Physics Book - User contributions [en]

Magnetic Force in a Moving Reference Frame

2022-04-25T02:45:13Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code is written in python and makes use of python's Numpy module to calculate a simple cross product of a particle's velocity, after accounting for a change in reference frame. The code is shown below.

''
import numpy as np

partVel = np.array([3,5,7],float)
magStrenght = np.array([0,0,1],float)
qCharge = 1

print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")
xRef = input("V_x = ")
yRef = input("V_y = ")
zRef = input("V_z = ")
refVel = np.array([xRef,yRef,zRef],float)

def magneticForce(velocity):
velocity -= refVel
return qCharge * np.cross(velocity,magStrength)

print(magneticForce(partVel))
''

This code does not make any relativistic adjustments for velocity, as it assumes a particle is moving much slower than the speed of light. However, relativistic adjustments can be made simply by including a <math>\gamma</math> term when calculating the velocity of the moving particle in the new reference frame. Since as a vector sum of two velocities (as is the case when switching reference frame) in relativistic cases can be represented by the following;

<math> \vec{v} + \vec{u} = \frac{\vec{v} + \vec{u}}{1 - \frac{\vec{v}\vec{u}}{c^2}} </math>

Adding the code snipped below adjusts the prior code to make relativistic adjustments - Noting that the effects of special relativity are always present, but insignificant when the velocities are much lower than the speed of light. The reason for this is that the value of gamma is almost exactly 1 until the particle's velocity approaches the speed of light, at which point it asymptotically goes to infinity at the speed of light. A graph of the value of gamma as a function of velocity is shown below.

newVel = (partVel + refVel)/(1 - (partVel*refVel)/c**2)

[[File:gammaFunc.png|thumb]]

''Note: Linked code does not run in the Wiki page, but can be copy pasted into another code IDE and run without issue. Code returns the force on a particle moving in a constant magnetic field adjusted to be measured with reference to an inputed reference frame. Also I tried to upload two different images, but the wiki page keeps throwing up images. The first is a graph of the value of gamma as a function of velocity, which I generated in python using matplotlib, and the second is just a picture pulled from the internet of magnetic field lines. ''

[[File:/Desktop/code.jpg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

File:GammaFunc.png

2022-04-25T02:40:16Z

Pvollrath3:

Magnetic Force in a Moving Reference Frame

2022-04-25T02:39:55Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code is written in python and makes use of python's Numpy module to calculate a simple cross product of a particle's velocity, after accounting for a change in reference frame. The code is shown below.

''
import numpy as np

partVel = np.array([3,5,7],float)
magStrenght = np.array([0,0,1],float)
qCharge = 1

print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")
xRef = input("V_x = ")
yRef = input("V_y = ")
zRef = input("V_z = ")
refVel = np.array([xRef,yRef,zRef],float)

def magneticForce(velocity):
velocity -= refVel
return qCharge * np.cross(velocity,magStrength)

print(magneticForce(partVel))
''

This code does not make any relativistic adjustments for velocity, as it assumes a particle is moving much slower than the speed of light. However, relativistic adjustments can be made simply by including a <math>\gamma</math> term when calculating the velocity of the moving particle in the new reference frame. Since as a vector sum of two velocities (as is the case when switching reference frame) in relativistic cases can be represented by the following;

<math> \vec{v} + \vec{u} = \frac{\vec{v} + \vec{u}}{1 - \frac{\vec{v}\vec{u}}{c^2}} </math>

Adding the code snipped below adjusts the prior code to make relativistic adjustments - Noting that the effects of special relativity are always present, but insignificant when the velocities are much lower than the speed of light. The reason for this is that the value of gamma is almost exactly 1 until the particle's velocity approaches the speed of light, at which point it asymptotically goes to infinity at the speed of light. A graph of the value of gamma as a function of velocity is shown below.

newVel = (partVel + refVel)/(1 - (partVel*refVel)/c**2)

[[File:gammaFunc.png|thumb]]

''Note: Linked code does not run in the Wiki page, but can be copy pasted into another code IDE and run without issue. Code returns the force on a particle moving in a constant magnetic field adjusted to be measured with reference to an inputed reference frame.''

