Physics Book - User contributions [en]

Potential Energy for a Magnetic Dipole

2015-12-03T23:01:47Z

Thenderlong3:

Page Claimed by Thomas Henderlong

==The Main Idea==
If a magnetic dipole is allowed to pivot freely without any outside forces, then it will match it's alignment with the applied magnetic field. The system favors a state of lower potential so the aligned magnetic dipole is associated with a lower potential energy in the applied magnetic field. Think of how a magnets interact with each other when inched closer to each other. They'll align in a way so that the north and south ends point in the same direction or have the north end of one magnet touching the south end of the other magnet (state of lowest potential).
===A Mathematical Model===

By calculating how much work it takes to move a magnetic dipole out of alignment, we can determine the increased potential energy for that dipole.

Let's take a look at a rectangular circuit on a horizontal axle in a magnetic field pictured below.

[[File:physics_potential_energy2.png]]

Now let's look at this system from the side.

[[File:physics_potential_energy3.png]]

We can see that the magnetic force acting on the circuit pushes the circuit out horizontally. The magnetic force is trying to make the circuit's magnetic dipole moment, μ, point in the same direction of the magnetic field. We can measure the amount of work it takes to move the circuit from an initial angle of θ<sub>i</sub> to a final angle of θ<sub>f</sub>. The work done by pushing the circuit out of alignment changes the magnetic potential energy of the system.

As we push the circuit to rotate a angle of dθ around it's horizontal axis, the total distance that the force is exerted on one side of the circuit is equal to (h/2)*dθ. Keep in mind though that we are exerted force on both sides of the circuit. In the diagram this is indicated as Force by Us. We will have to determine the total amount of work done by using an integral because the force exerted depends on the value of θ and θ increases as we push the circuit more and more out of alignment.

<p><math>Work = ΔU_m = \int\limits_{θ_i}^{θ_f}\ 2IwBsinθ(\frac{h}{2}dθ) = IwhB \int\limits_{θ_i}^{θ_f}\ sinθ dθ </math>
</p>
Where <math>IwBsinθ</math> is the perpendicular force exerted on only one side of the circuit. We are pushing on both sides so we multiply that by 2. <math>(\frac{h}{2}dθ)</math> is the distance that the force is exerted.
<p><math>ΔU_m = IwhB[-cosθ]_{θ_i}^{θ_f} = -IwhB[cosθ_f - cosθ_i]</math>
</p>

<p>
<math>
ΔU_m = Δ(-μBcosθ)</math> since <math>μ = IA = Iwh
</math>
</p>
so the potential energy for a dipole is
<math>
U_m = -μBcosθ
</math>.

Potential energy for a dipole can also be written as the dot product <math>U_m = -\overrightarrow{μ} \bullet \overrightarrow{B}\ </math>.

==Examples==

Let's now envision two magnets interacting with each other.

Knowing what we know now about the potential energy of a magnetic dipole, we can see why magnets move each other. Systems tend to favor states of low potential energy so when a magnet is inched closer to another magnet, their dipoles will align so that the potential energy takes on a negative value (state with the lowest potential energy). This action is illustrated below.

[[File:physics_potential_energy4.png]]

As the magnet on the left is held and inched closer to the magnet on the right, the magnet on the right will turn so that the magnetic dipoles align with each other.

----

Now let's look at the dipole moments and the magnetic field below. How would we go about ranking the potential energy from of each system from greatest to smallest.

[[File:physics_potential_energy5.png]]

When finding the potential energy keep in mind that there is a negative sign in front of the dot product of dipole moment and magnetic field. That being said System 4 would have the largest potential energy because the dot product of the two vectors would yield a negative value in the y-component. This system would be very unstable and if we were to move the dipole moment ever so slightly, it would immediately turn to point the same exact way as the magnetic field. System 1 & 2 would have the same potential energy of 0. When finding the dot product of System 3, we would get a positive value, but with the negative sign in the front of the formula, we have a negative potential energy. So system 3 shows the most stable and desired state. So the ranking of the potential energies would be 4 > 1 = 2 > 3.

== See also ==

Here are some other resources that may help.
<p>[http://www.physicsbook.gatech.edu/Potential_Energy Potential Energy]</p>
<p>[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html Magnetic Forces]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Dipole_Moment Magnetic Dipole Moment]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Field Magnetic Field]</p>
<p>[http://www.physicsbook.gatech.edu/Work Work]</p>

== References ==
Chabay, Ruth, and Bruce Sherwood. "Magnetic Force." Matter & Interactions. Fourth ed. Vol. 2. Hoboken: John Wiler & Sons, 2015. 829-833. Print

Potential Energy for a Magnetic Dipole

2015-12-03T22:46:13Z

Thenderlong3: /* References */

Page Claimed by Thomas Henderlong

==The Main Idea==
If a magnetic dipole is allowed to pivot freely without any outside forces, then it will match it's alignment with the applied magnetic field. The system favors a state of lower potential so the aligned magnetic dipole is associated with a lower potential energy in the applied magnetic field. Think of how a magnets interact with each other when inched closer to each other. They'll align in a way so that the north and south ends point in the same direction or have the north end of one magnet touching the south end of the other magnet (state of lowest potential).
===A Mathematical Model===

By calculating how much work it takes to move a magnetic dipole out of alignment, we can determine the increased potential energy for that dipole.

Let's take a look at a rectangular circuit on a horizontal axle in a magnetic field pictured below.

[[File:physics_potential_energy2.png]]

Now let's look at this system from the side.

[[File:physics_potential_energy3.png]]

We can see that the magnetic force acting on the circuit pushes the circuit out horizontally. The magnetic force is trying to make the circuit's magnetic dipole moment, μ, point in the same direction of the magnetic field. We can measure the amount of work it takes to move the circuit from an initial angle of θ<sub>i</sub> to a final angle of θ<sub>f</sub>. The work done by pushing the circuit out of alignment changes the magnetic potential energy of the system.

