d)''' How much string came off the wheel?
[[File:Midd.jpg|400px|center|]]

==Connectedness==

===Industrial Application===
[[File:World_of_Color_overview.jpg|thumb|left|200px|Mickey's Fun Wheel.]]
[[File:Stlouisflags.jpg|thumb|right|200px|Colossus at Six Flags]]
In the theme and amusement park industry (e.g. Six Flags and Disney World), the aforementioned method of predicting the position of a rotating system can be applied to determine how far a certain rider has moved on either Mickey's Fun Wheel or Colossus. This prediction of a rider's position after a certain amount of time could be applied by economists to determine the ideal speed ''and'' time interval to run their respective ferris wheels to yield an optimal economic profit with respect to the cost of admission tickets.

===Scientific Application===
[[File:fig3-11.jpg|150px|thumb|right|Magnetic field produced by current]]
[[File:29_22_Magnetic_dipole_moment.JPG|150px|thumb|left|Orbiting electron]]
Predicting the position of a rotating system can also pioneer revelations in scientific research fields (esp. biochemistry and chemistry). Given that the position of an electron in relation to the nucleus of a hydrogen atom can be predicted based upon the angular momentum of the electron, this technique can be applied to determining the magnetism exhibited by the electron with respect to some defined axis. Therefore, the relationship between the position of an electron at a certain time (at some distance from a defined axis) could be related to the electric current produced by a magnetic field at that same time.

==History==

The key mathematical equation to predicting the position of a rotating system, the update form of the Angular Momentum Principle, has historical roots in the Laws of Motion of [[Sir Isaac Newton]]. The conservation of angular momentum was further described and put into terms by [[Johannes Kepler]].

== See also ==
[[The Angular Momentum Principle]]

[[The Moments of Inertia]]

[[Angular Velocity]]

[[Systems with Zero Torque]]

[[Systems with Nonzero Torque]]

===Further reading===
Judd, Brian R. ''Angular Momentum Theory for Diatomic Molecules''. Academic Press, 1975. Print.

===External links===
[https://www.youtube.com/watch?v=0k276y9kuQQ Angular Momentum - Science Theater Video ]
[http://chaos.utexas.edu/wp-uploads/2012/03/Lecture_24_post.pdf A Guide to the Angular Momentum Principle]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. ''Matter & Interactions''. Hoboken, NJ: Wiley, 2015. 443-45. Print.

[http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_3.html Angular Momentum of an Electron in an H Atom]

[[Category:Momentum]]

Predicting the Position of a Rotating System

2015-12-05T22:33:54Z

Awhitacre7:

[[File:Rotating_Sphere.gif|thumb|right|300px|Visual of a rotating system.]]
In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of a rotating system.

==The Main Idea==
The position of a rotating system can be predicted by predicting the angle over which the object will rotate though out time. Basically, the key to finding out how much a rotating object has moved (over a specific time interval) is the angle through which it moves.

===A Mathematical Model===

Given that the system in question is indeed rotating, the update form of [[The Angular Momentum Principle]] is always applied about the the center of mass in our calculations.

The update form of the Angular Momentum Principle is as follows: <math>\vec{L}_{rot,f}=\vec{L}_{rot,i}+\vec{\tau}_{net}\Delta t</math> where <math>{L}</math> is rotational angular momentum and <math>\tau</math> is net torque from the surroundings.

In basic situations, the update form of the Angular Momentum Principle can further be simplified to account for [[The Moments of Inertia]], <math>I</math>, and the [[Angular Velocity]], <math>\omega</math> of the rotating system. This simplification of the update form of the Angular Momentum Principle yields the following mathematical equation: <math>I\omega _{f}=I\omega _{i}+RF\Delta t</math> where net torque, <math>\vec{\tau}_{net}</math> is simplified to the product of all the forces acting on the system and the locations to which these forces are applied, <math>RF</math>.

As mentioned before, the key to solving these types of problems is figuring out the angle, [math]\theta[/math], which the object rotates through. Given that the angle will always change at an instantaneous rate of [math]\omega=d\theta / dt[/math], the change in the angle [math]\theta[/math] is: [math]\Delta \theta=\omega_{avg} \Delta t[/math].

We will limit the complexity of this topic to situations where the angular speed [math]\omega[/math] changes at a constant rate [math]RF / I[/math]. Therefore, the average speed is said to be: [math]\omega_{avg}=\frac{\omega_{i} + \omega_{f} }{2}[/math]

===A Computational Model===
The position of a rotating system can be predicted using the following vPython code below. [https://trinket.io/python/22d3018e32 Try out the code here with different values!]. Take note that the default values in the code computationally calculate the answers to [[#Middling|this physics problem]].
[[File:Pythonscreenshot.png|center|550px|vPython code for solving rotational position.]]

==Examples==

===Simple===
A wheel of radius <math>R</math> and a moment of inertia <math>I</math> is mounted on a low-friction axle. A string is wrapped around the edge, and you pull on it with a force <math>F</math>, At a certain time the angular speed is <math>\omega_{i}</math>.

