Physics Book - User contributions [en]

Lorentz Force

2017-11-29T05:09:05Z

Aschatz3: /* Connectedness */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Edited by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, or <math> q\vec{v} ⨯ \vec{B}= q\vec{E} </math>. The charge on both sides cancels out to give <math> \vec{v} ⨯ \vec{B}= \vec{E} </math>. Calculating
<math> q\vec{v} ⨯ \vec{B}</math> = <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way.

2. In today's evolving world, one area of particular interest is sustainable and renewable energy. Wind turbines and hydropower plants work by harnessing the kinetic energy of wind or water and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T05:07:00Z

Aschatz3: /* Connectedness */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Edited by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, or <math> q\vec{v} ⨯ \vec{B}= q\vec{E} </math>. The charge on both sides cancels out to give <math> \vec{v} ⨯ \vec{B}= \vec{E} </math>. Calculating
<math> q\vec{v} ⨯ \vec{B}</math> = <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T05:06:08Z

Aschatz3: /* Connectedness */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Edited by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, or <math> q\vec{v} ⨯ \vec{B}= q\vec{E} </math>. The charge on both sides cancels out to give <math> \vec{v} ⨯ \vec{B}= \vec{E} </math>. Calculating
<math> q\vec{v} ⨯ \vec{B}</math> = <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T05:05:34Z

Aschatz3: /* Connectedness */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Edited by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, or <math> q\vec{v} ⨯ \vec{B}= q\vec{E} </math>. The charge on both sides cancels out to give <math> \vec{v} ⨯ \vec{B}= \vec{E} </math>. Calculating
<math> q\vec{v} ⨯ \vec{B}</math> = <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T05:04:23Z

Aschatz3:

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Edited by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, or <math> q\vec{v} ⨯ \vec{B}= q\vec{E} </math>. The charge on both sides cancels out to give <math> \vec{v} ⨯ \vec{B}= \vec{E} </math>. Calculating
<math> q\vec{v} ⨯ \vec{B}</math> = <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T05:04:10Z

Aschatz3:

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017
'''Edited by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, or <math> q\vec{v} ⨯ \vec{B}= q\vec{E} </math>. The charge on both sides cancels out to give <math> \vec{v} ⨯ \vec{B}= \vec{E} </math>. Calculating
<math> q\vec{v} ⨯ \vec{B}</math> = <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:59:48Z

Aschatz3: /* Difficult */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, or <math> q\vec{v} ⨯ \vec{B}= q\vec{E} </math>. The charge on both sides cancels out to give <math> \vec{v} ⨯ \vec{B}= \vec{E} </math>. Calculating
<math> q\vec{v} ⨯ \vec{B}</math> = <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:59:24Z

Aschatz3: /* Difficult */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, or <math> q\vec{v} ⨯ \vec{B}= q\vec{E} </math>. The charge on both sides cancels out to give <math> \vec{v} ⨯ \vec{B}= \vec{E} </math>.
<math> q\vec{v} ⨯ \vec{B}</math> = <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:59:07Z

Aschatz3: /* Difficult */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, or <math> q\vec{v} ⨯ \vec{B}= q\vec{E} </math>. The charge on both sides cancels out to give <math> \vec{v} ⨯ \vec{B}= \vec{E} </math>. <math> q\vec{v} ⨯ \vec{B}</math> = <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:58:21Z

Aschatz3: /* Difficult */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, <math> q\vec{v} ⨯ \vec{B}= q\vec{E} </math>. The charge on both sides cancel out, to <math> \vec{v} ⨯ \vec{B}= \vec{E} </math>. <math> q\vec{v} ⨯ \vec{B}</math> = <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:57:20Z

Aschatz3: /* Difficult */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, <math> q\vec{v} ⨯ \vec{B}= q\vec{E} </math>). The charge on both sides cancel out, to<math> \vec{v} ⨯ \vec{B}= \vec{E} </math>). The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.
<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>)
<math> q\vec{v} ⨯ \vec{B}</math>)

<math> \vec{v} ⨯ \vec{B}= \vec{E} </math>)

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:55:22Z

Aschatz3: /* A Computational Model */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:54:44Z

Aschatz3: /* Intermediate */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N at an angle 30 degrees down from the +x axis. The electric force on the proton is 100 N at an angle 30 degrees up from the +z axis. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:53:49Z

Aschatz3: /* Simple */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''
[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:53:40Z

Aschatz3: /* Simple */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:53:32Z

Aschatz3: /* Intermediate */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln1.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:53:23Z

Aschatz3: /* Simple */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln2.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:53:04Z

Aschatz3: /* Intermediate */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:52:05Z

Aschatz3: /* Simple */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:49:51Z

Aschatz3: /* Examples */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Example Problems==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Intermediate===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:49:21Z

Aschatz3: /* A Computational Model */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to Magnetic and Electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.