As we push the circuit to rotate a angle of dθ around it's horizontal axis, the total distance that the force is exerted on one side of the circuit is equal to (h/2)*dθ. Keep in mind though that we are exerted force on both sides of the circuit. In the diagram this is indicated as Force by Us. We will have to determine the total amount of work done by using an integral because the force exerted depends on the value of θ and θ increases as we push the circuit more and more out of alignment.

<p><math>Work = ΔU_m = \int\limits_{θ_i}^{θ_f}\ 2IwBsinθ(\frac{h}{2}dθ) = IwhB \int\limits_{θ_i}^{θ_f}\ sinθ dθ </math>
</p>
Where <math>IwBsinθ</math> is the perpendicular force exerted on only one side of the circuit. We are pushing on both sides so we multiply that by 2. <math>(\frac{h}{2}dθ)</math> is the distance that the force is exerted.
<p><math>ΔU_m = IwhB[-cosθ]_{θ_i}^{θ_f} = -IwhB[cosθ_f - cosθ_i]</math>
</p>

<p>
<math>
ΔU_m = Δ(-μBcosθ)</math> since <math>μ = IA = Iwh
</math>
</p>
so the potential energy for a dipole is
<math>
U_m = -μBcosθ
</math>.

Potential energy for a dipole can also be written as the dot product <math>U_m = -\overrightarrow{μ} \bullet \overrightarrow{B}\ </math>.

==Examples==

Let's now envision two magnets interacting with each other.

Knowing what we know now about the potential energy of a magnetic dipole, we can see why magnets move each other. Systems tend to favor states of low potential energy so when a magnet is inched closer to another magnet, their dipoles will align so that the potential energy takes on a negative value (state with the lowest potential energy). This action is illustrated below.

[[File:physics_potential_energy4.png]]

As the magnet on the left is held and inched closer to the magnet on the right, the magnet on the right will turn so that the magnetic dipoles align with each other.

----

Now let's look at the dipole moments and the magnetic field below. How would we go about ranking the potential energy from of each system from greatest to smallest.

[[File:physics_potential_energy5.png]]

When finding the potential energy keep in mind that there is a negative sign in front of the dot product of dipole moment and magnetic field. That being said System 4 would have the largest potential energy because the dot product of the two vectors would yield a negative value in the y-component. This system would be very unstable and if we were to move the dipole moment ever so slightly, it would immediately turn to point the same exact way as the magnetic field. System 1 & 2 would have the same potential energy of 0. When finding the dot product of System 3, we would get a positive value, but with the negative sign in the front of the formula, we have a negative potential energy. So system 3 shows the most stable and desired state. So the ranking of the potential energies would be 4 > 1 = 2 > 3.

== See also ==

Here are some other resources that may help.
<p>[http://www.physicsbook.gatech.edu/Potential_Energy Potential Energy]</p>
<p>[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html Magnetic Forces]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Dipole_Moment Magnetic Dipole Moment]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Field Magnetic Field]</p>

== References ==
Chabay, Ruth, and Bruce Sherwood. "Magnetic Force." Matter & Interactions. Fourth ed. Vol. 2. Hoboken: John Wiler & Sons, 2015. 829-833. Print

Potential Energy for a Magnetic Dipole

2015-12-03T21:53:28Z

Thenderlong3:

Page Claimed by Thomas Henderlong

==The Main Idea==
If a magnetic dipole is allowed to pivot freely without any outside forces, then it will match it's alignment with the applied magnetic field. The system favors a state of lower potential so the aligned magnetic dipole is associated with a lower potential energy in the applied magnetic field. Think of how a magnets interact with each other when inched closer to each other. They'll align in a way so that the north and south ends point in the same direction or have the north end of one magnet touching the south end of the other magnet (state of lowest potential).
===A Mathematical Model===

By calculating how much work it takes to move a magnetic dipole out of alignment, we can determine the increased potential energy for that dipole.

Let's take a look at a rectangular circuit on a horizontal axle in a magnetic field pictured below.

[[File:physics_potential_energy2.png]]

Now let's look at this system from the side.

[[File:physics_potential_energy3.png]]

We can see that the magnetic force acting on the circuit pushes the circuit out horizontally. The magnetic force is trying to make the circuit's magnetic dipole moment, μ, point in the same direction of the magnetic field. We can measure the amount of work it takes to move the circuit from an initial angle of θ<sub>i</sub> to a final angle of θ<sub>f</sub>. The work done by pushing the circuit out of alignment changes the magnetic potential energy of the system.

As we push the circuit to rotate a angle of dθ around it's horizontal axis, the total distance that the force is exerted on one side of the circuit is equal to (h/2)*dθ. Keep in mind though that we are exerted force on both sides of the circuit. In the diagram this is indicated as Force by Us. We will have to determine the total amount of work done by using an integral because the force exerted depends on the value of θ and θ increases as we push the circuit more and more out of alignment.

<p><math>Work = ΔU_m = \int\limits_{θ_i}^{θ_f}\ 2IwBsinθ(\frac{h}{2}dθ) = IwhB \int\limits_{θ_i}^{θ_f}\ sinθ dθ </math>
</p>
Where <math>IwBsinθ</math> is the perpendicular force exerted on only one side of the circuit. We are pushing on both sides so we multiply that by 2. <math>(\frac{h}{2}dθ)</math> is the distance that the force is exerted.
<p><math>ΔU_m = IwhB[-cosθ]_{θ_i}^{θ_f} = -IwhB[cosθ_f - cosθ_i]</math>
</p>

<p>
<math>
ΔU_m = Δ(-μBcosθ)</math> since <math>μ = IA = Iwh
</math>
</p>
so the potential energy for a dipole is
<math>
U_m = -μBcosθ
</math>.

Potential energy for a dipole can also be written as the dot product <math>U_m = -\overrightarrow{μ} \bullet \overrightarrow{B}\ </math>.

==Examples==

Let's now envision two magnets interacting with each other.

Knowing what we know now about the potential energy of a magnetic dipole, we can see why magnets move each other. Systems tend to favor states of low potential energy so when a magnet is inched closer to another magnet, their dipoles will align so that the potential energy takes on a negative value (state with the lowest potential energy). This action is illustrated below.