'''(a)''' After a time interval <math>\Delta t</math>, what is the angular speed <math>\omega_{f}</math>?
[[File:Simplea.jpg|400px|center|]]

'''(b)''' How far did your hand move during this time interval?
[[File:Easbi.jpg|400px|center|]]

[[File:Easbii.jpg|400px|center|]]
===Middling===
A uniform-density wheel of mass 6 kg and radius 0.3 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15 N for 0.6 s.

'''(a)''' What is the final angular speed?
[[File:Mida.jpg|400px|center|]]
'''(b)''' What is the average angular speed?
[[File:Midb.jpg|400px|center|]]
'''(c)''' Through how big an angle did the wheel turn?
[[File:Midc.jpg|400px|center|]]
'''(d)''' How much string came off the wheel?
[[File:Midd.jpg|400px|center|]]

==Connectedness==

===Industrial Application===
[[File:World_of_Color_overview.jpg|thumb|left|200px|Mickey's Fun Wheel.]]
[[File:Stlouisflags.jpg|thumb|right|200px|Colossus at Six Flags]]
In the theme and amusement park industry (e.g. Six Flags and Disney World), the aforementioned method of predicting the position of a rotating system can be applied to determine how far a certain rider has moved on either Mickey's Fun Wheel or Colossus. This prediction of a rider's position after a certain amount of time could be applied by economists to determine the ideal speed ''and'' time interval to run their respective ferris wheels to yield an optimal economic profit with respect to the cost of admission tickets.

===Scientific Application===
[[File:fig3-11.jpg|150px|thumb|right|Magnetic field produced by current]]
[[File:29_22_Magnetic_dipole_moment.JPG|150px|thumb|left|Orbiting electron]]
Predicting the position of a rotating system can also pioneer revelations in scientific research fields (esp. biochemistry and chemistry). Given that the position of an electron in relation to the nucleus of a hydrogen atom can be predicted based upon the angular momentum of the electron, this technique can be applied to determining the magnetism exhibited by the electron with respect to some defined axis. Therefore, the relationship between the position of an electron at a certain time (at some distance from a defined axis) could be related to the electric current produced by a magnetic field at that same time.

==History==

The key mathematical equation to predicting the position of a rotating system, the update form of the Angular Momentum Principle, has historical roots in the Laws of Motion of [[Sir Isaac Newton]]. The conservation of angular momentum was further described and put into terms by [[Johannes Kepler]].

== See also ==
[[The Angular Momentum Principle]]

[[The Moments of Inertia]]

[[Angular Velocity]]

[[Systems with Zero Torque]]

[[Systems with Nonzero Torque]]

===Further reading===
Judd, Brian R. ''Angular Momentum Theory for Diatomic Molecules''. Academic Press, 1975. Print.

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. ''Matter & Interactions''. Hoboken, NJ: Wiley, 2015. 443-45. Print.

[http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_3.html Angular Momentum of an Electron in an H Atom]

[[Category:Momentum]]

Predicting the Position of a Rotating System

2015-12-05T22:33:19Z

Awhitacre7:

[[File:Rotating_Sphere.gif|thumb|right|300px|Visual of a rotating system.]]
In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of the system.

==The Main Idea==
The position of a rotating system can be predicted by predicting the angle over which the object will rotate though out time. Basically, the key to finding out how much a rotating object has moved (over a specific time interval) is the angle through which it moves.

===A Mathematical Model===

Given that the system in question is indeed rotating, the update form of [[The Angular Momentum Principle]] is always applied about the the center of mass in our calculations.

The update form of the Angular Momentum Principle is as follows: <math>\vec{L}_{rot,f}=\vec{L}_{rot,i}+\vec{\tau}_{net}\Delta t</math> where <math>{L}</math> is rotational angular momentum and <math>\tau</math> is net torque from the surroundings.

In basic situations, the update form of the Angular Momentum Principle can further be simplified to account for [[The Moments of Inertia]], <math>I</math>, and the [[Angular Velocity]], <math>\omega</math> of the rotating system. This simplification of the update form of the Angular Momentum Principle yields the following mathematical equation: <math>I\omega _{f}=I\omega _{i}+RF\Delta t</math> where net torque, <math>\vec{\tau}_{net}</math> is simplified to the product of all the forces acting on the system and the locations to which these forces are applied, <math>RF</math>.

As mentioned before, the key to solving these types of problems is figuring out the angle, [math]\theta[/math], which the object rotates through. Given that the angle will always change at an instantaneous rate of [math]\omega=d\theta / dt[/math], the change in the angle [math]\theta[/math] is: [math]\Delta \theta=\omega_{avg} \Delta t[/math].

We will limit the complexity of this topic to situations where the angular speed [math]\omega[/math] changes at a constant rate [math]RF / I[/math]. Therefore, the average speed is said to be: [math]\omega_{avg}=\frac{\omega_{i} + \omega_{f} }{2}[/math]

===A Computational Model===
The position of a rotating system can be predicted using the following vPython code below. [https://trinket.io/python/22d3018e32 Try out the code here with different values!]. Take note that the default values in the code computationally calculate the answers to [[#Middling|this physics problem]].
[[File:Pythonscreenshot.png|center|550px|vPython code for solving rotational position.]]