[[File:/Desktop/code.jpg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-25T02:39:25Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code is written in python and makes use of python's Numpy module to calculate a simple cross product of a particle's velocity, after accounting for a change in reference frame. The code is shown below.

''
import numpy as np

partVel = np.array([3,5,7],float)
magStrenght = np.array([0,0,1],float)
qCharge = 1

print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")
xRef = input("V_x = ")
yRef = input("V_y = ")
zRef = input("V_z = ")
refVel = np.array([xRef,yRef,zRef],float)

def magneticForce(velocity):
velocity -= refVel
return qCharge * np.cross(velocity,magStrength)

print(magneticForce(partVel))
''

This code does not make any relativistic adjustments for velocity, as it assumes a particle is moving much slower than the speed of light. However, relativistic adjustments can be made simply by including a <math>\gamma</math> term when calculating the velocity of the moving particle in the new reference frame. Since as a vector sum of two velocities (as is the case when switching reference frame) in relativistic cases can be represented by the following;

<math> \vec{v} + \vec{u} = \frac{\vec{v} + \vec{u}}{1 - \frac{\vec{v}\vec{u}}{c^2}} </math>

Adding the code snipped below adjusts the prior code to make relativistic adjustments - Noting that the effects of special relativity are always present, but insignificant when the velocities are much lower than the speed of light. The reason for this is that the value of gamma is almost exactly 1 until the particle's velocity approaches the speed of light, at which point it asymptotically goes to infinity at the speed of light. A graph of the value of gamma as a function of velocity is shown below.

newVel = (partVel + refVel)/(1 - (partVel*refVel)/c**2)

[[File:gammaFunc.png|thumb|Gamma as a function of Velocity]]

''Note: Linked code does not run in the Wiki page, but can be copy pasted into another code IDE and run without issue. Code returns the force on a particle moving in a constant magnetic field adjusted to be measured with reference to an inputed reference frame.''

[[File:/Desktop/code.jpg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-25T02:29:39Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code is written in python and makes use of python's Numpy module to calculate a simple cross product of a particle's velocity, after accounting for a change in reference frame. The code is shown below.

''
import numpy as np

partVel = np.array([3,5,7],float)
magStrenght = np.array([0,0,1],float)
qCharge = 1

print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")
xRef = input("V_x = ")
yRef = input("V_y = ")
zRef = input("V_z = ")
refVel = np.array([xRef,yRef,zRef],float)

def magneticForce(velocity):
velocity -= refVel
return qCharge * np.cross(velocity,magStrength)

print(magneticForce(partVel))
''

This code does not make any relativistic adjustments for velocity, as it assumes a particle is moving much slower than the speed of light. However, relativistic adjustments can be made simply by including a <math>\gamma</math> term when calculating the velocity of the moving particle in the new reference frame. Since as a vector sum of two velocities (as is the case when switching reference frame) in relativistic cases can be represented by the following;

<math> \vec{v} + \vec{u} = \frac{\vec{v} + \vec{u}}{1 - \frac{\vec{v}\vec{u}}{c^2}} </math>

Adding the code snipped below adjusts the prior code to make relativistic adjustments - Noting that the effects of special relativity are always present, but insignificant when the velocities are much lower than the speed of light.

newVel = (partVel + refVel)/(1 - (partVel*refVel)/c**2)

''Note: Linked code does not run in the Wiki page, but can be copy pasted into another code IDE and run without issue. Code returns the force on a particle moving in a constant magnetic field adjusted to be measured with reference to an inputed reference frame.''

[[File:/Desktop/code.jpg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-24T20:56:45Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code is written in python and makes use of python's Numpy module to calculate a simple cross product of a particle's velocity, after accounting for a change in reference frame. The code is shown below.