[[File:physics_potential_energy4.png]]

As the magnet on the left is held and inched closer to the magnet on the right, the magnet on the right will turn so that the magnetic dipoles align with each other.

----

Now let's look at the dipole moments and the magnetic field below. How would we go about ranking the potential energy from of each system from greatest to smallest.

[[File:physics_potential_energy5.png]]

When finding the potential energy keep in mind that there is a negative sign in front of the dot product of dipole moment and magnetic field. That being said System 4 would have the largest potential energy because the dot product of the two vectors would yield a negative value in the y-component. This system would be very unstable and if we were to move the dipole moment ever so slightly, it would immediately turn to point the same exact way as the magnetic field. System 1 & 2 would have the same potential energy of 0. When finding the dot product of System 3, we would get a positive value, but with the negative sign in the front of the formula, we have a negative potential energy. So system 3 shows the most stable and desired state. So the ranking of the potential energies would be 4 > 1 = 2 > 3.

== See also ==

Here are some other resources that may help.
<p>[http://www.physicsbook.gatech.edu/Potential_Energy Potential Energy]</p>
<p>[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html Magnetic Forces]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Dipole_Moment Magnetic Dipole Moment]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Field Magnetic Field]</p>

== References ==

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

Potential Energy for a Magnetic Dipole

2015-12-03T20:38:23Z

Thenderlong3: /* Examples */

Page Claimed by Thomas Henderlong

==The Main Idea==
If a magnetic dipole is allowed to pivot freely without any outside forces, then it will match it's alignment with the applied magnetic field. The system favors a state of lower potential so the aligned magnetic dipole is associated with a lower potential energy in the applied magnetic field. Think of how a magnets interact with each other when inched closer to each other. They'll align in a way so that the north and south ends point in the same direction or have the north end of one magnet touching the south end of the other magnet (state of lowest potential).
===A Mathematical Model===

By calculating how much work it takes to move a magnetic dipole out of alignment, we can determine the increased potential energy for that dipole.

Let's take a look at a rectangular circuit on a horizontal axle in a magnetic field pictured below.

[[File:physics_potential_energy2.png]]

Now let's look at this system from the side.

[[File:physics_potential_energy3.png]]

We can see that the magnetic force acting on the circuit pushes the circuit out horizontally. The magnetic force is trying to make the circuit's magnetic dipole moment, μ, point in the same direction of the magnetic field. We can measure the amount of work it takes to move the circuit from an initial angle of θ<sub>i</sub> to a final angle of θ<sub>f</sub>. The work done by pushing the circuit out of alignment changes the magnetic potential energy of the system.

As we push the circuit to rotate a angle of dθ around it's horizontal axis, the total distance that the force is exerted on one side of the circuit is equal to (h/2)*dθ. Keep in mind though that we are exerted force on both sides of the circuit. In the diagram this is indicated as Force by Us. We will have to determine the total amount of work done by using an integral because the force exerted depends on the value of θ and θ increases as we push the circuit more and more out of alignment.

<p><math>Work = ΔU_m = \int\limits_{θ_i}^{θ_f}\ 2IwBsinθ(\frac{h}{2}dθ) = IwhB \int\limits_{θ_i}^{θ_f}\ sinθ dθ </math>
</p>
Where <math>IwBsinθ</math> is the perpendicular force exerted on only one side of the circuit. We are pushing on both sides so we multiply that by 2. <math>(\frac{h}{2}dθ)</math> is the distance that the force is exerted.
<p><math>ΔU_m = IwhB[-cosθ]_{θ_i}^{θ_f} = -IwhB[cosθ_f - cosθ_i]</math>
</p>

<p>
<math>
ΔU_m = Δ(-μBcosθ)</math> since <math>μ = IA = Iwh
</math>
</p>
so the potential energy for a dipole is
<math>
U_m = -μBcosθ
</math>.

Potential energy for a dipole can also be written as the dot product <math>U_m = -\overrightarrow{μ} \bullet \overrightarrow{B}\ </math>.

==Examples==

Let's now envision two magnets interacting with each other.

Knowing what we know now about the potential energy of a magnetic dipole, we can see why magnets move each other. Systems tend to favor states of low potential energy so when a magnet is inched closer to another magnet, their dipoles will align so that the potential energy takes on a negative value (state with the lowest potential energy). This action is illustrated below.

[[File:physics_potential_energy4.png]]

As the magnet on the left is held and inched closer to the magnet on the right, the magnet on the right will turn so that the magnetic dipoles align with each other.

----

Now let's look at the dipole moments and the magnetic field below. How would we go about ranking the potential energy from of each system from greatest to smallest.

[[File:physics_potential_energy5.png]]

When finding the potential energy keep in mind that there is a negative sign in front of the dot product of dipole moment and magnetic field. That being said System 4 would have the largest potential energy because the dot product of the two vectors would yield a negative value in the y-component. This system would be very unstable and if we were to move the dipole moment ever so slightly, it would immediately turn to point the same exact way as the magnetic field. System 1 & 2 would have the same potential energy of 0. When finding the dot product of System 3, we would get a positive value, but with the negative sign in the front of the formula, we have a negative potential energy. So system 3 shows the most stable and desired state. So the ranking of the potential energies would be 4 > 1 = 2 > 3.

==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 ==

Here are some other resources that may help.
<p>[http://www.physicsbook.gatech.edu/Potential_Energy Potential Energy]</p>
<p>[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html Magnetic Forces]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Dipole_Moment Magnetic Dipole Moment]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Field Magnetic Field]</p>

===Further reading===

Books, Articles or other print media on this topic

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

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

File:Physics potential energy5.png

2015-12-03T20:37:39Z

Thenderlong3: Thenderlong3 uploaded a new version of "File:Physics potential energy5.png"

File:Physics potential energy5.png

2015-12-03T20:36:08Z

Thenderlong3: Thenderlong3 uploaded a new version of "File:Physics potential energy5.png"

File:Physics potential energy5.png

2015-12-03T20:35:11Z

Thenderlong3:

Potential Energy for a Magnetic Dipole

2015-12-03T20:34:57Z

Thenderlong3: /* Examples */

Page Claimed by Thomas Henderlong

==The Main Idea==
If a magnetic dipole is allowed to pivot freely without any outside forces, then it will match it's alignment with the applied magnetic field. The system favors a state of lower potential so the aligned magnetic dipole is associated with a lower potential energy in the applied magnetic field. Think of how a magnets interact with each other when inched closer to each other. They'll align in a way so that the north and south ends point in the same direction or have the north end of one magnet touching the south end of the other magnet (state of lowest potential).
===A Mathematical Model===

By calculating how much work it takes to move a magnetic dipole out of alignment, we can determine the increased potential energy for that dipole.

