Physics Book - User contributions [en]

The Differential Form of Ampere's Law

2015-12-06T03:50:38Z

Jpetroni3:

Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativistic retardation, a term for how changes in magnetic and electric fields propagate at the speed of light so they cannot be measured instantly. Typically this is not an issue if the particles are moving much slower than the speed of light because although these physical laws are technically incorrect, the margin of error is so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

==Curl==
To have a model that is consistent with the theory of relativity, the property of a magnetic field called the "curl" must be utilized. The curl is the path integral of magnetic field per unit area, in the limit as the area goes to zero. This is useful because its value is proportional to the current density at the same location and time so there is an established relationship. This is known as a local relationship because both are evaluated at the same place and time, making it relativisticly correct because it isn't effected by relativistic retardation.

Lecture Video: https://www.youtube.com/watch?v=mj2ahFjnpmY

===A Mathematical Model===
Curl is the measurement of how much magnetic field loops around a line. It is a vector in the same direction of the flow of current.

Definition of curl:
[[File:realdefofcurl.png]]

Curl can also be expressed in terms of a "del" operator or gradient operator. This is the same operator that relates the (x, y, z) components of electric field to voltage. Expressing the components as the the partial derivative of voltage is the gradient of it.

Gradient Operator:
[[File:otherways.png]]

===A Computational Model===

[[File:curltext.png]]

The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

==Examples==

[[File:curlexample.png]]

==Connectedness==
#The differential form of Ampere's Law interests me because it is one of the first laws that we learned that is relativistically correct, although it is not the complete form of Ampere's Law.
#As a ME major I imagine Ampere's Law will pop up again in either fluids or thermodynamics.
#An interesting application of Ampere's Law is in MRI machines to be able to find the magnetic field around a loop.

== See also ==

#Gauss's Law
#The Integral form of Ampere's Law
#Gradient Operations

===Further reading===
http://www.physnet.org/modules/pdf_modules/m138.pdf

http://ww3.haverford.edu/physics-astro/songs/ampere.PDF

==References==

http://www.physics.byu.edu/faculty/rees/220/book/Lesson8.pdf
Matter and Interactions, 4th Edition

[[Category: Maxwell's Equations]]

The Differential Form of Ampere's Law

2015-12-06T03:48:27Z

Jpetroni3:

Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativistic retardation, a term for how changes in magnetic and electric fields propagate at the speed of light so they cannot be measured instantly. Typically this is not an issue if the particles are moving much slower than the speed of light because although these physical laws are technically incorrect, the margin of error is so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

==Curl==
To have a model that is consistent with the theory of relativity, the property of a magnetic field called the "curl" must be utilized. The curl is the path integral of magnetic field per unit area, in the limit as the area goes to zero. This is useful because its value is proportional to the current density at the same location and time so there is an established relationship. This is known as a local relationship because both are evaluated at the same place and time, making it relativisticly correct because it isn't effected by relativistic retardation.

Lecture Video: https://www.youtube.com/watch?v=mj2ahFjnpmY

===A Mathematical Model===
Curl is the measurement of how much magnetic field loops around a line. It is a vector in the same direction of the flow of current.

Definition of curl:
[[File:realdefofcurl.png]]

Curl can also be expressed in terms of a "del" operator or gradient operator. This is the same operator that relates the (x, y, z) components of electric field to voltage. Expressing the components as the the partial derivative of voltage is the gradient of it.

Gradient Operator:
[[File:otherways.png]]

===A Computational Model===

[[File:curltext.png]]

The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

==Examples==

[[File:curlexample.png]]

==Connectedness==
#The differential form of Ampere's Law interests me because it is one of the first laws that we learned that is relativistically correct, although it is not the complete form of Ampere's Law.
#As a ME major I imagine Ampere's Law will pop up again in either fluids or thermodynamics.
#An interesting application of Ampere's Law is in MRI machines to be able to find the magnetic field around a loop.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Gauss's Law
The Integral form of Ampere's Law
Gradient Operations

===Further reading===
http://www.physnet.org/modules/pdf_modules/m138.pdf

http://ww3.haverford.edu/physics-astro/songs/ampere.PDF

==References==

http://www.physics.byu.edu/faculty/rees/220/book/Lesson8.pdf

[[Category: Maxwell's Equations]]

The Differential Form of Ampere's Law

2015-12-06T03:46:40Z

Jpetroni3:

Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativistic retardation, a term for how changes in magnetic and electric fields propagate at the speed of light so they cannot be measured instantly. Typically this is not an issue if the particles are moving much slower than the speed of light because although these physical laws are technically incorrect, the margin of error is so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

==Curl==
To have a model that is consistent with the theory of relativity, the property of a magnetic field called the "curl" must be utilized. The curl is the path integral of magnetic field per unit area, in the limit as the area goes to zero. This is useful because its value is proportional to the current density at the same location and time so there is an established relationship. This is known as a local relationship because both are evaluated at the same place and time, making it relativisticly correct because it isn't effected by relativistic retardation.