==Examples==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Middling===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:47:56Z

Aschatz3: /* A Computational Model */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

Initially a negatively charged particle is traveling in the -z direction. There is a constant Electric field in the -x direction and a constant Magnetic field in the +y direction. The Magnetic force on the negatively charged particle is equal to q(vxB) <math> q\vec{v} ⨯ \vec{B}</math> or the charge of the particle times the cross product of the particle’s velocity and the Magnetic field it travels through. The Electric force on the particle is equal to qE <math> q\vec{E} </math>, or the charge of the particle times the Electric field that the particle travels through. Since the Magnetic Force on the particle is related to the particle’s velocity, the Magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to magnetic and Electric forces (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, thus changing the particle’s velocity.

==Examples==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Middling===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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:Lorentzdiagram.png

2017-11-29T04:38:08Z

Aschatz3: Aschatz3 uploaded a new version of "File:Lorentzdiagram.png"

Lorentz Force

2017-11-29T04:35:58Z

Aschatz3: /* A Computational Model */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a negatively charged particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

==Examples==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Middling===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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:Lorentzdiagram.png

2017-11-29T04:34:55Z

Aschatz3: Aschatz3 uploaded a new version of "File:Lorentzdiagram.png"

File:Lorentzdiagram.png

2017-11-29T04:33:17Z

Aschatz3: Aschatz3 uploaded a new version of "File:Lorentzdiagram.png"

Lorentz Force

2017-11-29T04:32:04Z

Aschatz3: /* A Computational Model */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a particle moving through a constant electric and magnetic field.

[[File:Lorentzdiagram.png]]

==Examples==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Middling===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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:Lorentzdiagram.png

2017-11-29T04:31:27Z

Aschatz3:

Lorentz Force

2017-11-29T04:30:12Z

Aschatz3: /* A Computational Model */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a particle moving through a constant electric and magnetic field.

==Examples==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Middling===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:29:09Z

Aschatz3: /* A Computational Model */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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===

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a particle moving through a constant electric and magnetic field.

==Examples==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Middling===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:28:55Z

Aschatz3: /* A Computational Model */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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]]
[[File:tower-linkedin.jpg]]

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a particle moving through a constant electric and magnetic field.

==Examples==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Middling===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:27:07Z

Aschatz3: /* A Computational Model */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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]]

[https://trinket.io/embed/glowscript/43e56e9c64 Here is a visualization] on VPython of a particle moving through a constant electric and magnetic field.

==Examples==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Middling===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:26:24Z

Aschatz3: /* A Computational Model */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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]]

["https://trinket.io/embed/glowscript/43e56e9c64" Here is a visualization] on VPython of a particle moving through a constant electric and magnetic field.

==Examples==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Middling===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:25:55Z

Aschatz3: /* A Computational Model */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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]]

["https://trinket.io/embed/glowscript/43e56e9c64" Here is a visualization] on VPython of a particle moving through a constant electric and magnetic field. Here is a preview:
[[File:Lorentzforcepythonsim.PNG]]

==Examples==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Middling===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-29T04:24:18Z

Aschatz3: /* A Computational Model */

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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]]

[<iframe src="https://trinket.io/embed/glowscript/43e56e9c64" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>Here is a visualization] on VPython of a particle moving through a constant electric and magnetic field. Here is a preview:
[[File:Lorentzforcepythonsim.PNG]]

==Examples==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Middling===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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

2017-11-18T21:17:35Z

Aschatz3:

Edited by Chris Mickas Fall 2016
Yiqiao Wu Spring 2017

'''Claimed by Adam Schatz Fall 2017'''

[[File:Headerlorentz.png|400px|thumb|right|Lorentz force diagram]]
==The Main Idea==
The Lorentz Force is a name for the sum of the magnetic and electric forces on a particle. The net force on some particles is often primarily determined by the electric and magnetic forces because other forces are negligible. In these cases, the Lorentz Force refers to the net force found by adding the magnetic and electric forces.
===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]]

[https://trinket.io/glowscript/680b501444 Here is a visualization] on VPython of a particle moving through a constant electric and magnetic field. Here is a preview:
[[File:Lorentzforcepythonsim.PNG]]

==Examples==

===Simple===

The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

'''Solution: Lorentz force = <-500,-200,300> N'''

[[File:Soln1.PNG]]

===Middling===

The magnetic force on a proton is 100 N 30 degrees down from the +x direction. The electric force on the same proton is 100 N 30 degrees up from the +z direction. What is the magnitude of the Lorentz Force on the proton?