Let's take a look at a rectangular circuit on a horizontal axle in a magnetic field pictured below.

[[File:physics_potential_energy2.png]]

Now let's look at this system from the side.

[[File:physics_potential_energy3.png]]

We can see that the magnetic force acting on the circuit pushes the circuit out horizontally. The magnetic force is trying to make the circuit's magnetic dipole moment, μ, point in the same direction of the magnetic field. We can measure the amount of work it takes to move the circuit from an initial angle of θ<sub>i</sub> to a final angle of θ<sub>f</sub>. The work done by pushing the circuit out of alignment changes the magnetic potential energy of the system.

As we push the circuit to rotate a angle of dθ around it's horizontal axis, the total distance that the force is exerted on one side of the circuit is equal to (h/2)*dθ. Keep in mind though that we are exerted force on both sides of the circuit. In the diagram this is indicated as Force by Us. We will have to determine the total amount of work done by using an integral because the force exerted depends on the value of θ and θ increases as we push the circuit more and more out of alignment.

<p><math>Work = ΔU_m = \int\limits_{θ_i}^{θ_f}\ 2IwBsinθ(\frac{h}{2}dθ) = IwhB \int\limits_{θ_i}^{θ_f}\ sinθ dθ </math>
</p>
Where <math>IwBsinθ</math> is the perpendicular force exerted on only one side of the circuit. We are pushing on both sides so we multiply that by 2. <math>(\frac{h}{2}dθ)</math> is the distance that the force is exerted.
<p><math>ΔU_m = IwhB[-cosθ]_{θ_i}^{θ_f} = -IwhB[cosθ_f - cosθ_i]</math>
</p>

<p>
<math>
ΔU_m = Δ(-μBcosθ)</math> since <math>μ = IA = Iwh
</math>
</p>
so the potential energy for a dipole is
<math>
U_m = -μBcosθ
</math>.

Potential energy for a dipole can also be written as the dot product <math>U_m = -\overrightarrow{μ} \bullet \overrightarrow{B}\ </math>.

==Examples==

Let's now envision two magnets interacting with each other.

Knowing what we know now about the potential energy of a magnetic dipole, we can see why magnets move each other. Systems tend to favor states of low potential energy so when a magnet is inched closer to another magnet, their dipoles will align so that the potential energy takes on a negative value (state with the lowest potential energy). This action is illustrated below.

[[File:physics_potential_energy4.png]]

As the magnet on the left is held and inched closer to the magnet on the right, the magnet on the right will turn so that the magnetic dipoles align with each other.

Now let's look at the dipole moments and the magnetic field below. How would we go about ranking the potential energy from of each system from greatest to smallest.

[[File:physics_potential_energy5.png]]

When finding the potential energy keep in mind that there is a negative sign in front of the dot product of dipole moment and magnetic field. That being said System 4 would have the largest potential energy because the dot product of the two vectors would yield a negative value in the y-component. This system would be very unstable and if we were to move the dipole moment ever so slightly, it would immediately turn to point the same exact way as the magnetic field. System 1 & 2 would have the same potential energy of 0. When finding the dot product of System 3, we would get a positive value, but with the negative sign in the front of the formula, we have a negative potential energy. So system 3 shows the most stable and desired state. So the ranking of the potential energies would be 4 > 1 = 2 > 3.

==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 ==

Here are some other resources that may help.
<p>[http://www.physicsbook.gatech.edu/Potential_Energy Potential Energy]</p>
<p>[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html Magnetic Forces]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Dipole_Moment Magnetic Dipole Moment]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Field Magnetic Field]</p>

===Further reading===

Books, Articles or other print media on this topic

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

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

Potential Energy for a Magnetic Dipole

2015-12-03T20:22:39Z

Thenderlong3: /* A Mathematical Model */

Page Claimed by Thomas Henderlong

==The Main Idea==
If a magnetic dipole is allowed to pivot freely without any outside forces, then it will match it's alignment with the applied magnetic field. The system favors a state of lower potential so the aligned magnetic dipole is associated with a lower potential energy in the applied magnetic field. Think of how a magnets interact with each other when inched closer to each other. They'll align in a way so that the north and south ends point in the same direction or have the north end of one magnet touching the south end of the other magnet (state of lowest potential).
===A Mathematical Model===

By calculating how much work it takes to move a magnetic dipole out of alignment, we can determine the increased potential energy for that dipole.

Let's take a look at a rectangular circuit on a horizontal axle in a magnetic field pictured below.

[[File:physics_potential_energy2.png]]

Now let's look at this system from the side.

[[File:physics_potential_energy3.png]]

We can see that the magnetic force acting on the circuit pushes the circuit out horizontally. The magnetic force is trying to make the circuit's magnetic dipole moment, μ, point in the same direction of the magnetic field. We can measure the amount of work it takes to move the circuit from an initial angle of θ<sub>i</sub> to a final angle of θ<sub>f</sub>. The work done by pushing the circuit out of alignment changes the magnetic potential energy of the system.

As we push the circuit to rotate a angle of dθ around it's horizontal axis, the total distance that the force is exerted on one side of the circuit is equal to (h/2)*dθ. Keep in mind though that we are exerted force on both sides of the circuit. In the diagram this is indicated as Force by Us. We will have to determine the total amount of work done by using an integral because the force exerted depends on the value of θ and θ increases as we push the circuit more and more out of alignment.