[[Media:https://www.youtube.com/watch?v=mj2ahFjnpmY]]

===A Mathematical Model===
Curl is the measurement of how much magnetic field loops around a line. It is a vector in the same direction of the flow of current.

Definition of curl:
[[File:realdefofcurl.png]]

Curl can also be expressed in terms of a "del" operator or gradient operator. This is the same operator that relates the (x, y, z) components of electric field to voltage. Expressing the components as the the partial derivative of voltage is the gradient of it.

Gradient Operator:
[[File:otherways.png]]

===A Computational Model===

[[File:curltext.png]]

The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

==Examples==

[[File:curlexample.png]]

==Connectedness==
#The differential form of Ampere's Law interests me because it is one of the first laws that we learned that is relativistically correct, although it is not the complete form of Ampere's Law.
#As a ME major I imagine Ampere's Law will pop up again in either fluids or thermodynamics.
#An interesting application of Ampere's Law is in MRI machines to be able to find the magnetic field around a loop.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Gauss's Law
The Integral form of Ampere's Law
Gradient Operations

===Further reading===
http://www.physnet.org/modules/pdf_modules/m138.pdf

http://ww3.haverford.edu/physics-astro/songs/ampere.PDF

==References==

http://www.physics.byu.edu/faculty/rees/220/book/Lesson8.pdf

[[Category: Maxwell's Equations]]

The Differential Form of Ampere's Law

2015-12-06T03:22:24Z

Jpetroni3:

Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativistic retardation, a term for how changes in magnetic and electric fields propagate at the speed of light so they cannot be measured instantly. Typically this is not an issue if the particles are moving much slower than the speed of light because although these physical laws are technically incorrect, the margin of error is so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

==Curl==
To have a model that is consistent with the theory of relativity, the property of a magnetic field called the "curl" must be utilized. The curl is the path integral of magnetic field per unit area, in the limit as the area goes to zero. This is useful because its value is proportional to the current density at the same location and time so there is an established relationship. This is known as a local relationship because both are evaluated at the same place and time, making it relativisticly correct because it isn't effected by relativistic retardation.

===A Mathematical Model===
Curl is the measurement of how much magnetic field loops around a line. It is a vector in the same direction of the flow of current.

Definition of curl:
[[File:realdefofcurl.png]]

Curl can also be expressed in terms of a "del" operator or gradient operator. This is the same operator that relates the (x, y, z) components of electric field to voltage. Expressing the components as the the partial derivative of voltage is the gradient of it.

Gradient Operator:
[[File:otherways.png]]

===A Computational Model===

[[File:curltext.png]]

The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

==Examples==

[[File:curlexample.png]]

==Connectedness==
#The differential form of Ampere's Law interests me because it is one of the first laws that we learned that is relativistically correct, although it is not the complete form of Ampere's Law.
#As a ME major I imagine Ampere's Law will pop up again in either fluids or thermodynamics.
#An interesting application of Ampere's Law is in MRI machines to be able to find the magnetic field around a loop.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Gauss's Law
The Integral form of Ampere's Law
Gradient Operations

===Further reading===
http://www.physnet.org/modules/pdf_modules/m138.pdf

http://ww3.haverford.edu/physics-astro/songs/ampere.PDF

==References==

http://www.physics.byu.edu/faculty/rees/220/book/Lesson8.pdf

[[Category: Maxwell's Equations]]

The Differential Form of Ampere's Law

2015-12-06T03:02:37Z

Jpetroni3:

Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativistic retardation, a term for how changes in magnetic and electric fields propagate at the speed of light so they cannot be measured instantly. Typically this is not an issue if the particles are moving much slower than the speed of light because although these physical laws are technically incorrect, the margin of error is so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

==Curl==
To have a model that is consistent with the theory of relativity, the property of a magnetic field called the "curl" must be utilized. The curl is the path integral of magnetic field per unit area, in the limit as the area goes to zero. This is useful because its value is proportional to the current density at the same location and time so there is an established relationship. This is known as a local relationship because both are evaluated at the same place and time, making it relativisticly correct because it isn't effected by relativistic retardation.