''
import numpy as np

partVel = np.array([3,5,7],float)
magStrenght = np.array([0,0,1],float)
qCharge = 1

print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")
xRef = input("V_x = ")
yRef = input("V_y = ")
zRef = input("V_z = ")
refVel = np.array([xRef,yRef,zRef],float)

def magneticForce(velocity):
velocity -= refVel
return qCharge * np.cross(velocity,magStrength)

print(magneticForce(partVel))
''

This code does not make any relativistic adjustments for velocity, as it assumes a particle is moving much slower than the speed of light. However, relativistic adjustments can be made simply by including a <math>\gamma</math> term when calculating the velocity of the moving particle in the new reference frame. Since as a vector sum of two velocities (as is the case when switching reference frame) in relativistic cases can be represented by the following;

<math> \vec{v} + \vec{u} = \frac{\vec{v} + \vec{u}}{1 - \frac{\vec{v}\vec{u}}{c^2}} </math>

Adding the code snipped below adjusts the prior code to make relativistic adjustments - Noting that the effects of special relativity are always present, but insignificant when the velocities are much lower than the speed of light.

newVel = (partVel + refVel)/(1 - (partVel*refVel)/c**2)

[[File:/Desktop/code.jpg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-24T20:47:40Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code is written in python and makes use of python's Numpy module to calculate a simple cross product of a particle's velocity, after accounting for a change in reference frame. The code is shown below.

''
import numpy as np

partVel = np.array([3,5,7],float)
magStrenght = np.array([0,0,1],float)
qCharge = 1

print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")
xRef = input("V_x = ")
yRef = input("V_y = ")
zRef = input("V_z = ")
refVel = np.array([xRef,yRef,zRef],float)

def magneticForce(velocity):
velocity -= refVel
return qCharge * np.cross(velocity,magStrength)

print(magneticForce(partVel))
''

[[File:/Desktop/code.jpg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-24T20:47:06Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code is written in python and makes use of python's Numpy module to calculate a simple cross product of a particle's velocity, after accounting for a change in reference frame. The code is shown below.

''
import numpy as np

partVel = np.array([3,5,7],float)
magStrenght = np.array([0,0,1],float)
qCharge = 1

print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")
xRef = input("V_x = ")
yRef = input("V_y = ")
zRef = input("V_z = ")
refVel = np.array([xRef,yRef,zRef],float)

def magneticForce(velocity):
velocity -= refVel
return qCharge * np.cross(velocity,magStrength)

print(magneticForce(partVel))
''

[[File:/Desktop/code.jpg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-24T20:46:36Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code is written in python and makes use of python's Numpy module to calculate a simple cross product of a particle's velocity, after accounting for a change in reference frame. The code is shown below.

''
import numpy as np

partVel = np.array([3,5,7],float)
magStrenght = np.array([0,0,1],float)
qCharge = 1

print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")
xRef = input("V_x = ")
yRef = input("V_y = ")
zRef = input("V_z = ")
refVel = np.array([xRef,yRef,zRef],float)

def magneticForce(velocity):
velocity -= refVel
return qCharge * np.cross(velocity,magStrength)

print(magneticForce(partVel))
''

[[File:/Desktop/code.jpg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

File:-Desktop-code.jpg

2022-04-24T20:35:14Z

Pvollrath3:

Magnetic Force in a Moving Reference Frame

2022-04-24T20:32:53Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code computes the magnitude of the magnetic force on a moving particle with reference to an observer moving with any inputed velocity relative to the stationary observer.

[[File:/Desktop/code.jpg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-24T20:30:30Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code computes the magnitude of the magnetic force on a moving particle with reference to an observer moving with any inputed velocity relative to the stationary observer.

import numpy as np

partVel = np.array([3,5,7],float)
magStrenght = np.array([0,0,1],float)
qCharge = 1

print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")
xRef = input("V_x = ")
yRef = input("V_y = ")
zRef = input("V_z = ")
refVel = np.array([xRef,yRef,zRef],float)

def magneticForce(velocity):
velocity -= refVel
return qCharge * np.cross(velocity,magStrength)

print(magneticForce(partVel))

[[File:magnetic.jpeg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-24T20:29:45Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code computes the magnitude of the magnetic force on a moving particle with reference to an observer moving with any inputed velocity relative to the stationary observer.

