Physics Book - User contributions [en]

Magnetic Dipole Moment

2020-11-17T15:35:41Z

Ssahetiya6: /* Main Idea */

'''Claimed by Sonica Sahetiya Fall 2020'''

==Main Idea==
The magnetic dipole moment of a loop of current may be considered to be a measure of the strength of the magnetic field. The magnetic field generated by a magnet points from south to north and is proportional to its magnetic dipole moment. In a loop of current, the magnetic dipole moment is a vector that is perpendicular to the loop and can be found using the right-hand-rule. The magnetic dipole moment is a measure of the strength of the magnetic dipole.

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic moment. The magnetic moment is a vector quantity that is used to calculate the torque generated by a magnetic field while the magnetic dipole moment is a value used to define the current of a loop to find the magnetic field on axis.

The magnetic dipole moment can be thought of as a compass needle. When there is an external magnetic field, a current-carrying loop will rotate to align the magnetic dipole moment along the magnetic field.

===Mathematical Model===
[[File:Magnetic dipole copy.jpg|right|400px]]

The magnetic dipole moment is represented by a vector <math>\mathbf{µ}</math>. The magnitude of this is set equal to the current running through the wire multiplied by the area of the circular loop the current runs through. Here the area of the circular loop is defined as <math>\pi R^2</math>. Its direction is determined by the right hand rule. The units for the magnetic dipole moment are amperes times meters squared:

::<math>|\boldsymbol{ \mu }| = \mu = I A = I \cdot \pi R^2</math>

A '''coil of <math>N</math> current loops''' would thus have a magnetic moment of:

:::<math> |\boldsymbol{\mu}| = \mu = N I A</math>

*The equation for the '''magnitude of the magnetic field at the center of a current loop''' simplifies as (See [[Magnetic Field of a Loop]]):

:::<math>\begin{align}
B & = \frac{\mu_0}{4 \pi} \frac{2 \pi I R^2}{(z^2 + R^2)^{3/2}} \text{, where } z = 0 \\
& = \frac{\mu_0}{4 \pi} \frac{2 \pi I R^2}{R^3} \text{, and the } R^2 \text{ cancels} \\
& = \frac{\mu_0}{4 \pi} \frac{2 \pi I}{R} \\
& = \frac{\mu_0}{4 \pi} \frac{2 \pi \frac{\mu}{\pi R^2}}{R} \text{, where } I = \frac{\mu}{\pi R^2} \\
B & = \frac{\mu_0}{4 \pi} \frac{2 \mu}{R^3} \ \mathbf{(2)}\\
\end{align}</math>

*The '''magnitude of the magnetic moment <math>\mu</math> of an electron in circular orbit''' is given by:

:::<math> |\boldsymbol{\mu}| = \mu = I A = - \frac{e}{2m_{e}} L</math>

::::<math>L</math> is the magnitude of the angular momentum of the electron

*The '''torque experienced by a current loop''' due to an external magnetic field is defined as the cross product of the magnetic dipole moment of the loop and the external magnetic field applied to the loop:

:::<math>\boldsymbol{\tau} = \boldsymbol{\mu} \times \boldsymbol{B}</math>

*The '''magnetic potential energy of the loop''' is also defined as the negated dot product between the magnetic dipole moment of the loop and the external magnetic field applied to the loop:

[[File:MagneticMomentEnergy.gif|right|300px]]

:::<math>U(\theta) = - \boldsymbol{\mu} \bullet \mathbf{B} = - [\mu B] \ \text{cos}(\theta)</math>

::::<math>\theta</math> is the angle between the magnetic moment and the external magnetic field

:*For example, if <math>\theta = 0°</math>, then we see:

:::<math>U(0°) = -[\mu B] \ \text{cos}(0°) = -\mu B</math>

:*For <math>\theta = 180°</math>, we get:

:::<math>U(180°) = -[\mu B] \ \text{cos}(180°) = \mu B</math>

:::From this we see that, when there is no separation between the magnetic field's direction and the magnetic moment's direction, the loop is at its lowest possible magnetic potential energy state, and when the directions are anti-parallel, the loop is at its highest possible magnetic potential energy state, as shown in the figure.

===Computational Model===
::'''Insert Computational Model here'''

==Examples==

===Simple===
A <math>1,200</math> turn circular coil of radius <math>10 \text{ cm}</math> carries <math>2 \text{ Amps}</math>.

:'''a) What is the magnitude of the magnetic dipole moment of the coil. What direction does it point?'''