==Examples==

===Simple===
A wheel of radius <math>R</math> and a moment of inertia <math>I</math> is mounted on a low-friction axle. A string is wrapped around the edge, and you pull on it with a force <math>F</math>, At a certain time the angular speed is <math>\omega_{i}</math>.

'''(a)''' After a time interval <math>\Delta t</math>, what is the angular speed <math>\omega_{f}</math>?
[[File:Simplea.jpg|400px|center|]]

'''(b)''' How far did your hand move during this time interval?
[[File:Easbi.jpg|400px|center|]]

[[File:Easbii.jpg|400px|center|]]
===Middling===
A uniform-density wheel of mass 6 kg and radius 0.3 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15 N for 0.6 s.

'''(a)''' What is the final angular speed?
[[File:Mida.jpg|400px|center|]]
'''(b)''' What is the average angular speed?
[[File:Midb.jpg|400px|center|]]
'''(c)''' Through how big an angle did the wheel turn?
[[File:Midc.jpg|400px|center|]]
'''(d)''' How much string came off the wheel?
[[File:Midd.jpg|400px|center|]]

==Connectedness==

===Industrial Application===
[[File:World_of_Color_overview.jpg|thumb|left|200px|Mickey's Fun Wheel.]]
[[File:Stlouisflags.jpg|thumb|right|200px|Colossus at Six Flags]]
In the theme and amusement park industry (e.g. Six Flags and Disney World), the aforementioned method of predicting the position of a rotating system can be applied to determine how far a certain rider has moved on either Mickey's Fun Wheel or Colossus. This prediction of a rider's position after a certain amount of time could be applied by economists to determine the ideal speed ''and'' time interval to run their respective ferris wheels to yield an optimal economic profit with respect to the cost of admission tickets.

===Scientific Application===
[[File:fig3-11.jpg|150px|thumb|right|Magnetic field produced by current]]
[[File:29_22_Magnetic_dipole_moment.JPG|150px|thumb|left|Orbiting electron]]
Predicting the position of a rotating system can also pioneer revelations in scientific research fields (esp. biochemistry and chemistry). Given that the position of an electron in relation to the nucleus of a hydrogen atom can be predicted based upon the angular momentum of the electron, this technique can be applied to determining the magnetism exhibited by the electron with respect to some defined axis. Therefore, the relationship between the position of an electron at a certain time (at some distance from a defined axis) could be related to the electric current produced by a magnetic field at that same time.

==History==

The key mathematical equation to predicting the position of a rotating system, the update form of the Angular Momentum Principle, has historical roots in the Laws of Motion of [[Sir Isaac Newton]]. The conservation of angular momentum was further described and put into terms by [[Johannes Kepler]].

== See also ==
[[The Angular Momentum Principle]]

[[The Moments of Inertia]]

[[Angular Velocity]]

[[Systems with Zero Torque]]

[[Systems with Nonzero Torque]]

===Further reading===
Judd, Brian R. ''Angular Momentum Theory for Diatomic Molecules''. Academic Press, 1975. Print.

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. ''Matter & Interactions''. Hoboken, NJ: Wiley, 2015. 443-45. Print.

[http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_3.html Angular Momentum of an Electron in an H Atom]

[[Category:Momentum]]

File:Pythonscreenshot.png

2015-12-05T22:27:02Z

Awhitacre7:

Predicting the Position of a Rotating System

2015-12-05T22:25:26Z

Awhitacre7:

''(claimed by Anna Marie Whitacre, awhitacre7)''
[[File:Rotating_Sphere.gif|thumb|right|300px|Visual of a rotating system.]]
In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of the system.

==The Main Idea==
The position of a rotating system can be predicted by predicting the angle over which the object will rotate though out time. Basically, the key to finding out how much a rotating object has moved (over a specific time interval) is the angle through which it moves.

===A Mathematical Model===

Given that the system in question is indeed rotating, the update form of [[The Angular Momentum Principle]] is always applied about the the center of mass in our calculations.

The update form of the Angular Momentum Principle is as follows: <math>\vec{L}_{rot,f}=\vec{L}_{rot,i}+\vec{\tau}_{net}\Delta t</math> where <math>{L}</math> is rotational angular momentum and <math>\tau</math> is net torque from the surroundings.

In basic situations, the update form of the Angular Momentum Principle can further be simplified to account for [[The Moments of Inertia]], <math>I</math>, and the [[Angular Velocity]], <math>\omega</math> of the rotating system. This simplification of the update form of the Angular Momentum Principle yields the following mathematical equation: <math>I\omega _{f}=I\omega _{i}+RF\Delta t</math> where net torque, <math>\vec{\tau}_{net}</math> is simplified to the product of all the forces acting on the system and the locations to which these forces are applied, <math>RF</math>.

As mentioned before, the key to solving these types of problems is figuring out the angle, [math]\theta[/math], which the object rotates through. Given that the angle will always change at an instantaneous rate of [math]\omega=d\theta / dt[/math], the change in the angle [math]\theta[/math] is: [math]\Delta \theta=\omega_{avg} \Delta t[/math].