===A Mathematical Model===
Curl is the measurement of how much magnetic field loops around a line. It is a vector in the same direction of the flow of current.

Definition of curl:
[[File:realdefofcurl.png]]

Curl can also be expressed in terms of a "del" operator or gradient operator. This is the same operator that relates the (x, y, z) components of electric field to voltage. Expressing the components as the the partial derivative of voltage is the gradient of it.

Gradient Operator:
[[File:otherways.png]]

===A Computational Model===

[[File:curltext.png]]

The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

==Examples==

[[File:curlexample.png]]

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

==References==

http://www.physics.byu.edu/faculty/rees/220/book/Lesson8.pdf

[[Category: Maxwell's Equations]]

File:Curlexample.png

2015-12-06T03:02:06Z

Jpetroni3:

The Differential Form of Ampere's Law

2015-12-06T02:55:23Z

Jpetroni3:

Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativistic retardation, a term for how changes in magnetic and electric fields propagate at the speed of light so they cannot be measured instantly. Typically this is not an issue if the particles are moving much slower than the speed of light because although these physical laws are technically incorrect, the margin of error is so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

==Curl==
To have a model that is consistent with the theory of relativity, the property of a magnetic field called the "curl" must be utilized. The curl is the path integral of magnetic field per unit area, in the limit as the area goes to zero. This is useful because its value is proportional to the current density at the same location and time so there is an established relationship. This is known as a local relationship because both are evaluated at the same place and time, making it relativisticly correct because it isn't effected by relativistic retardation.

===A Mathematical Model===
Curl is the measurement of how much magnetic field loops around a line. It is a vector in the same direction of the flow of current.

Definition of curl:
[[File:realdefofcurl.png]]

Curl can also be expressed in terms of a "del" operator or gradient operator. This is the same operator that relates the (x, y, z) components of electric field to voltage. Expressing the components as the the partial derivative of voltage is the gradient of it.

Gradient Operator:
[[File:otherways.png]]

===A Computational Model===

[[File:curltext.png]]

The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

==Examples==

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

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

==References==

http://www.physics.byu.edu/faculty/rees/220/book/Lesson8.pdf

[[Category: Maxwell's Equations]]

The Differential Form of Ampere's Law

2015-12-06T02:48:04Z

Jpetroni3:

Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativistic retardation, a term for how changes in magnetic and electric fields propagate at the speed of light so they cannot be measured instantly. Typically this is not an issue if the particles are moving much slower than the speed of light because although these physical laws are technically incorrect, the margin of error is so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

==Curl==
To have a model that is consistent with the theory of relativity, the property of a magnetic field called the "curl" must be utilized. The curl is the path integral of magnetic field per unit area, in the limit as the area goes to zero. This is useful because its value is proportional to the current density at the same location and time so there is an established relationship. This is known as a local relationship because both are evaluated at the same place and time, making it relativisticly correct because it isn't effected by relativistic retardation.

===A Mathematical Model===

Definition of curl:
[[File:realdefofcurl.png]]

Gradient Operator:
[[File:otherways.png]]

===A Computational Model===

[[File:curltext.png]]

The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

==Examples==

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

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

==References==

http://www.physics.byu.edu/faculty/rees/220/book/Lesson8.pdf

[[Category: Maxwell's Equations]]

File:Realdefofcurl.png

2015-12-06T02:47:17Z

Jpetroni3:

The Differential Form of Ampere's Law

2015-12-06T02:41:13Z

Jpetroni3:

Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativistic retardation, a term for how changes in magnetic and electric fields propagate at the speed of light so they cannot be measured instantly. Typically this is not an issue if the particles are moving much slower than the speed of light because although these physical laws are technically incorrect, the margin of error is so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

==Curl==
To have a model that is consistent with the theory of relativity, the property of a magnetic field called the "curl" must be utilized. The curl is the path integral of magnetic field per unit area, in the limit as the area goes to zero. This is useful because its value is proportional to the current density at the same location and time so there is an established relationship. This is known as a local relationship because both are evaluated at the same place and time, making it relativisticly correct because it isn't effected by relativistic retardation.