'''Solution: Lorentz force = 122.5 N'''

[[File:Soln2.PNG]]

===Difficult===
An electron is traveling with a constant velocity of <0.75c, 0, 0>. You measure the magnetic field to be <0.4, 0.3, 0.5>T everywhere. What is the electric field?

'''Solution: E = <0, 1.13e8, -6.75e7> N/C '''

Since the electron is traveling at constant velocity, the net force must be zero. Thus, the magnetic field must equal the electric field, qvxB = -qE. The charge on both sides cancel out, to vxB = -E. The cross product of v and B is <0, -1.13e8, 6.75e7>, so the electric field must point in the opposite direction.

==Connectedness==

1. I'm very interested in music and sound amplification. Speakers use the Lorentz force of an electromagnet to move a cone that creates sound waves in the air. When current flows through the wires in the electromagnetic in different quantities, the speakers move in unique ways to produce the different sounds that we recognize. Amplifiers for electric guitars and basses work in the same way. As a guitar player, I'm interested by the physics of how electric guitars work.

[[File:Speaker-Diagram-1.png]]

2. One of my areas of interest as a mechanical engineering student is sustainable and renewable energy. Wind turbines and hydropower plants both work by harnessing the kinetic energy of water or wind and using it to induce an electrical current. The turbines rotate and move a permanent magnet that induces a current in an electromagnet placed inside of the magnet, which is shaped like a hollow cylinder. The induced current is then carried via wires to external sources to provide energy.

[[File:Electrodynamics papers 70.jpg]]

3. Several industries manufacture products that induce current using the Lorentz Force. For example, electric guitars and basses work by magnetizing the strings and relying on the Lorentz force to create a current in pickups that is then transmitted to an amplifier. Pickups are small electromagnet coils surrounding a magnet that are placed beneath the strings. The strings become magnetized because of the magnet inside the pickup. When they are played and vibrate, they induce current in the electromagnet. The Lorentz force causes the strings to exert forces that move mobile charges and induce the current. The current is then increased through a potentiometer and sent to an amplifier through a cable.

[[File:Eg-magnets copy.jpg]]

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

The Lorentz Force is named after Hendrik Lorentz, who derived the formula in the late 19th century following a previous derivation by [[Oliver Heaviside]] in 1889. However, scientists had tried to find formulas for one electromagnetic force for over a hundred years before.Some scientists such as [[Henry Cavendish]] argued that the magnetic poles of an object could create an electric force on a particle that obeys an inverse-square law. However, the experimental proof was not enough to definitively publish. In 1784, [[Charles de Coulomb]], using a torsion balance, was able to definitively show through experiment that this was true. After [[Hans Christian Ørsted]] discovered that a magnetic needle is acted on by a voltaic current, [[Andre Marie Ampere]] derived a new formula for the angular dependence of the force between two current elements. However, the force was still given in terms of the properties of the objects involved and the distances between, not in terms of electric and magnetic fields or forces.

[[Michael Faraday]] introduced modern ideas of magnetic and electric fields, including their interactions and relations with each other, later to be given full mathematical description by [[William Thomson (Lord Kelvin)]] and [[James Maxwell]]. From a modern perspective it is possible to identify in Maxwell's 1865 formulation of his field equations a form of the Lorentz force equation in relation to electric currents, however, it was not initially evident how his equations related to the forces on moving charged objects. [[J.J. Thomson]] was the first to attempt to derive from Maxwell's field equations the electromagnetic forces on a moving charged object in terms of the object's properties and external fields. Interested in determining the electromagnetic behavior of the charged particles in cathode rays, Thomson published a paper in 1881 wherein he gave the force on the particles due to an external magnetic field as <math>\vec{F} = q\vec{E} + \frac{q}{2}\vec{v} ⨯ \vec{B}</math>. Finally, Heaviside and later Lorentz were able to combine the information into the currently accepted Lorentz Force equation.