<math>
import numpy as np

partVel = np.array([3,5,7],float)
magStrenght = np.array([0,0,1],float)
qCharge = 1

print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")
xRef = input("V_x = ")
yRef = input("V_y = ")
zRef = input("V_z = ")
refVel = np.array([xRef,yRef,zRef],float)

def magneticForce(velocity):
velocity -= refVel
return qCharge * np.cross(velocity,magStrength)

print(magneticForce(partVel))
</math>

[[File:magnetic.jpeg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

File:MagneticField.jpeg

2022-04-24T20:15:31Z

Pvollrath3:

File:Magnetic.jpeg

2022-04-24T20:14:26Z

Pvollrath3:

Magnetic Force in a Moving Reference Frame

2022-04-24T20:13:37Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

[[File:magnetic.jpeg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-24T20:10:51Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

[[File:magnetic.jpg|thumb|Simulated image of magnetic field lines]]
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-22T17:08:24Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, <math>e_{1}</math> and <math>e_{2}</math>, traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-22T17:04:26Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, ''e_{1}'' and ''e_{2}'', traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

According to the Special Theory of Relativity, distance and time are dilated as a result of relative motion, and is dependent on the reference frame from which observations are made. Since from the reference frame of each electron, the velocity of the other electron is dilated by the \gamma factor, from the reference frame of an electron, the other electron is no longer traveling at the same velocity. Hence, now there is relative motion between these two electrons, and there is a magnetic force between these two particles.

''Note: the derivation of electromagnetism from special relativity is presented more formally here - [https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity]''

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-22T16:59:36Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, ''e_{1}'' and ''e_{2}'', traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

However, with Einstein's special theory of relativity, the understanding of this system is altered since from the reference point of either electron, the velocity of the other electron is dilated to account for its motion through space - dilated by the ''gamma factor'';

<math>\gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}}</math>

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-22T16:56:49Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

Magnetic fields were initially formalized under Maxwell's framework in 1865 given by the following equations known as ''Maxwell's Equations'';

<math>\nabla \cdot \textbf{E} = \rho</math>

<math>\nabla \cdot \textbf{B} = 0</math>

<math>\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}</math>

<math>\nabla \times \textbf{B} = \mu_{0}\textbf{j} + \mu_{0}\epsilon{0}\frac{\partial\textbf{E}}{\partial t}</math>

These equations have remained remarkably robust in the face of more recent discoveries in physics such as Einstein's theories of special and general relativity, as well as quantum mechanics. However, limited as Maxwell was by the knowledge and technology of his time, magnetism is more formally derived from special relativity in most modern textbooks.

Take two electrons, ''e_{1}'' and ''e_{2}'', traveling parallel to one another with the same velocity, as seen from a stationary observer. The equation for the magnetic force between these two electrons is zero from the more classical definition of magnetism, since the relative motion of these charges is zero;

<math>\textbf{F}=q\vec{v} \times \textbf{B}</math>

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Magnetic Force in a Moving Reference Frame

2022-04-22T16:43:20Z

Pvollrath3:

Magnetic Force in a Moving Reference Frame

2022-04-22T16:41:13Z

Pvollrath3:

Magnetic Force in a Moving Reference Frame

2022-04-22T16:41:01Z

Pvollrath3:

Magnetic Force in a Moving Reference Frame

2022-04-22T16:40:45Z

Pvollrath3:

Magnetic Force in a Moving Reference Frame

2022-04-22T16:40:19Z

Pvollrath3:

Magnetic Force in a Moving Reference Frame

2022-04-22T16:30:18Z

Pvollrath3:

This page is claimed by Paul Vollrath Spring 2022
==The Main Idea==

The magnetic force of a moving charge depends on the velocity of the charge, and thus can differ according to different moving reference frames.

===A Mathematical Model===

Let's consider two moving protons to simplify the case. Suppose the two protons are initially traveling parallel to each other with the the same speed. The speed is v, and the two particles are distance, r, apart.
[[File:forceprotons.png|200px|thumb|left|Two protons, distance r apart, moving parallel with velocity, v]]
How would we find the electric and magnetic force that the top proton exerts on the bottom?

First:
Electric force is easily calculated by calculating the electric field, <math>{\vec{E}_{top}}</math>, at the location of proton<math>_{bottom}</math>. The equation for electric force is
<math>{\vec{F}_{E, bottom}} = q_{bottom}{\vec{E}_{top}}</math>.
Therefore:
<math>{\vec{F}_{E, bottom}} = {\frac{1}{4πϵ_0}}{\frac{e^{2}}{r^{2}}}</math>.