===A Mathematical Model===

Definition of curl:
[[File:Defofcurl.png]]

Gradient Operator:
[[File:otherways.png]]

===A Computational Model===

[[File:curltext.png]]

The direction of curl is given by the right hand rule by putting your thumb in the direction of the current. The way your hand curls is the way the magnetic field curls.

==Examples==

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

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

==References==

http://www.physics.byu.edu/faculty/rees/220/book/Lesson8.pdf

[[Category: Maxwell's Equations]]

File:Otherways.png

2015-12-06T02:35:12Z

Jpetroni3:

File:Curltext.png

2015-12-06T02:34:51Z

Jpetroni3:

The Differential Form of Ampere's Law

2015-12-06T02:34:26Z

Jpetroni3:

Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativistic retardation, a term for how changes in magnetic and electric fields propagate at the speed of light so they cannot be measured instantly. Typically this is not an issue if the particles are moving much slower than the speed of light because although these physical laws are technically incorrect, the margin of error is so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

==Curl==
To have a model that is consistent with the theory of relativity, the property of a magnetic field called the "curl" must be utilized. The curl is the path integral of magnetic field per unit area, in the limit as the area goes to zero. This is useful because its value is proportional to the current density at the same location and time so there is an established relationship. This is known as a local relationship because both are evaluated at the same place and time, making it relativisticly correct because it isn't effected by relativistic retardation.

===A Mathematical Model===

Definition of curl:
[[File:Defofcurl.png]]

===A Computational Model===

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

==Examples==

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

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

==References==

http://www.physics.byu.edu/faculty/rees/220/book/Lesson8.pdf

[[Category:Maxwell's Equations]]

The Differential Form of Ampere's Law

2015-12-06T02:29:45Z

Jpetroni3:

Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativistic retardation, a term for how changes in magnetic and electric fields propagate at the speed of light so they cannot be measured instantly. Typically this is not an issue if the particles are moving much slower than the speed of light because although these physical laws are technically incorrect, the margin of error is so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

==Curl==
To have a model that is consistent with the theory of relativity, the property of a magnetic field called the "curl" must be utilized. The curl is the path integral of magnetic field per unit area, in the limit as the area goes to zero. This is useful because its value is proportional to the current density at the same location and time so there is an established relationship. This is known as a local relationship because both are evaluated at the same place and time, making it relativisticly correct because it isn't effected by relativistic retardation.

===A Mathematical Model===

Definition of curl:
[[File:Defofcurl.png]]

===A Computational Model===

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

==Examples==

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

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

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

File:Defofcurl.png

2015-12-06T02:28:30Z

Jpetroni3:

The Differential Form of Ampere's Law

2015-12-06T02:26:51Z

Jpetroni3:

Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativistic retardation, a term for how changes in magnetic and electric fields propagate at the speed of light so they cannot be measured instantly. Typically this is not an issue if the particles are moving much slower than the speed of light because although these physical laws are technically incorrect, the margin of error is so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

==Curl==
To have a model that is consistent with the theory of relativity, the property of a magnetic field called the "curl" must be utilized. The curl is the path integral of magnetic field per unit area, in the limit as the area goes to zero. This is useful because its value is proportional to the current density at the same location and time so there is an established relationship. This is known as a local relationship because both are evaluated at the same place and time, making it relativisticly correct because it isn't effected by relativistic retardation.

===A Mathematical Model===

Definition of curl:
[[File:Example.jpg]]

===A Computational Model===

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

==Examples==

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

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

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

The Differential Form of Ampere's Law

2015-12-06T01:03:24Z

Jpetroni3: Created page with "Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativist..."

Many physical laws taught in Physics I and II are only correct at non-relativistic speeds (where the speed is much less than the speed of light). This is caused by relativistic retardation, a term for how changes in magnetic and electric fields propagate at the speed of light so they cannot be measured instantly. Typically this is not an issue if the particles are moving much slower than the speed of light because although these physical laws are technically incorrect, the margin of error is so small that it is irrelevant. As particles approach speeds close to the speed of light these differences can become significant and methods for finding electric or magnetic fields (such as the Biot-Savart law) are no longer accurate. This is not true for Ampere's Law which makes it useful for problems involving particles moving at near light speeds.