We will limit the complexity of this topic to situations where the angular speed [math]\omega[/math] changes at a constant rate [math]RF / I[/math]. Therefore, the average speed is said to be: [math]\omega_{avg}=\frac{\omega_{i} + \omega_{f} }{2}[/math]

===A Computational Model===

The position of a rotating system can be predicted using the following vPython code [https://trinket.io/python/22d3018e32 Try out the code here with different values!]. The default values in the code computationally calculate the answers to [[#Middling|this physics problem]].

==Examples==

===Simple===
A wheel of radius <math>R</math> and a moment of inertia <math>I</math> is mounted on a low-friction axle. A string is wrapped around the edge, and you pull on it with a force <math>F</math>, At a certain time the angular speed is <math>\omega_{i}</math>.

'''(a)''' After a time interval <math>\Delta t</math>, what is the angular speed <math>\omega_{f}</math>?
[[File:Simplea.jpg|400px|center|]]

'''(b)''' How far did your hand move during this time interval?
[[File:Easbi.jpg|400px|center|]]

[[File:Easbii.jpg|400px|center|]]
===Middling===
A uniform-density wheel of mass 6 kg and radius 0.3 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15 N for 0.6 s.

'''(a)''' What is the final angular speed?
[[File:Mida.jpg|400px|center|]]
'''(b)''' What is the average angular speed?
[[File:Midb.jpg|400px|center|]]
'''(c)''' Through how big an angle did the wheel turn?
[[File:Midc.jpg|400px|center|]]
'''(d)''' How much string came off the wheel?
[[File:Midd.jpg|400px|center|]]

==Connectedness==

===Industrial Application===
[[File:World_of_Color_overview.jpg|thumb|left|200px|Mickey's Fun Wheel.]]
[[File:Stlouisflags.jpg|thumb|right|200px|Colossus at Six Flags]]
In the theme and amusement park industry (e.g. Six Flags and Disney World), the aforementioned method of predicting the position of a rotating system can be applied to determine how far a certain rider has moved on either Mickey's Fun Wheel or Colossus. This prediction of a rider's position after a certain amount of time could be applied by economists to determine the ideal speed ''and'' time interval to run their respective ferris wheels to yield an optimal economic profit with respect to the cost of admission tickets.

===Scientific Application===
[[File:fig3-11.jpg|150px|thumb|right|Magnetic field produced by current]]
[[File:29_22_Magnetic_dipole_moment.JPG|150px|thumb|left|Orbiting electron]]
Predicting the position of a rotating system can also pioneer revelations in scientific research fields (esp. biochemistry and chemistry). Given that the position of an electron in relation to the nucleus of a hydrogen atom can be predicted based upon the angular momentum of the electron, this technique can be applied to determining the magnetism exhibited by the electron with respect to some defined axis. Therefore, the relationship between the position of an electron at a certain time (at some distance from a defined axis) could be related to the electric current produced by a magnetic field at that same time.

==History==

The key mathematical equation to predicting the position of a rotating system, the update form of the Angular Momentum Principle, has historical roots in the Laws of Motion of [[Sir Isaac Newton]]. The conservation of angular momentum was further described and put into terms by [[Johannes Kepler]].

== See also ==
[[The Angular Momentum Principle]]

[[The Moments of Inertia]]

[[Angular Velocity]]

[[Systems with Zero Torque]]

[[Systems with Nonzero Torque]]

===Further reading===
Judd, Brian R. ''Angular Momentum Theory for Diatomic Molecules''. Academic Press, 1975. Print.

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. ''Matter & Interactions''. Hoboken, NJ: Wiley, 2015. 443-45. Print.

[http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_3.html Angular Momentum of an Electron in an H Atom]

[[Category:Momentum]]

Predicting the Position of a Rotating System

2015-12-05T22:20:01Z

Awhitacre7:

''(claimed by Anna Marie Whitacre, awhitacre7)''
[[File:Rotating_Sphere.gif|thumb|right|300px|Visual of a rotating system.]]
In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of the system.

==The Main Idea==
The position of a rotating system can be predicted by predicting the angle over which the object will rotate though out time. Basically, the key to finding out how much a rotating object has moved (over a specific time interval) is the angle through which it moves.

===A Mathematical Model===

Given that the system in question is indeed rotating, the update form of [[The Angular Momentum Principle]] is always applied about the the center of mass in our calculations.

The update form of the Angular Momentum Principle is as follows: <math>\vec{L}_{rot,f}=\vec{L}_{rot,i}+\vec{\tau}_{net}\Delta t</math> where <math>{L}</math> is rotational angular momentum and <math>\tau</math> is net torque from the surroundings.

In basic situations, the update form of the Angular Momentum Principle can further be simplified to account for [[The Moments of Inertia]], <math>I</math>, and the [[Angular Velocity]], <math>\omega</math> of the rotating system. This simplification of the update form of the Angular Momentum Principle yields the following mathematical equation: <math>I\omega _{f}=I\omega _{i}+RF\Delta t</math> where net torque, <math>\vec{\tau}_{net}</math> is simplified to the product of all the forces acting on the system and the locations to which these forces are applied, <math>RF</math>.