<p><math>Work = ΔU_m = \int\limits_{θ_i}^{θ_f}\ 2IwBsinθ(\frac{h}{2}dθ) = IwhB \int\limits_{θ_i}^{θ_f}\ sinθ dθ </math>
</p>
Where <math>IwBsinθ</math> is the perpendicular force exerted on only one side of the circuit. We are pushing on both sides so we multiply that by 2. <math>(\frac{h}{2}dθ)</math> is the distance that the force is exerted.
<p><math>ΔU_m = IwhB[-cosθ]_{θ_i}^{θ_f} = -IwhB[cosθ_f - cosθ_i]</math>
</p>

<p>
<math>
ΔU_m = Δ(-μBcosθ)</math> since <math>μ = IA = Iwh
</math>
</p>
so the potential energy for a dipole is
<math>
U_m = -μBcosθ
</math>.

Potential energy for a dipole can also be written as the dot product <math>U_m = -\overrightarrow{μ} \bullet \overrightarrow{B}\ </math>.

==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 ==

Here are some other resources that may help.
<p>[http://www.physicsbook.gatech.edu/Potential_Energy Potential Energy]</p>
<p>[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html Magnetic Forces]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Dipole_Moment Magnetic Dipole Moment]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Field Magnetic Field]</p>

===Further reading===

Books, Articles or other print media on this topic

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

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

Potential Energy for a Magnetic Dipole

2015-12-03T20:13:29Z

Thenderlong3: /* A Mathematical Model */

Page Claimed by Thomas Henderlong

==The Main Idea==
If a magnetic dipole is allowed to pivot freely without any outside forces, then it will match it's alignment with the applied magnetic field. The system favors a state of lower potential so the aligned magnetic dipole is associated with a lower potential energy in the applied magnetic field. Think of how a magnets interact with each other when inched closer to each other. They'll align in a way so that the north and south ends point in the same direction or have the north end of one magnet touching the south end of the other magnet (state of lowest potential).
===A Mathematical Model===

By calculating how much work it takes to move a magnetic dipole out of alignment, we can determine the increased potential energy for that dipole.

Let's take a look at a rectangular circuit on a horizontal axle in a magnetic field pictured below.

[[File:physics_potential_energy2.png]]

Now let's look at this system from the side.

[[File:physics_potential_energy3.png]]

We can see that the magnetic force acting on the circuit pushes the circuit out horizontally. The magnetic force is trying to make the circuit's magnetic dipole moment, μ, point in the same direction of the magnetic field. We can measure the amount of work it takes to move the circuit from an initial angle of θ<sub>i</sub> to a final angle of θ<sub>f</sub>. The work done by pushing the circuit out of alignment changes the magnetic potential energy of the system.

As we push the circuit to rotate a angle of dθ around it's horizontal axis, the total distance that the force is exerted on one side of the circuit is equal to (h/2)*dθ. Keep in mind though that we are exerted force on both sides of the circuit. In the diagram this is indicated as Force by Us. We will have to determine the total amount of work done by using an integral because the force exerted depends on the value of θ and θ increases as we push the circuit more and more out of alignment.

<p><math>Work = ΔU_m = \int\limits_{θ_i}^{θ_f}\ 2IwBsinθ(\frac{h}{2}dθ) = IwhB \int\limits_{θ_i}^{θ_f}\ sinθ dθ </math>
</p>
Where <math>IwBsinθ</math> is the perpendicular force exerted on only one side of the circuit. We are pushing on both sides so we multiply that by 2. <math>(\frac{h}{2}dθ)</math> is the distance that the force is exerted.
<p><math>ΔU_m = IwhB[-cosθ]_{θ_i}^{θ_f} = -IwhB[cosθ_f - cosθ_i]</math>
</p>

<p>
<math>
ΔU_m = Δ(-μBcosθ)</math> since <math>μ = IA = Iwh
</math>
</p>
so the potential energy for a dipole is
<math>
U_m = -μBcosθ
</math>.

Potential energy for a dipole can also be written as the dot product <math>U_m = -\overrightarrow{μ} \bullet \overrightarrow{B}\ </math>.

Let's now envision two magnets interacting with each other.

Knowing what we know now about the potential energy of a magnetic dipole, we can see why magnets move each other. Systems tend to favor states of low potential energy so when a magnet is inched closer to another magnet, their dipoles will align so that the potential energy takes on a negative value (state with the lowest potential energy). This action is illustrated below.

[[File:physics_potential_energy4.png]]

As the magnet on the left is held and inched closer to the magnet on the right, the magnet on the right will turn so that the magnetic dipoles align with each other.

==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 ==

Here are some other resources that may help.
<p>[http://www.physicsbook.gatech.edu/Potential_Energy Potential Energy]</p>
<p>[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html Magnetic Forces]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Dipole_Moment Magnetic Dipole Moment]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Field Magnetic Field]</p>

===Further reading===

Books, Articles or other print media on this topic

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

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

Potential Energy for a Magnetic Dipole

2015-12-03T20:12:36Z

Thenderlong3:

Page Claimed by Thomas Henderlong

==The Main Idea==
If a magnetic dipole is allowed to pivot freely without any outside forces, then it will match it's alignment with the applied magnetic field. The system favors a state of lower potential so the aligned magnetic dipole is associated with a lower potential energy in the applied magnetic field. Think of how a magnets interact with each other when inched closer to each other. They'll align in a way so that the north and south ends point in the same direction or have the north end of one magnet touching the south end of the other magnet (state of lowest potential).
===A Mathematical Model===

By calculating how much work it takes to move a magnetic dipole out of alignment, we can determine the increased potential energy for that dipole.

Let's take a look at a rectangular circuit on a horizontal axle in a magnetic field pictured below.

[[File:physics_potential_energy2.png]]

Now let's look at this system from the side.

[[File:physics_potential_energy3.png]]

We can see that the magnetic force acting on the circuit pushes the circuit out horizontally. The magnetic force is trying to make the circuit's magnetic dipole moment, μ, point in the same direction of the magnetic field. We can measure the amount of work it takes to move the circuit from an initial angle of θ<sub>i</sub> to a final angle of θ<sub>f</sub>. The work done by pushing the circuit out of alignment changes the magnetic potential energy of the system.