==Curl==
To have a model that is consistent with the theory of relativity, the property of a magnetic field called the "curl" must be utilized. The curl is the path integral of magnetic field per unit area, in the limit as the area goes to zero. This is useful because its value is proportional to the current density at the same location and time so there is an established relationship.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

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

==Examples==

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

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

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

Main Page

2015-12-06T00:31:57Z

Jpetroni3: /* Maxwell's Equations */

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

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

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

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

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

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Detecting Interactions]]
*[[Escape Velocity]]
*[[Fundamental Interactions]]
*[[Determinism]]
*[[System & Surroundings]]
*[[Free Body Diagram]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Conservation of Energy]]
*[[Conservation of Charge]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
*[[Center of Mass]]
*[[Reaction Time]]
*[[Time Dilation]]
*[[Pauli exclusion principle]]
</div>
</div>

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

===Modeling with 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]]
</div>
</div>

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

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Einstein's Theory of General Relativity]]
*[[Quantum Theory]]
*[[Maxwell's Electromagnetic Theory]]
*[[Atomic Theory]]
*[[String Theory]]
*[[Elementary Particles and Particle Physics Theory]]
*[[Law of Gravitation]]
*[[Newton's Laws]]
*[[Higgs field]]
*[[Supersymmetry]]
</div>
</div>

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

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Alexei Alexeyevich Abrikosov]]
*[[Christian Doppler]]
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Joseph Henry]]
*[[Michael Faraday]]
*[[J.J. Thomson]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]

*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[Count Alessandro Volta]]
*[[Josiah Willard Gibbs]]
*[[Richard Phillips Feynman]]
*[[Sir David Brewster]]
*[[Daniel Bernoulli]]
*[[William Thomson]]
*[[Leonhard Euler]]
*[[Robert Fox Bacher]]
*[[Stephen Hawking]]
*[[Amedeo Avogadro]]
*[[Wilhelm Conrad Roentgen]]
*[[Pierre Laplace]]
*[[Thomas Edison]]
*[[Hendrik Lorentz]]
*[[Jean-Baptiste Biot]]
*[[Lise Meitner]]
*[[Lisa Randall]]
*[[Felix Savart]]
*[[Heinrich Lenz]]
*[[Max Born]]
*[[Archimedes]]
*[[Jean Baptiste Biot]]
*[[Carl Sagan]]
*[[Eugene Wigner]]
*[[Marie Curie]]
*[[Pierre Curie]]
*[[Werner Heisenberg]]
*[[Johannes Diderik van der Waals]]
*[[Louis de Broglie]]
*[[Aristotle]]
*[[Émilie du Châtelet]]
*[[Blaise Pascal]]
*[[Siméon Denis Poisson]]
*[[Benjamin Franklin]]
*[[James Chadwick]]
*[[Henry Cavendish]]
*[[Thomas Young]]
*[[James Prescott Joule]]
*[[John Bardeen]]
*[[Leo Baekeland]]
*[[Alhazen]]
*[[Willebrord Snell]]
*[[Fritz Walther Meissner]]
*[[Johannes Kepler]]
*[[Johann Wilhelm Ritter]]
*[[Philipp Lenard]]
*[[Robert A. Millikan]]
*[[Joseph Louis Gay-Lussac]]
*[[Guglielmo Marconi]]
*[[William Lawrence Bragg]]
*[[Robert Goddard]]
*[[Léon Foucault]]
*[[Henri Poincaré]]
*[[Steven Weinberg]]
*[[Arthur Compton]]
*[[Pythagoras of Samos]]
*[[Subrahmanyan Chandrasekhar]]
*[[Wilhelm Eduard Weber]]
*[[Edmond Becquerel]]
*[[Joseph Rotblat]]
*[[Carl David Anderson]]
*[[Hermann von Helmholtz]]
*[[Nicolas Leonard Sadi Carnot]]
*[[Wallace Carothers]]
*[[David J. Wineland]]
*[[Rudolf Clausius]]
*[[Edward L. Norton]]
*[[Shuji Nakamura]]
*[[Pierre Laplace Pt. 2]]
*[[William B. Shockley]]
*[[Osborne Reynolds]]
*[[Alexander Graham Bell]]
*[[Hans Bethe]]
*[[Erwin Schrodinger]]
*[[Wolfgang Pauli]]
*[[Paul Dirac]]
*[[Bill Nye]]
*[[Arnold Sommerfeld]]