As mentioned before, the key to solving these types of problems is figuring out the angle, [math]\theta[/math], which the object rotates through. Given that the angle will always change at an instantaneous rate of [math]\omega=d\theta / dt[/math], the change in the angle [math]\theta[/math] is: [math]\Delta \theta=\omega_{avg} \Delta t[/math].

We will limit the complexity of this topic to situations where the angular speed [math]\omega[/math] changes at a constant rate [math]RF / I[/math]. Therefore, the average speed is said to be: [math]\omega_{avg}=\frac{\omega_{i} + \omega_{f} }{2}[/math]

===A Computational Model===

The position of a rotating system can be predicted using the following vPython code [https://trinket.io/python/22d3018e32]. The default values in the code computationally calculate the answers to [[#Middling|this physics problem]].

==Examples==

===Simple===
A wheel of radius <math>R</math> and a moment of inertia <math>I</math> is mounted on a low-friction axle. A string is wrapped around the edge, and you pull on it with a force <math>F</math>, At a certain time the angular speed is <math>\omega_{i}</math>.

'''(a)''' After a time interval <math>\Delta t</math>, what is the angular speed <math>\omega_{f}</math>?
[[File:Simplea.jpg|400px|center|]]

'''(b)''' How far did your hand move during this time interval?
[[File:Easbi.jpg|400px|center|]]

[[File:Easbii.jpg|400px|center|]]
===Middling===
A uniform-density wheel of mass 6 kg and radius 0.3 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15 N for 0.6 s.

'''(a)''' What is the final angular speed?
[[File:Mida.jpg|400px|center|]]
'''(b)''' What is the average angular speed?
[[File:Midb.jpg|400px|center|]]
'''(c)''' Through how big an angle did the wheel turn?
[[File:Midc.jpg|400px|center|]]
'''(d)''' How much string came off the wheel?
[[File:Midd.jpg|400px|center|]]

==Connectedness==

===Industrial Application===
[[File:World_of_Color_overview.jpg|thumb|left|200px|Mickey's Fun Wheel.]]
[[File:Stlouisflags.jpg|thumb|right|200px|Colossus at Six Flags]]
In the theme and amusement park industry (e.g. Six Flags and Disney World), the aforementioned method of predicting the position of a rotating system can be applied to determine how far a certain rider has moved on either Mickey's Fun Wheel or Colossus. This prediction of a rider's position after a certain amount of time could be applied by economists to determine the ideal speed ''and'' time interval to run their respective ferris wheels to yield an optimal economic profit with respect to the cost of admission tickets.

===Scientific Application===
[[File:fig3-11.jpg|150px|thumb|right|Magnetic field produced by current]]
[[File:29_22_Magnetic_dipole_moment.JPG|150px|thumb|left|Orbiting electron]]
Predicting the position of a rotating system can also pioneer revelations in scientific research fields (esp. biochemistry and chemistry). Given that the position of an electron in relation to the nucleus of a hydrogen atom can be predicted based upon the angular momentum of the electron, this technique can be applied to determining the magnetism exhibited by the electron with respect to some defined axis. Therefore, the relationship between the position of an electron at a certain time (at some distance from a defined axis) could be related to the electric current produced by a magnetic field at that same time.

==History==

The key mathematical equation to predicting the position of a rotating system, the update form of the Angular Momentum Principle, has historical roots in the Laws of Motion of [[Sir Isaac Newton]]. The conservation of angular momentum was further described and put into terms by [[Johannes Kepler]].

== See also ==
[[The Angular Momentum Principle]]

[[The Moments of Inertia]]

[[Angular Velocity]]

[[Systems with Zero Torque]]

[[Systems with Nonzero Torque]]

===Further reading===
Judd, Brian R. ''Angular Momentum Theory for Diatomic Molecules''. Academic Press, 1975. Print.

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. ''Matter & Interactions''. Hoboken, NJ: Wiley, 2015. 443-45. Print.

[http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_3.html Angular Momentum of an Electron in an H Atom]

[[Category:Momentum]]

Predicting the Position of a Rotating System

2015-12-05T21:49:45Z

Awhitacre7: /* Middling */

''(claimed by Anna Marie Whitacre, awhitacre7)''
[[File:Rotating_Sphere.gif|thumb|right|300px|Visual of a rotating system.]]
In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of the system.

==The Main Idea==
The position of a rotating system can be predicted by predicting the angle over which the object will rotate though out time. Basically, the key to finding out how much a rotating object has moved (over a specific time interval) is the angle through which it moves.

===A Mathematical Model===

Given that the system in question is indeed rotating, the update form of [[The Angular Momentum Principle]] is always applied about the the center of mass in our calculations.

The update form of the Angular Momentum Principle is as follows: <math>\vec{L}_{rot,f}=\vec{L}_{rot,i}+\vec{\tau}_{net}\Delta t</math> where <math>{L}</math> is rotational angular momentum and <math>\tau</math> is net torque from the surroundings.