Second:
Determine magnetic field. <math>{\vec{F}_{M, bottom}}</math> by calculating the magnetic field <math>{\vec{B}_{top}}</math>.
<math>{\vec{B}_{top}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{q_{top}{\vec{v}_{top}}{\times}{\hat{r}}}{r^{2}}} </math>.
Using this equation and right hand rule, we can see that the magnetic field goes into the page at the location of proton 2. Additionally <math>{\vec{v}_{top}}{\times}{\hat{r}}</math> can be rewritten as sin(90), which equals +1.

Three:
The magnetic field from the previous step can be used to determine the magnetic force on the bottom proton.
<math>{\vec{F}_{M, bottom}} = q_{bottom}{\vec{v}_{bottom}}{\times}{\vec{B}_{top}}</math>.

The magnetic force is found to be upward and can be found with the equation:
<math>{\vec{F}_{M, bottom}} = {\frac{\mu_{0}}{4\pi}}</math>
<math>{\frac{e^{2}v^{2}}{r^{2}}}</math>.
[[File:finalprotonforce.png|200px|thumb|left|Magnetic force and Electric force on two parallel protons]]

When we take the ratio of the magnetic force to the electric force, we find that the forces have relations to the speed of light. When particles move at ordinary speed the magnetic interaction is insignificant when compared to the electric interaction. However, if the speed reaches the speed of light the magnetic force comes to par with the electric force.
===A Computational Model===
Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).
==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A proton travels in the x-direction, with speed 1E5 m/s. At the location of the proton there is a magnetic field of 0.25T in the y-direction, because of a coil. What are the direction and magnitude of the magnetic force on the proton?

Step 1:
The magnetic force can be calculated by using:
<math>{\vec{F}} = q({\vec{v}}{\times}{\vec{B}})</math>

q - charge of proton (1.6E-19 C)

<math>{\vec{v}}</math> - velocity

<math>{\vec{B}}</math> - magnetic field

Step 2:
Plug in values into the equation to find the magnetic force.

<math>{\vec{v}}{\times}{\vec{B}} = [(1e5 m/s){\times}(0.25)][(\hat{i}){\times}(\hat{j})] = 2.5e4 mT/s (\hat{k})</math>

<math>
{\vec{F}} = (1.6e-19 C){\times}(2.5e4 mT/s) = 4e-15 N
</math>

===Middling===
An electron moves with speed v, in a region with uniform magnetic field B into the page due to large cols. Draw the trajectory of the electron.

Step 1: Apply magnetic force equation.

<math>
{\vec{F}} = -evB{\sin{90}}
</math>

Step 2: Draw the trajectory of the electron.
[[File:Trajectory.png]]

===Difficult===
A long solenoid with diameter of 4cm is in a vacuum and a lithium nucleous is in a clockwise circular orbit inside the solenoid. It takes 50ns for the lithium nucleus to complete one orbit

(a) Does the current in the solenoid run clockwise or counterclockwise? Explain.

The current in the solenoid in the lithium is clockwise and solenoid. You just never ran my products officially.

(b) What is the magnitude of the magnetic field made by the solenoid?

Q = 3p
= 3*1.6*10^19
=7m_{p}
<math> {\vec{F}_B} = {QvB}

QvB = mv^2/R

B = mv/QR</math>

<math>{\frac{v}{R}} = \frac{2\pi}{t}</math>
[[File:pay.png|200px|thumb|right|Side view of solenoid with current and magnetic field]]

<math> B = m {\frac{2\pi}{Qt}} </math>
=(7x1.67e-27)(2pi/(50e-9)(3x1.6e-19)
= 3.05 T

==Connectedness==
#How is this topic connected to something that you are interested in? This topic is interesting because it can be confusing exactly what causes a magnetic force when both the object in question and the reference frame is in motion. The changes in magnetic and electric field due to a change in the reference frame is interesting to note.
#How is it connected to your major? As a BME it is important to be able to understand the consequences or benefits of looking at a phenomenon in a different angle. However, it is important to note that there is only one force resulting from the magnetic and electric fields. Additionally, magnetic forces would be beneficial when dealing with development of devices including current-carrying wires.
#Is there an interesting industrial application? Magnetic forces on current-carrying wires are usually larger than the electric force on the same wire, because the net charge is zero. Moreover, when the speed of the particle is less than the speed of light there is less magnetic interaction between 2 charged particles. When the speed exceeds the speed of light, magnetic force between two charged particles can be compared to the electric force.