*[[James Franck]]
*[[Chen-Ning Yang]]
*[[Albert A. Micheleson & Edward W. Morley]]
</div>
</div>

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

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Relative Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]
*[[Heat Capacity]]
*[[Specific Heat]]
*[[Wavelength]]
*[[Conductivity]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Inertia]]
*[[Non-Newtonian Fluids]]
*[[Ferrofluids]]
*[[Color]]
*[[Temperature]]
*[[Plasma]]
</div>
</div>

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

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Static Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
* [[Speed of Sound in Solids]]
* [[Iterative Prediction of Spring-Mass System]]
</div>
</div>

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

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* [[Conservation of Momentum]]
* [[Predicting Change in multiple dimensions]]
* [[Derivation of the Momentum Principle]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Projectile Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
* [[Analytical Prediction]]
* [[Newton's Laws and Linear Momentum]]
* [[Net Force]]
* [[Center of Mass]]
* [[Momentum at High Speeds]]
* [[Change in Momentum in Time for Curving Motion]]
* [[Momentum with respect to external Forces]]
</div>
</div>

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

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Moment of Inertia for a cylinder]]
* [[Rotation]]
* [[Torque]]
* [[Systems with Zero Torque]]
* [[Systems with Nonzero Torque]]
* [[Torque vs Work]]
* [[Angular Impulse]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Angular Momentum of Multiparticle Systems]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]
* [[Angular Momentum Compared to Linear Momentum]]
*[[Torque 2]]

</div>
</div>

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

===Energy===
<div class="mw-collapsible-content">
*[[The Photoelectric Effect]]
*[[Photons]]
*[[The Energy Principle]]
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
**[[Potential Energy for a Magnetic Dipole]]
**[[Potential Energy of a Multiparticle System]]
*[[Work]]
**[[Work Done By A Nonconstant Force]]
*[[Work and Energy for an Extended System]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power (Mechanical)]]
*[[Transformation of Energy]]

*[[Energy Graphs]]
**[[Energy graphs and the Bohr model]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
**[[Spontaneous Photon Emission]]
*[[Path Independence of Electric Potential]]
*[[Energy in a Circuit]]
*[[The Photovoltaic Effect]]
</div>
</div>

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

===Collisions===
<div class="mw-collapsible-content">
[[File:opener.png]]

*[[Collisions]]
Collisions are events that happen very frequently in our day-to-day world. In the realm of Physics, a collision is defined as any sort of process in which before and after a short time interval there is little interaction, but during that short time interval there are large interactions. When looking at collisions, it is first important to understand two very important principles: the Momentum Principle and the Energy Principle. Both principles serve use when talking of collisions because they provide a way in which to analyze these collisions. Collisions themselves can be categorized into 3 main different types: elastic collisions, inelastic collisions, maximally inelastic collisions. All 3 collisions will get touched on in more detail further on.
[[File:pe.png]]

*[[Elastic Collisions]]
A collision is deemed "elastic" when the internal energy of the objects in the system does not change (in other words, change in internal energy equals 0). Because in an elastic collision no kinetic energy is converted over to internal energy, in any elastic collision Kfinal always equals Kinitial.
[[File:Elco.png]]

*[[Inelastic Collisions]]
A collision is said to be "inelastic" when it is not elastic; therefore, an inelastic collision is an interaction in which some change in internal energy occurs between the colliding objects (in other words, change in internal energy does not equal 0). Examples of such changes that occur between colliding objects include, but are not limited to, things like they get hot, or they vibrate/rotate, or they deform. Because some of the kinetic energy is converted to internal energy during an inelastic collision, Kfinal does not equal Kinitial.
There are a few characteristics that one can search for when identifying inelasticity. These indications include things such as:
*Objects stick together after the collision
*An object is in an excited state after the collision
*An object becomes deformed after the collision
*The objects become hotter after the collision
*There exists more vibration or rotation after the collision
[[File:inve.gif]]

*[[Maximally Inelastic Collision]]
Maximally inelastic collisions, also known as "sticking collisions", are the most extreme kinds of inelastic collisions. Just as its secondary name implies, a maximally inelastic collision is one in which the colliding objects stick together creating maximum dissipation. This does not automatically mean that the colliding objects stop dead because the law of conservation of momentum. In a maximally inelastic collision, the remaining kinetic energy is present only because total momentum can't change and must be conserved.
[[File:inel.gif]]