As we push the circuit to rotate a angle of dθ around it's horizontal axis, the total distance that the force is exerted on one side of the circuit is equal to (h/2)*dθ. Keep in mind though that we are exerted force on both sides of the circuit. In the diagram this is indicated as Force by Us. We will have to determine the total amount of work done by using an integral because the force exerted depends on the value of θ and θ increases as we push the circuit more and more out of alignment.

<p><math>Work = ΔU_m = \int\limits_{θ_i}^{θ_f}\ 2IwBsinθ(\frac{h}{2}dθ) = IwhB \int\limits_{θ_i}^{θ_f}\ sinθ dθ </math>
</p>
Where <math>IwBsinθ</math> is the perpendicular force exerted by us on only one side of the circuit. We are pushing on both sides so we multiply that by 2. <math>(\frac{h}{2}dθ)</math> is the distance that the force is exerted.
<p><math>ΔU_m = IwhB[-cosθ]_{θ_i}^{θ_f} = -IwhB[cosθ_f - cosθ_i]</math>
</p>

<p>
<math>
ΔU_m = Δ(-μBcosθ)</math> since <math>μ = IA = Iwh
</math>
</p>
so the potential energy for a dipole is
<math>
U_m = -μBcosθ
</math>.

Potential energy for a dipole can also be written as the dot product <math>U_m = -\overrightarrow{μ} \bullet \overrightarrow{B}\ </math>.

Let's now envision two magnets interacting with each other.

Knowing what we know now about the potential energy of a magnetic dipole, we can see why magnets move each other. Systems tend to favor states of low potential energy so when a magnet is inched closer to another magnet, their dipoles will align so that the potential energy takes on a negative value (state with the lowest potential energy). This action is illustrated below.

[[File:physics_potential_energy4.png]]

As the magnet on the left is held and inched closer to the magnet on the right, the magnet on the right will turn so that the magnetic dipoles align with each other.

==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 ==

Here are some other resources that may help.
<p>[http://www.physicsbook.gatech.edu/Potential_Energy Potential Energy]</p>
<p>[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html Magnetic Forces]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Dipole_Moment Magnetic Dipole Moment]</p>
<p>[http://www.physicsbook.gatech.edu/Magnetic_Field Magnetic Field]</p>

===Further reading===

Books, Articles or other print media on this topic

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

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

Potential Energy for a Magnetic Dipole

2015-12-03T19:32:39Z

Thenderlong3: /* A Mathematical Model */

Page Claimed by Thomas Henderlong

==The Main Idea==
If a magnetic dipole is allowed to pivot freely without any outside forces, then it will match it's alignment with the applied magnetic field. The system favors a state of lower potential so the aligned magnetic dipole is associated with a lower potential energy in the applied magnetic field. Think of how a magnets interact with each other when inched closer to each other. They'll align in a way so that the north and south ends point in the same direction or have the north end of one magnet touching the south end of the other magnet (state of lowest potential).
===A Mathematical Model===

By calculating how much work it takes to move a magnetic dipole out of alignment, we can determine the increased potential energy for that dipole.

Let's take a look at a rectangular circuit on a horizontal axle in a magnetic field pictured below.

[[File:physics_potential_energy2.png]]

Now let's look at this system from the side.

[[File:physics_potential_energy3.png]]

We can see that the magnetic force acting on the circuit pushes the circuit out horizontally. The magnetic force is trying to make the circuit's magnetic dipole moment, μ, point in the same direction of the magnetic field. We can measure the amount of work it takes to move the circuit from an initial angle of θ<sub>i</sub> to a final angle of θ<sub>f</sub>. The work done by pushing the circuit out of alignment changes the magnetic potential energy of the system.

As we push the circuit to rotate a angle of dθ around it's horizontal axis, the total distance that the force is exerted on one side of the circuit is equal to (h/2)*dθ. Keep in mind though that we are exerted force on both sides of the circuit. In the diagram this is indicated as Force by Us. We will have to determine the total amount of work done by using an integral because the force exerted depends on the value of θ and θ increases as we push the circuit more and more out of alignment.

<p><math>Work = ΔU_m = \int\limits_{θ_i}^{θ_f}\ 2IwBsinθ(\frac{h}{2}dθ) = IwhB \int\limits_{θ_i}^{θ_f}\ sinθ dθ </math>
</p>
Where <math>IwBsinθ</math> is the perpendicular force exerted by us on only one side of the circuit. We are pushing on both sides so we multiply that by 2. <math>(\frac{h}{2}dθ)</math> is the distance that the force is exerted.
<p><math>ΔU_m = IwhB[-cosθ]_{θ_i}^{θ_f} = -IwhB[cosθ_f - cosθ_i]</math>
</p>

<p>
<math>
ΔU_m = Δ(-μBcosθ)</math> since <math>μ = IA = Iwh
</math>
</p>
so the potential energy for a dipole is
<math>
U_m = -μBcosθ
</math>.

Potential energy for a dipole can also be written as the dot product <math>U_m = -\overrightarrow{μ} \bullet \overrightarrow{B}\ </math>.

Let's now envision two magnets interacting with each other.

Knowing what we know now about the potential energy of a magnetic dipole, we can see why magnets move each other. Systems tend to favor states of low potential energy so when a magnet is inched closer to another magnet, their dipoles will align so that the potential energy takes on a negative value (state with the lowest potential energy). This action is illustrated below.

[[File:physics_potential_energy4.png]]

As the magnet on the left is held and inched closer to the magnet on the right, the magnet on the right will turn so that the magnetic dipoles align with each other.

===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===

Internet resources on this topic

==References==

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

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

File:Physics potential energy4.png

2015-12-03T19:27:44Z

Thenderlong3:

Potential Energy for a Magnetic Dipole

2015-12-03T19:26:51Z

Thenderlong3: /* A Mathematical Model */

Page Claimed by Thomas Henderlong

==The Main Idea==
If a magnetic dipole is allowed to pivot freely without any outside forces, then it will match it's alignment with the applied magnetic field. The system favors a state of lower potential so the aligned magnetic dipole is associated with a lower potential energy in the applied magnetic field. Think of how a magnets interact with each other when inched closer to each other. They'll align in a way so that the north and south ends point in the same direction or have the north end of one magnet touching the south end of the other magnet (state of lowest potential).
===A Mathematical Model===

By calculating how much work it takes to move a magnetic dipole out of alignment, we can determine the increased potential energy for that dipole.