== See also ==
The [[Hall Effect]] is a special case in which the magnetic and electric forces on a particle or object cancel out, meaning that there is zero net force. Solving these problems involves setting the two forces equal to each other and using given information to find values for <math>\vec{B}</math>, <math>\vec{v}</math>, or <math>\vec{E}</math>.

[https://www.youtube.com/watch?v=8QWB8IfNoIs This video] demonstrates a few everyday applications and examples of the Lorentz Force.

===Further reading===

[[Hall Effect]]
*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:Heatcap.jpg

2015-12-01T19:13:35Z

Aschatz3: Aschatz3 uploaded a new version of "File:Heatcap.jpg"

File:Heatcap.jpg

2015-12-01T19:12:08Z

Aschatz3:

File:Koppsrule.jpg

2015-12-01T04:25:33Z

Aschatz3: Aschatz3 uploaded a new version of "File:Koppsrule.jpg"

File:Koppsrule.jpg

2015-12-01T04:25:04Z

Aschatz3:

Main Page

2015-11-30T03:00:42Z

Aschatz3: /* Properties of Matter */

__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#Copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Terminal Velocity and Friction Due to Air]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Quantum Theory]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Joseph Henry]]
*[[Michael Faraday]]
*[[J.J. Thomson]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Marie Curie]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
*[[Erwin Schrödinger]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[Josiah Willard Gibbs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]
*[[Heat Capacity]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* [[Predicting Change in multiple dimensions]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Rotation]]
* [[Torque]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting a Change in Rotation]]
* [[Conservation of Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[Total Angular Momentum]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Energy===
<div class="mw-collapsible-content">
*[[The Energy Principle]]
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
*[[Internal Energy]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power]]
*[[Energy Graphs]]
*[[Photons]]
*[[Air Resistance]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Collisions===
<div class="mw-collapsible-content">
*[[Collisions]]
*[[Maximally Inelastic Collision]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Rutherford Experiment and Atomic Collisions]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Electric Potential]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
*[[Electric Force]]
*[[Polarization]]
*[[Charge Motion in Metals]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Magnetic Field of a Long Straight Wire]]
**[[Magnetic Field of a Loop]]
**[[Bar Magnet]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Motors and Generators]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
*[[Ohm's Law]]
*[[RC]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
*[[Feedback]]
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Ampere's Law]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
*[[Ampere-Maxwell Law]]
**[[Superconducters]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
*[[Lenses]]
*[[Energy and Momentum Analysis in Radiation]]
*[[Electromagnetic Propagation]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
*[[Nature, Behavior, and Properties of Sound]]
*[[Resonance]]
*[[Sound Barrier]]
</div>
</div>
*[[blahb]]
</div>
</div>

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* An overview of [[VPython]]

Main Page

2015-11-30T03:00:25Z

Aschatz3: /* Properties of Matter */

__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#Copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Terminal Velocity and Friction Due to Air]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Quantum Theory]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Joseph Henry]]
*[[Michael Faraday]]
*[[J.J. Thomson]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Marie Curie]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
*[[Erwin Schrödinger]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[Josiah Willard Gibbs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]
[[Heat Capacity]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* [[Predicting Change in multiple dimensions]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Rotation]]
* [[Torque]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting a Change in Rotation]]
* [[Conservation of Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[Total Angular Momentum]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Energy===
<div class="mw-collapsible-content">
*[[The Energy Principle]]
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
*[[Internal Energy]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power]]
*[[Energy Graphs]]
*[[Photons]]
*[[Air Resistance]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Collisions===
<div class="mw-collapsible-content">
*[[Collisions]]
*[[Maximally Inelastic Collision]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Rutherford Experiment and Atomic Collisions]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Electric Potential]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
*[[Electric Force]]
*[[Polarization]]
*[[Charge Motion in Metals]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Magnetic Field of a Long Straight Wire]]
**[[Magnetic Field of a Loop]]
**[[Bar Magnet]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Motors and Generators]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
*[[Ohm's Law]]
*[[RC]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
*[[Feedback]]
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Ampere's Law]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
*[[Ampere-Maxwell Law]]
**[[Superconducters]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
*[[Lenses]]
*[[Energy and Momentum Analysis in Radiation]]
*[[Electromagnetic Propagation]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
*[[Nature, Behavior, and Properties of Sound]]
*[[Resonance]]
*[[Sound Barrier]]
</div>
</div>
*[[blahb]]
</div>
</div>

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* An overview of [[VPython]]

Main Page

2015-11-30T02:58:42Z

Aschatz3: /* Properties of Matter */