*[[Head-on Collision of Equal Masses]]
The easiest way to understand this phenomenon is to look at it through an example. In this case, we can analyze it through the common game of billiards. Taking the two, equally massed billiard balls as the system, we can neglect the small frictional force exerted on the balls by the billiard table. The Momentum Principle states that in this head-on collision of billiard balls the total final momentum in the x direction must equal the total initial momentum. However, this alone does not give us the knowledge to know how the momentum will be divided up between the two balls. Considering the law of conservation of energy, we can more accurately depict what will happen. This will also allow for one to identify what kind of collision occurs (elastic, inelastic, or maximally inelastic). It is important to know that head-on collisions of equal masses do not have a definite type of collision associated with it.
[[File:momentum-real-life-applications-2895.jpg]] [[File:8ball.gif]]

*[[Head-on Collision of Unequal Masses]]
Just as with head-on collisions of equal masses, it is easy to understand head-on collisions of unequal masses by viewing it through an example. Let's take for example two balls of unequal masses like a ping-pong ball and a bowling ball. For the purpose of this example (so as to allow for no friction and no other significant external forces), let's imagine these objects collide in outer space inside an orbiting spacecraft. If there were to be a collision between the two, what would one expect to happen? One could expect to see the ping-pong ball collide with the bowling ball and bounce straight back with a very small change of speed. What one might not expect as much is that the bowling ball also moves, just very slowly. Again, this can all be explained through the conservation of momentum and the conservation of energy.
[[File:mi3e.jpg]]

*[[Frame of Reference]]
In the world of Physics, a frame of reference is the perspective from which a system is observed. It can be stationary or sometimes it can even be moving at a constant velocity. In some rare cases, the frame of reference moves at an nonconstant velocity and is deemed "noninertial" meaning the basic laws of physics do not apply. Continuing with the trend of examples, pretend you are at a train station observing trains as they pass by. From your stationary frame of reference, you observe that the passenger on the train is moving at the same velocity as the train. However, from a moving frame of reference, say from the eyes of the train conductor, he would view the train passengers as "anchored" to the train.
[[File:train.png]]

*[[Scattering: Collisions in 2D and 3D]]
Experiments that involve scattering are often used to study the structure and behavior of atoms, nuclei, as well as of other small particles. In an experiment like such, a beam of particles collides with other particles. If it is an atomic or nuclear collision, we are unable to observe the curving trajectories inside the tiny region of interaction. Instead, we can only truly observe the trajectories before and after the collision. This is only possible because the particles are at a farther distance apart and have a very weak mutual interaction; this essentially means that the particles are moving almost in a straight line. A good example which demonstrates scattering is the collision between an alpha particle (the nucleus of a helium atom) and the nucleus of a gold atom. One will understand this phenomenon more in depth after first understanding the Rutherford Experiment which will get touched on later.

*[[Rutherford Experiment and Atomic Collisions]]
In England in 1911, a famous experiment was performed by a group of scientists led by Mr. Ernest Rutherford. This experiment, later known as "The Rutherford Experiment", was a tremendous breakthrough for its time because it led to the discovery of the nucleus inside the atom. Rutherford's experiment involved the scattering of a high-speed alpha particle (now known as a helium nuclei - 2 protons and 2 neutrons) as it was shot at a thin gold foil (consisting of a nuclei with 79 protons and 118 neutrons). In the experiment, Rutherford and his team discovered that the velocity of the alpha particles was not high enough to allow the particles to make actual contact with the gold nucleus. Although they never actually made contact, it is still deemed a collision because there exists a sizable force between the alpha particle and the gold nucleus over a very short period of time. In conclusion, we say the alpha particle is "scattered" by its interaction with the nucleus of a gold atom and experiments like such are called "scattering" experiments.
[[File:ruthef.jpg]]

*[[Coefficient of Restitution]]
The coefficient of restitution is a measure of the elasticity in a collision. It is the ratio of the differences in velocities before and after the collision. The coefficient is evaluated by taking the difference in the velocities of the colliding objects after the collision and dividing by the difference in the velocities of the colliding objects before the collision.

All of the following information was collected from the Matter and Interactions 4th Edition physics textbook. The book is cited as follows...

Chabay, Ruth W., and Bruce A. Sherwood. "Chapter 10: Collisions." Matter & Interactions. Fourth Edition ed. Wiley, 2015. 383-409. Print.