Let's take a look at a rectangular circuit on a horizontal axle in a magnetic field pictured below.

[[File:physics_potential_energy2.png]]

Now let's look at this system from the side.

[[File:physics_potential_energy3.png]]

We can see that the magnetic force acting on the circuit pushes the circuit out horizontally. The magnetic force is trying to make the circuit's magnetic dipole moment, μ, point in the same direction of the magnetic field. We can measure the amount of work it takes to move the circuit from an initial angle of θ<sub>i</sub> to a final angle of θ<sub>f</sub>. The work done by pushing the circuit out of alignment changes the magnetic potential energy of the system.

As we push the circuit to rotate a angle of dθ around it's horizontal axis, the total distance that the force is exerted on one side of the circuit is equal to (h/2)*dθ. Keep in mind though that we are exerted force on both sides of the circuit. In the diagram this is indicated as Force by Us. We will have to determine the total amount of work done by using an integral because the force exerted depends on the value of θ and θ increases as we push the circuit more and more out of alignment.

<p><math>Work = ΔU_m = \int\limits_{θ_i}^{θ_f}\ 2IwBsinθ(\frac{h}{2}dθ) = IwhB \int\limits_{θ_i}^{θ_f}\ sinθ dθ </math>
</p>
Where <math>IwBsinθ</math> is the perpendicular force exerted by us on only one side of the circuit. We are pushing on both sides so we multiply that by 2. <math>(\frac{h}{2}dθ)</math> is the distance that the force is exerted.
<p><math>ΔU_m = IwhB[-cosθ]_{θ_i}^{θ_f} = -IwhB[cosθ_f - cosθ_i]</math>
</p>

<p>
<math>
ΔU_m = Δ(-μBcosθ)</math> since <math>μ = IA = Iwh
</math>
</p>
so the potential energy for a dipole is
<math>
U_m = -μBcosθ
</math>.

Potential energy for a dipole can also be written as the dot product <math>U_m = -\overrightarrow{μ} \bullet \overrightarrow{B}\ </math>.

Let's now envision two magnets interacting with each other.

Knowing what we know now about the potential energy of a magnetic dipole, we can see why magnets move each other. Systems tend to favor states of low potential energy so when a magnet is inched closer to another magnet, their dipoles will align so that the potential energy takes on a negative value (state with the lowest potential energy). This action is illustrated below.

[[File:physics_potential_energy4.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===

Internet resources on this topic

==References==

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

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

Potential Energy for a Magnetic Dipole

2015-12-03T18:54:25Z

Thenderlong3: /* A Mathematical Model */

Potential Energy for a Magnetic Dipole

2015-12-03T18:46:44Z

Thenderlong3: /* A Mathematical Model */

Potential Energy for a Magnetic Dipole

2015-12-03T18:36:57Z

Thenderlong3: /* A Mathematical Model */

Potential Energy for a Magnetic Dipole

2015-12-03T18:33:10Z

Thenderlong3: /* A Mathematical Model */

Potential Energy for a Magnetic Dipole

2015-12-03T18:15:23Z

Thenderlong3: /* A Mathematical Model */

File:Physics potential energy3.png

2015-12-03T17:50:27Z

Thenderlong3: Thenderlong3 uploaded a new version of "File:Physics potential energy3.png"

File:Physics potential energy3.png

2015-12-03T17:43:31Z

Thenderlong3:

File:Physics potential energy2.png

2015-12-03T16:15:41Z

Thenderlong3: Thenderlong3 uploaded a new version of "File:Physics potential energy2.png"

File:Physics potential energy2.png

2015-12-03T16:14:19Z

Thenderlong3: Thenderlong3 uploaded a new version of "File:Physics potential energy2.png"

File:Physics potential energy2.png

2015-12-03T16:14:02Z

Thenderlong3: Thenderlong3 uploaded a new version of "File:Physics potential energy2.png"

File:Physics potential energy2.png

2015-12-03T16:03:06Z

Thenderlong3:

Potential Energy for a Magnetic Dipole

2015-12-03T15:26:08Z

Thenderlong3: /* The Main Idea */

Potential Energy for a Magnetic Dipole

2015-12-02T22:06:10Z

Thenderlong3:

Potential Energy for a Magnetic Dipole

2015-12-02T21:52:26Z

Thenderlong3:

Potential Energy for a Magnetic Dipole

2015-12-02T21:03:19Z

Thenderlong3:

Page Claimed by Thomas Henderlong

==The Main Idea==

State, in your own words, the main idea for this topic
Electric Field of Capacitor

===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===

Internet resources on this topic

==References==

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

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

Potential Energy for a Magnetic Dipole

2015-12-02T20:58:00Z

Thenderlong3: Created page with "Page Claimed by Thomas Henderlong"

Page Claimed by Thomas Henderlong

Main Page

2015-12-02T20:57:33Z

Thenderlong3: /* Energy */

__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]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Conservation of Charge]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
*[[Center of Mass]]
*[[Reaction Time]]
</div>
</div>

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

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Quantum Theory]]
*[[Big Bang Theory]]
*[[Maxwell's Electromagnetic Theory]]
*[[Atomic Theory]]
*[[Wave-Particle Duality]]
*[[String Theory]]
</div>
</div>

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

===Notable Scientists===
<div class="mw-collapsible-content">
*[[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]]
*[[Erwin Schrödinger]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[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]]
*[[Benjamin Franklin]]
*[[James Chadwick]]
*[[Henry Cavendish]]
*[[Thomas Young]]
</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]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Higgs Boson]]
</div>
</div>