==History==

In 20th century, relativity and quantum mechanics were brought into light. In 1905, Albert Einstein published a paper which proved that electric and magnetic fields both take part in the same phenomenon when viewed from different referenced frames.[https://en.wikipedia.org/wiki/Magnetic_field] Einstein developed his theory of relativity through a simple experiment of a moving magnet and a conductor. In this experiment, the current in the conductor is calculated in the frame of reference of both the magnet and the conductor. [https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] According to the basic principle of relativity the only known variable, current, is unchanging in both reference frames. However, when Maxwell's Equations are applied there is a magnetic force in the magnet frame and an electric force in the conductor frame. This thought experiment as well as Fizeau experiment, the aberration of light, and negative aether drift tests formed the foundation for the theory of relativity.[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem] With a new found understanding of relativity, quantum mechanics combined with electrodynamics to create
a new science called quantum electrodynamics (QED). Simply put, QED describes the interaction between light and matter. Additionally, it is the first theory where there is no discord between quantum mechanics and special relativity.[https://en.wikipedia.org/wiki/Quantum_electrodynamics]

===Further reading===

American Physical Society [http://dx.doi.org/10.1103/PhysRevLett.111.160404]

===External links===

Michigan State University: Moving Reference Frames[https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html]

University of Melbourne: Why do Magnetic Forces Depend on Who Measures Them?[http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm]

==References==
#http://dx.doi.org/10.1103/PhysRevLett.111.160404
#https://www.pa.msu.edu/courses/2000fall/PHY232/lectures/magforces/frames.html
#http://www.ph.unimelb.edu.au/~dnj/teaching/160mag/160mag.htm
#https://en.wikipedia.org/wiki/Magnetic_field
#https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
#https://en.wikipedia.org/wiki/Quantum_electrodynamics
#http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.160404

[[Category:Magnetic Force in a Moving Reference Frame]]

Main Page

2022-04-22T16:27:27Z

Pvollrath3: /* Matter Waves */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

This resource 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 for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then 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 written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* 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 intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* 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]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== 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]]
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">

==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====GlowScript 101====
<div class="mw-collapsible-content">
*[[Python Syntax]]
*[[GlowScript]]
</div>
</div>

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

====VPython====

<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

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

====Vectors and Units====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

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

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

</div>
</div>

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

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

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

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[Energy of a Single Particle]]
*[[Kinetic Energy]]
*[[Work/Energy]]
*[[The Energy Principle]]
*[[Conservation of Energy]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation, and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====

<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

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

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

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

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

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

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

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

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</div>
</div>

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

====Charging and Discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Field of a Charged Rod|Charged Rod]]
</div>
</div>

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

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

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

====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

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

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

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

====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Kirchoff's Laws]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Electric Potential Difference]]
</div>
</div>

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

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

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

====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

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

====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
<h1><strong>Alayna Baker Spring 2020</strong></h1>
[[File:Hall Effect 1.jpg]]
[[File:Hall Effect 2.jpg]]

*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>

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

]]]====Motional EMF====

<div class="mw-collapsible-content">
*[[Motional Emf]]
<h1><strong>Adeline Boswell Fall 2019</strong></h1>
[[File:Motional EMF Example.jpg]]

*[[Motional Emf using Faraday's Law]]
</div>
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page

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

If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"

[[File:MotEMFCR.jpg]]

====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

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

====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

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

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
*[[The Photoelectric Effect]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
*[[Particle in a 1-Dimensional box]]
*[[Heisenberg Uncertainty Principle]]
</div>
</div>

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

====Schrödinger Equation====
<div class="mw-collapsible-content">
*[[Solution for a Single Free Particle]]
<div class="mw-collapsible-content">
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]
<div class="mw-collapsible-content"></div>
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Quantum Mechanics====
<div class="mw-collapsible-content">
*[[Quantum Tunneling through Potential Barriers]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
*[[Molecules]]
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
*[[Application of Statistics in Physics]]
*[[Temperature & Entropy]]
</div>
<div class="mw-collapsible-content">

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>

Main Page

2022-04-22T15:43:15Z

Pvollrath3: /* Matter Waves */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

This resource 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 for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then 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 written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* 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 intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* 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]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== 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]]
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">