</div>
</div>

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

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[integrating the spherical shell]]
** [[Charged Cylinder]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Charge Density]]
*[[Superposition Principle]]
*[[Electric Potential]]
**[[Potential Difference Path Independence]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Potential Difference at One Location]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
**[[Energy Density and Electric Field]]
** [[Systems of Charged Objects]]
*[[Electric Force]]
*[[Polarization]]
**[[Polarization of an Atom]]
**[[Charged Conductor and Charged Insulator]]
*[[Charge Motion in Metals]]
*[[Charge Transfer]]
**[[Electrostatic Discharge]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Magnetic Field of a Long Straight Wire]]
**[[Magnetic Field of a Loop]]
**[[Magnetic Field of a Solenoid]]
**[[Bar Magnet]]
**[[Magnetic Dipole Moment]]
***[[Stern-Gerlach Experiment]]
**[[Magnetic Torque]]
**[[Magnetic Force]]
***[[Applying Magnetic Force to Currents]]
**[[Earth's Magnetic Field]]
**[[Atomic Structure of Magnets]]
*[[Combining Electric and Magnetic Forces]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Electric Motors]]
**[[Solenoid Applications]]
</div>
</div>

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

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Charging and Discharging a Capacitor]]
*[[Work and Power In A Circuit]]
*[[Thin and Thick Wires]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Resistivity]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
**[[AC]]
*[[Ohm's Law]]
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[RC]]
*[[Parallel Circuits vs. Series Circuits]]
*[[AC vs DC]]
**[[Rectification (Converting AC to DC)]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit]]
*[[Circular Loop of Wire]]
*[[Current in a RL Circuit]]
*[[RL Circuit]]
*[[Feedback]]
*[[Transformers (Circuits)]]
*[[Resistors and Conductivity]]
*[[Semiconductor Devices]]
*[[Insulators]]
*[[Voltage]]
</div>
</div>

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

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
***[[Examples of Flux Through Surfaces and Objects]]
**[[Magnetic Fields]]
**[[Proof of Gauss's Law]]
*[[Ampere's 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]]
**[[The Differential Form of Ampere's Law]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers (Physics)]]
***[[Energy Density]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
**[[Lenz's Rule]]
**[[Motional Emf using Faraday's Law]]
*[[Ampere-Maxwell Law]]
*[[Superconductors]]
**[[Meissner effect]]
</div>
</div>

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

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
*[[Lenses]]
*[[Energy and Momentum Analysis in Radiation]]
**[[Poynting Vector]]
*[[Electromagnetic Propagation]]
**[[Wavelength and Frequency]]
*[[Snell's Law]]
*[[Effects of Radiation on Matter]]
*[[Light Propagation Through a Medium]]
*[[Light Scaterring: Why is the Sky Blue]]
*[[Light Refraction: Bending of light]]
*[[Cherenkov Radiation]]
*[[Rayleigh Effect]]
*[[Image Formation]]
</div>
<div class="toccolours mw-collapsible mw-collapsed">

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

===Waves===
<div class="mw-collapsible-content">
*[[Bragg's Law]]
*[[Standing waves]]
*[[Gravitational waves]]
*[[Plasma waves]]
*[[Wave-Particle Duality]]
*[[Electromagnetic Spectrum]]
*[[Color Light Wave]]
*[[The Wave Equation]]
*[[Pendulum Motion]]
*[[Transverse and Longitudinal Waves]]
*[[Planck's Relation]]
*[[interference]]
*[[Polarization of Waves]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Real Life Applications of Electromagnetic Principles===
<div class="mw-collapsible-content">
*[[Electromagnetic Junkyard Cranes]]
*[[Maglev Trains]]
*[[Spark Plugs]]
*[[Metal Detectors]]
*[[Speakers]]
*[[Radios]]
*[[Ampullae of Lorenzini]]
*[[Electrocytes]]
*[[Generator]]
*[[Using Capacitors to Measure Fluid Level]]
*[[Cyclotron]]
*[[Railgun]]
*[[Magnetic Resonance Imaging]]
*[[Electric Eels]]
*[[Windshield Wipers]]
*[[Galvanic Cells]]
*[[Magnetoreception]]
*[[Memory Storage Devices]]

</div>
</div>

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

===Optics===
<div class="mw-collapsible-content">
*[[Mirrors]]
*[[Refraction]]
*[[Quantum Properties of Light]]
*[[Lasers]]
*[[Lenses]]

</div>
</div>

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