In basic situations, the update form of the Angular Momentum Principle can further be simplified to account for [[The Moments of Inertia]], <math>I</math>, and the [[Angular Velocity]], <math>\omega</math> of the rotating system. This simplification of the update form of the Angular Momentum Principle yields the following mathematical equation: <math>I\omega _{f}=I\omega _{i}+RF\Delta t</math> where net torque, <math>\vec{\tau}_{net}</math> is simplified to the product of all the forces acting on the system and the locations to which these forces are applied, <math>RF</math>.

As mentioned before, the key to solving these types of problems is figuring out the angle, [math]\theta[/math], which the object rotates through. Given that the angle will always change at an instantaneous rate of [math]\omega=d\theta / dt[/math], the change in the angle [math]\theta[/math] is: [math]\Delta \theta=\omega_{avg} \Delta t[/math].

We will limit the complexity of this topic to situations where the angular speed [math]\omega[/math] changes at a constant rate [math]RF / I[/math]. Therefore, the average speed is said to be: [math]\omega_{avg}=\frac{\omega_{i} + \omega_{f} }{2}[/math]

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
A wheel of radius <math>R</math> and a moment of inertia <math>I</math> is mounted on a low-friction axle. A string is wrapped around the edge, and you pull on it with a force <math>F</math>, At a certain time the angular speed is <math>\omega_{i}</math>.

'''(a)''' After a time interval <math>\Delta t</math>, what is the angular speed <math>\omega_{f}</math>?
[[File:Simplea.jpg|400px|center|]]

'''(b)''' How far did your hand move during this time interval?
[[File:Easbi.jpg|400px|center|]]

[[File:Easbii.jpg|400px|center|]]
===Middling===
A uniform-density wheel of mass 6 kg and radius 0.3 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15 N for 0.6 s.

'''(a)''' What is the final angular speed?
[[File:Mida.jpg|400px|center|]]
'''(b)''' What is the average angular speed?
[[File:Midb.jpg|400px|center|]]
'''(c)''' Through how big an angle did the wheel turn?
[[File:Midc.jpg|400px|center|]]
'''(d)''' How much string came off the wheel?
[[File:Midd.jpg|400px|center|]]

==Connectedness==

===Industrial Application===
[[File:World_of_Color_overview.jpg|thumb|left|200px|Mickey's Fun Wheel.]]
[[File:Stlouisflags.jpg|thumb|right|200px|Colossus at Six Flags]]
In the theme and amusement park industry (e.g. Six Flags and Disney World), the aforementioned method of predicting the position of a rotating system can be applied to determine how far a certain rider has moved on either Mickey's Fun Wheel or Colossus. This prediction of a rider's position after a certain amount of time could be applied by economists to determine the ideal speed ''and'' time interval to run their respective ferris wheels to yield an optimal economic profit with respect to the cost of admission tickets.

===Scientific Application===
[[File:fig3-11.jpg|150px|thumb|right|Magnetic field produced by current]]
[[File:29_22_Magnetic_dipole_moment.JPG|150px|thumb|left|Orbiting electron]]
Predicting the position of a rotating system can also pioneer revelations in scientific research fields (esp. biochemistry and chemistry). Given that the position of an electron in relation to the nucleus of a hydrogen atom can be predicted based upon the angular momentum of the electron, this technique can be applied to determining the magnetism exhibited by the electron with respect to some defined axis. Therefore, the relationship between the position of an electron at a certain time (at some distance from a defined axis) could be related to the electric current produced by a magnetic field at that same time.

==History==

The key mathematical equation to predicting the position of a rotating system, the update form of the Angular Momentum Principle, has historical roots in the Laws of Motion of [[Sir Isaac Newton]]. The conservation of angular momentum was further described and put into terms by [[Johannes Kepler]].

== See also ==
[[The Angular Momentum Principle]]

[[The Moments of Inertia]]

[[Angular Velocity]]

[[Systems with Zero Torque]]

[[Systems with Nonzero Torque]]

===Further reading===
Judd, Brian R. ''Angular Momentum Theory for Diatomic Molecules''. Academic Press, 1975. Print.

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. ''Matter & Interactions''. Hoboken, NJ: Wiley, 2015. 443-45. Print.

[http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_3.html Angular Momentum of an Electron in an H Atom]

[[Category:Momentum]]

File:Midd.jpg

2015-12-05T21:48:20Z

Awhitacre7:

File:Midc.jpg

2015-12-05T21:47:44Z

Awhitacre7:

File:Midb.jpg

2015-12-05T21:47:06Z

Awhitacre7:

File:Mida.jpg

2015-12-05T21:46:41Z

Awhitacre7:

Predicting the Position of a Rotating System

2015-12-05T21:45:36Z

Awhitacre7:

''(claimed by Anna Marie Whitacre, awhitacre7)''
[[File:Rotating_Sphere.gif|thumb|right|300px|Visual of a rotating system.]]
In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of the system.

==The Main Idea==
The position of a rotating system can be predicted by predicting the angle over which the object will rotate though out time. Basically, the key to finding out how much a rotating object has moved (over a specific time interval) is the angle through which it moves.