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

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
* [[Speed of Sound in a Solid]]
* [[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]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
* [[Newton's Laws and Linear Momentum]]
* [[Net Force]]
* [[Center of Mass]]
* [[Momentum at High Speeds]]
</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 ring]]
* [[Rotation]]
* [[Torque]]
* [[Systems with Zero Torque]]
* [[Systems with Nonzero Torque]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]

</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]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power (Mechanical)]]
*[[Energy Graphs]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Path Independence of Electric Potential]]
</div>
</div>

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

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

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

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
** [[How Objects Become Charged]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Electric Potential]]
**[[Potential Difference Path Independence]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
**[[Energy Density and Electric Field]]
** [[Systems of Charged Objects]]
*[[Electric Force]]
*[[Polarization]]
**[[Polarization of an Atom]]
*[[Charge Motion in Metals]]
*[[Charge Transfer]]
*[[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]]
**[[Magnetic Force]]
**[[Magnetic Torque]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Motors and Generators]]
**[[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]]
*[[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]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
*[[Feedback]]
*[[Transformers (Circuits)]]
*[[Resistors and Conductivity]]
</div>
</div>

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

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Ampere's Law]]
**[[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]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers from a physics standpoint]]
***[[Energy Density]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
**[[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]]
*[[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]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

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

===Waves===
<div class="mw-collapsible-content">
*[[Multisource Interference: Diffraction]]
*[[Standing waves]]
*[[Gravitational waves]]
*[[Wave-Particle Duality]]
</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]]
</div>
</div>

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

Main Page

2015-12-02T20:39:19Z

Thenderlong3: /* Fields */

__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]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Conservation of Charge]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
*[[Center of Mass]]
*[[Reaction Time]]
</div>
</div>

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

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Quantum Theory]]
*[[Big Bang Theory]]
*[[Maxwell's Electromagnetic Theory]]
*[[Atomic Theory]]
*[[Wave-Particle Duality]]
*[[String Theory]]
</div>
</div>

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

===Notable Scientists===
<div class="mw-collapsible-content">
*[[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]]
*[[Erwin Schrödinger]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[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]]
*[[Benjamin Franklin]]
*[[James Chadwick]]
*[[Henry Cavendish]]
*[[Thomas Young]]
</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]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Higgs Boson]]
</div>
</div>

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

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
* [[Speed of Sound in a Solid]]
* [[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]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
* [[Newton's Laws and Linear Momentum]]
* [[Net Force]]
* [[Center of Mass]]
* [[Momentum at High Speeds]]
</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 ring]]
* [[Rotation]]
* [[Torque]]
* [[Systems with Zero Torque]]
* [[Systems with Nonzero Torque]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]

</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]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power (Mechanical)]]
*[[Energy Graphs]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Path Independence of Electric Potential]]
</div>
</div>

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

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

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

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
** [[How Objects Become Charged]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Electric Potential]]
**[[Potential Difference Path Independence]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
**[[Energy Density and Electric Field]]
** [[Systems of Charged Objects]]
*[[Electric Force]]
*[[Polarization]]
**[[Polarization of an Atom]]
*[[Charge Motion in Metals]]
*[[Charge Transfer]]
*[[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]]
**[[Magnetic Force]]
**[[Magnetic Torque]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Motors and Generators]]
**[[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]]
*[[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]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
*[[Feedback]]
*[[Transformers (Circuits)]]
*[[Resistors and Conductivity]]
</div>
</div>

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

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Ampere's Law]]
**[[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]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers from a physics standpoint]]
***[[Energy Density]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
**[[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]]
*[[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]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

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

===Waves===
<div class="mw-collapsible-content">
*[[Multisource Interference: Diffraction]]
*[[Standing waves]]
*[[Gravitational waves]]
*[[Wave-Particle Duality]]
</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]]
</div>
</div>

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

Main Page

2015-12-02T02:36:21Z

Thenderlong3: /* Fields */

__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]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Conservation of Charge]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
</div>
</div>

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

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Quantum Theory]]
*[[Big Bang Theory]]
*[[Maxwell's Electromagnetic Theory]]
*[[Atomic Theory]]
*[[Wave-Particle Duality]]
*[[String Theory]]
</div>
</div>

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

===Notable Scientists===
<div class="mw-collapsible-content">
*[[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]]
*[[Erwin Schrödinger]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[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]]
*[[Wolfgang Pauli]]
*[[Émilie du Châtelet]]
*[[Blaise Pascal]]
</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]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Higgs Boson]]
</div>
</div>

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

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
* [[Speed of Sound in a Solid]]
* [[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]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
* [[Newton's Laws and Linear Momentum]]
* [[Net Force]]
* [[Center of Mass]]
</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 ring]]
* [[Rotation]]
* [[Torque]]
* [[Systems with Zero Torque]]
* [[Systems with Nonzero Torque]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]

</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]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power]]
*[[Energy Graphs]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Path Independence of Electric Potential]]
</div>
</div>

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

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

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

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
** [[Charged Hollow Cylinder]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Electric Potential]]
**[[Potential Difference Path Independence]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
**[[Energy Density and Electric Field]]
** [[Systems of Charged Objects]]
*[[Electric Force]]
*[[Polarization]]
*[[Charge Motion in Metals]]
*[[Charge Transfer]]
*[[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]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Motors and Generators]]
**[[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]]
*[[Thin and Thick Wires]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electrical Resistance]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
**[[AC]]
*[[Ohm's Law]]
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[RC]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
*[[Feedback]]
*[[Transformers]]
*[[Resistors and Conductivity]]
</div>
</div>

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

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Ampere's Law]]
**[[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]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers]]
***[[Energy Density]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
**[[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]]
*[[Electromagnetic Propagation]]
**[[Wavelength and Frequency]]
*[[Snell's Law]]
*[[Light Propagation Through a Medium]]
*[[Light Scaterring: Why is the Sky Blue]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

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

===Waves===
<div class="mw-collapsible-content">
*[[Multisource Interference: Diffraction]]
*[[Standing waves]]
*[[Gravitational waves]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Real Life Applications of Electromagnetic Principles===
<div class="mw-collapsible-content">
*[[Electromagnetic Junkyard Cranes]]
</div>
</div>

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

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