==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====GlowScript 101====
<div class="mw-collapsible-content">
*[[Python Syntax]]
*[[GlowScript]]
</div>
</div>

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

====VPython====

<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

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

====Vectors and Units====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

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

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

</div>
</div>

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

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

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

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[Energy of a Single Particle]]
*[[Kinetic Energy]]
*[[Work/Energy]]
*[[The Energy Principle]]
*[[Conservation of Energy]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation, and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====

<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

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

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

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

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

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

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

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

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</div>
</div>

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

====Charging and Discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Field of a Charged Rod|Charged Rod]]
</div>
</div>

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

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

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

====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

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

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

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

====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Kirchoff's Laws]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Electric Potential Difference]]
</div>
</div>

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

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

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

====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

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

====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
<h1><strong>Alayna Baker Spring 2020</strong></h1>
[[File:Hall Effect 1.jpg]]
[[File:Hall Effect 2.jpg]]

*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>

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

]]]====Motional EMF====

<div class="mw-collapsible-content">
*[[Motional Emf]]
<h1><strong>Adeline Boswell Fall 2019</strong></h1>
[[File:Motional EMF Example.jpg]]

*[[Motional Emf using Faraday's Law]]
</div>
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page

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

If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"

[[File:MotEMFCR.jpg]]

====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

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

====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

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

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
*[[The Photoelectric Effect]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
*[[Particle in a 1-Dimensional box]]
*[[Heisenberg Uncertainty Principle]]
*[[De Broglie Wavelength]]
</div>
</div>

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

====Schrödinger Equation====
<div class="mw-collapsible-content">
*[[Solution for a Single Free Particle]]
<div class="mw-collapsible-content">
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]
<div class="mw-collapsible-content"></div>
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Quantum Mechanics====
<div class="mw-collapsible-content">
*[[Quantum Tunneling through Potential Barriers]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
*[[Molecules]]
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
*[[Application of Statistics in Physics]]
*[[Temperature & Entropy]]
</div>
<div class="mw-collapsible-content">

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>

Main Page

2022-04-22T15:42:53Z

Pvollrath3: /* Matter Waves */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

This resource 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 for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then 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 written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* 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 intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* 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]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== 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]]
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">

==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====GlowScript 101====
<div class="mw-collapsible-content">
*[[Python Syntax]]
*[[GlowScript]]
</div>
</div>

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

====VPython====

<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

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

====Vectors and Units====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

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

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

</div>
</div>

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

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

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

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[Energy of a Single Particle]]
*[[Kinetic Energy]]
*[[Work/Energy]]
*[[The Energy Principle]]
*[[Conservation of Energy]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation, and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====

<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

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

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

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

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

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

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

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

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</div>
</div>

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

====Charging and Discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Field of a Charged Rod|Charged Rod]]
</div>
</div>

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

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

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

====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

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

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

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

====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Kirchoff's Laws]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Electric Potential Difference]]
</div>
</div>

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

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

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

====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

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

====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
<h1><strong>Alayna Baker Spring 2020</strong></h1>
[[File:Hall Effect 1.jpg]]
[[File:Hall Effect 2.jpg]]

*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>

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

]]]====Motional EMF====

<div class="mw-collapsible-content">
*[[Motional Emf]]
<h1><strong>Adeline Boswell Fall 2019</strong></h1>
[[File:Motional EMF Example.jpg]]

*[[Motional Emf using Faraday's Law]]
</div>
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page

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

If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"

[[File:MotEMFCR.jpg]]

====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

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

====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

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

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
*[[The Photoelectric Effect]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
*[[Particle in a 1-Dimensional box]]
*[[Heisenberg Uncertainty Principle]]
*[[The de Broglie wavelength]]
</div>
</div>

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

====Schrödinger Equation====
<div class="mw-collapsible-content">
*[[Solution for a Single Free Particle]]
<div class="mw-collapsible-content">
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]
<div class="mw-collapsible-content"></div>
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Quantum Mechanics====
<div class="mw-collapsible-content">
*[[Quantum Tunneling through Potential Barriers]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
*[[Molecules]]
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
*[[Application of Statistics in Physics]]
*[[Temperature & Entropy]]
</div>
<div class="mw-collapsible-content">

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>