===A Mathematical Model===

Given that the system in question is indeed rotating, the update form of [[The Angular Momentum Principle]] is always applied about the the center of mass in our calculations.

The update form of the Angular Momentum Principle is as follows: <math>\vec{L}_{rot,f}=\vec{L}_{rot,i}+\vec{\tau}_{net}\Delta t</math> where <math>{L}</math> is rotational angular momentum and <math>\tau</math> is net torque from the surroundings.

In basic situations, the update form of the Angular Momentum Principle can further be simplified to account for [[The Moments of Inertia]], <math>I</math>, and the [[Angular Velocity]], <math>\omega</math> of the rotating system. This simplification of the update form of the Angular Momentum Principle yields the following mathematical equation: <math>I\omega _{f}=I\omega _{i}+RF\Delta t</math> where net torque, <math>\vec{\tau}_{net}</math> is simplified to the product of all the forces acting on the system and the locations to which these forces are applied, <math>RF</math>.

As mentioned before, the key to solving these types of problems is figuring out the angle, [math]\theta[/math], which the object rotates through. Given that the angle will always change at an instantaneous rate of [math]\omega=d\theta / dt[/math], the change in the angle [math]\theta[/math] is: [math]\Delta \theta=\omega_{avg} \Delta t[/math].

We will limit the complexity of this topic to situations where the angular speed [math]\omega[/math] changes at a constant rate [math]RF / I[/math]. Therefore, the average speed is said to be: [math]\omega_{avg}=\frac{\omega_{i} + \omega_{f} }{2}[/math]

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
A wheel of radius <math>R</math> and a moment of inertia <math>I</math> is mounted on a low-friction axle. A string is wrapped around the edge, and you pull on it with a force <math>F</math>, At a certain time the angular speed is <math>\omega_{i}</math>.

'''(a)''' After a time interval <math>\Delta t</math>, what is the angular speed <math>\omega_{f}</math>?
[[File:Simplea.jpg|400px|center|]]

'''(b)''' How far did your hand move during this time interval?
[[File:Easbi.jpg|400px|center|]]

[[File:Easbii.jpg|400px|center|]]
===Middling===
A uniform-density wheel of mass 6 kg and radius 0.3 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15 N for 0.6 s.

'''(a)''' What is the final angular speed?
[[File:Mida.jpg|400px|center|]]
'''(b)''' What is the average angular speed?

'''(c)''' Through how big an angle did the wheel turn?

'''(d)''' How much string came off the wheel?

==Connectedness==

===Industrial Application===
[[File:World_of_Color_overview.jpg|thumb|left|200px|Mickey's Fun Wheel.]]
[[File:Stlouisflags.jpg|thumb|right|200px|Colossus at Six Flags]]
In the theme and amusement park industry (e.g. Six Flags and Disney World), the aforementioned method of predicting the position of a rotating system can be applied to determine how far a certain rider has moved on either Mickey's Fun Wheel or Colossus. This prediction of a rider's position after a certain amount of time could be applied by economists to determine the ideal speed ''and'' time interval to run their respective ferris wheels to yield an optimal economic profit with respect to the cost of admission tickets.

===Scientific Application===
[[File:fig3-11.jpg|150px|thumb|right|Magnetic field produced by current]]
[[File:29_22_Magnetic_dipole_moment.JPG|150px|thumb|left|Orbiting electron]]
Predicting the position of a rotating system can also pioneer revelations in scientific research fields (esp. biochemistry and chemistry). Given that the position of an electron in relation to the nucleus of a hydrogen atom can be predicted based upon the angular momentum of the electron, this technique can be applied to determining the magnetism exhibited by the electron with respect to some defined axis. Therefore, the relationship between the position of an electron at a certain time (at some distance from a defined axis) could be related to the electric current produced by a magnetic field at that same time.

==History==

The key mathematical equation to predicting the position of a rotating system, the update form of the Angular Momentum Principle, has historical roots in the Laws of Motion of [[Sir Isaac Newton]]. The conservation of angular momentum was further described and put into terms by [[Johannes Kepler]].

== See also ==
[[The Angular Momentum Principle]]

[[The Moments of Inertia]]

[[Angular Velocity]]

[[Systems with Zero Torque]]

[[Systems with Nonzero Torque]]

===Further reading===
Judd, Brian R. ''Angular Momentum Theory for Diatomic Molecules''. Academic Press, 1975. Print.

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. ''Matter & Interactions''. Hoboken, NJ: Wiley, 2015. 443-45. Print.

[http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_3.html Angular Momentum of an Electron in an H Atom]

[[Category:Momentum]]

File:Easbii.jpg

2015-12-05T21:41:23Z

Awhitacre7:

File:Easbi.jpg

2015-12-05T21:40:56Z

Awhitacre7:

File:Simpleb.jpg

2015-12-05T21:05:02Z

Awhitacre7:

File:Simplea.jpg

2015-12-05T21:00:00Z

Awhitacre7:

File:Rotation of wheel.png

2015-12-05T20:25:24Z

Awhitacre7:

Predicting the Position of a Rotating System

2015-12-05T20:19:20Z

Awhitacre7: /* Examples */

''(claimed by Anna Marie Whitacre, awhitacre7)''
[[File:Rotating_Sphere.gif|thumb|right|300px|Visual of a rotating system.]]
In order to provide a cohesive and detailed model of the motion of a rotating object (including [[Systems with Zero Torque]] and [[Systems with Nonzero Torque]]) it is necessary to predict the position of the system.

==The Main Idea==
The position of a rotating system can be predicted by predicting the angle over which the object will rotate though out time. Basically, the key to finding out how much a rotating object has moved (over a specific time interval) is the angle through which it moves.

===A Mathematical Model===

Given that the system in question is indeed rotating, the update form of [[The Angular Momentum Principle]] is always applied about the the center of mass in our calculations.

The update form of the Angular Momentum Principle is as follows: <math>\vec{L}_{rot,f}=\vec{L}_{rot,i}+\vec{\tau}_{net}\Delta t</math> where <math>{L}</math> is rotational angular momentum and <math>\tau</math> is net torque from the surroundings.

In basic situations, the update form of the Angular Momentum Principle can further be simplified to account for [[The Moments of Inertia]], <math>I</math>, and the [[Angular Velocity]], <math>\omega</math> of the rotating system. This simplification of the update form of the Angular Momentum Principle yields the following mathematical equation: <math>I\omega _{f}=I\omega _{i}+RF\Delta t</math> where net torque, <math>\vec{\tau}_{net}</math> is simplified to the product of all the forces acting on the system and the locations to which these forces are applied, <math>RF</math>.

As mentioned before, the key to solving these types of problems is figuring out the angle, [math]\theta[/math], which the object rotates through. Given that the angle will always change at an instantaneous rate of [math]\omega=d\theta / dt[/math], the change in the angle [math]\theta[/math] is: [math]\Delta \theta=\omega_{avg} \Delta t[/math].

We will limit the complexity of this topic to situations where the angular speed [math]\omega[/math] changes at a constant rate [math]RF / I[/math]. Therefore, the average speed is said to be: [math]\omega_{avg}=\frac{\omega_{i} + \omega_{f} }{2}[/math]

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
A wheel of radius <math>R</math> and a moment of inertia <math>I</math> is mounted on a low-friction axle. A string is wrapped around the edge, and you pull on it with a force <math>F</math>, At a certain time the angular speed is <math>\omega_{i}</math>.

'''(a)''' After a time interval <math>\Delta t</math>, what is the angular speed <math>\omega_{f}</math>?

'''(b)''' How far did your hand move during this time interval?

===Middling===
A uniform-density wheel of mass 6 kg and radius 0.3 m rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15 N for 0.6 s.

'''(a)''' What is the final angular speed?

'''(b)''' What is the average angular speed?

'''(c)''' Through how big an angle did the wheel turn?

'''(d)''' How much string came off the wheel?

==Connectedness==

===Industrial Application===
[[File:World_of_Color_overview.jpg|thumb|left|200px|Mickey's Fun Wheel.]]
[[File:Stlouisflags.jpg|thumb|right|200px|Colossus at Six Flags]]
In the theme and amusement park industry (e.g. Six Flags and Disney World), the aforementioned method of predicting the position of a rotating system can be applied to determine how far a certain rider has moved on either Mickey's Fun Wheel or Colossus. This prediction of a rider's position after a certain amount of time could be applied by economists to determine the ideal speed ''and'' time interval to run their respective ferris wheels to yield an optimal economic profit with respect to the cost of admission tickets.

===Scientific Application===
[[File:fig3-11.jpg|150px|thumb|right|Magnetic field produced by current]]
[[File:29_22_Magnetic_dipole_moment.JPG|150px|thumb|left|Orbiting electron]]
Predicting the position of a rotating system can also pioneer revelations in scientific research fields (esp. biochemistry and chemistry). Given that the position of an electron in relation to the nucleus of a hydrogen atom can be predicted based upon the angular momentum of the electron, this technique can be applied to determining the magnetism exhibited by the electron with respect to some defined axis. Therefore, the relationship between the position of an electron at a certain time (at some distance from a defined axis) could be related to the electric current produced by a magnetic field at that same time.

==History==

The key mathematical equation to predicting the position of a rotating system, the update form of the Angular Momentum Principle, has historical roots in the Laws of Motion of [[Sir Isaac Newton]]. The conservation of angular momentum was further described and put into terms by [[Johannes Kepler]].

== See also ==
[[The Angular Momentum Principle]]

[[The Moments of Inertia]]

[[Angular Velocity]]

[[Systems with Zero Torque]]

[[Systems with Nonzero Torque]]

===Further reading===
Judd, Brian R. ''Angular Momentum Theory for Diatomic Molecules''. Academic Press, 1975. Print.

===External links===

Internet resources on this topic

==References==

Chabay, Ruth W., and Bruce A. Sherwood. ''Matter & Interactions''. Hoboken, NJ: Wiley, 2015. 443-45. Print.

[http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_3.html Angular Momentum of an Electron in an H Atom]

[[Category:Momentum]]