::We can use our [[Magnetic Dipole Moment#Mathematical Model| Mathematical Model]] to answer this:

:::<math>\mu = N I A = N I \cdot \pi R^2</math>

::In this problem, the following values have been specified for us:

:::<math>N = 1,200 \text{ turns or loops}</math>

:::<math>R = 0.1 \text{ m}</math>

:::<math>I = 2 \text{ Amps}</math>

::Therefore, <math>\mu</math> is:

:::<math>\mu = 1,200 \times 2 \times \pi \times (0.1)^2 = 75.4 \text{ A} \cdot \text{m}^2</math>

===Middling===
A current loop with a radius of <math>2 \text{ m}</math> and a current of <math>5 \text{ Amps}</math> is in an external magnetic field. This magnetic field is given by:

::<math>\mathbf{B_{ext}} = (x, y, z) = (1, 1, 1) = \sqrt{3} \left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \right)</math>

A unit vector normal to the area of the current loop (and has a direction consistent with the right-hand rule) is given by:

::<math>\mathbf{\hat n} = (x, y, z) = \left(-\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}\right)</math>

:'''a) What is the magnetic potential energy of the current loop?'''

::The magnetic potential energy of a current loop is defined as:

:::<math>U(\theta) = - \boldsymbol{\mu} \bullet \mathbf{B_{ext}} = - [\mu B_{ext}] \ \text{cos}(\theta) \ \mathbf{(1)}</math>

::Since <math>\mathbf{\hat n}</math> is consistent with the direction of <math>\boldsymbol{\mu}</math> and has a magnitude of <math>1</math>, we can define <math>\boldsymbol{\mu}</math> as the its magnitude times its unit direction:

:::<math>\boldsymbol{\mu} = \mu \mathbf{\hat n} \ \mathbf{(2)}</math>

::We know <math>\mu</math> is:

:::<math>\mu = I A = I \cdot \pi R^2 \ \mathbf{(3)}</math>

::Putting '''2''' and '''3''' together shows:

:::<math>\boldsymbol{\mu} = \left( I \cdot \pi R^2 \right) \mathbf{\hat n}</math>

::Plugging this into '''1''' gives:

:::<math>U(\theta) = - \left( I \cdot \pi R^2 \right) \mathbf{\hat n} \bullet \mathbf{B_{ext}}</math>

::The dot product is calculated as:

:::<math>\begin{align}
\mathbf{\hat n} \bullet \mathbf{B_{ext}} & = \left(-\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}\right) \bullet \sqrt{3} \left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \right) \\
& = \sqrt{3} \left(-\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}\right) \bullet \left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \right) \\
& = \sqrt{3} \Biggr[ \left(-\frac{1}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}} \right) + \left(-\frac{1}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}} \right) + \left(-\frac{1}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}} \right) \Biggr] \\
& = \sqrt{3} \Biggr[ -\frac{1}{3} -\frac{1}{3} -\frac{1}{3} \Biggr] \\
& = \sqrt{3} \Bigr[- 1 \Bigr] \\
\mathbf{\hat n} \bullet \mathbf{B_{ext}} & = -\sqrt{3} \\
\end{align}</math>

::We can now find the magnetic potential energy of the loop:

:::<math>U(\theta) = \sqrt{3} \times 5 \times \pi \times (2)^2 = 20 \sqrt{3} \pi \approx 108.83 \text{ J}</math>

::Keep in mind we could have found the angle between <math>\mathbf{\hat n}</math> and <math>\mathbf{B_{ext}}</math> and used

:::<math>U(\theta) = - [\mu B_{ext}] \ \text{cos}(\theta)</math>

::to find the magnetic potential energy. The angle found would be <math>\pm 180°</math>, corresponding to an anti-parallel relation between the magnetic field and the magnetic moment, and therefore a max potential energy.

===Difficult===
[[File:MagneticMoment.png|right|400px]]

A thin uniform ring of radius <math>R</math> and mass <math>M</math>, carrying a uniformly distributed charge <math>+Q</math>, rotates clockwise (as seen from above) about its axis with a constant angular speed <math>\omega</math>. It lies in the xy-plane.

:'''a) Find the ratio of the magnitude of the ring's magnetic dipole moment <math>(\mu)</math> to its angular momentum <math>(L)</math>.'''

::The current in the ring can be calculated using the period of the rotation <math>(T)</math> and the charge on the ring as:

:::<math>I = \frac{dQ}{dt} = \frac{\Delta Q}{\Delta t} = \frac{Q}{T} = \frac{Q \omega}{2 \pi}</math>

::The magnetic moment is:

:::<math>\mu = I A = \frac{Q \omega}{2 \pi} \cdot \pi R^2 = \frac{1}{2} QωR^2</math>

::The angular momentum is calculated as the loops rotational inertia (moment of inertia) times its angular speed. The rotational inertia of a ring is given by <math>m R^2</math>:

:::<math> L = I \omega = m R^2 \omega</math>

::Therefore, the ratio is:

:::<math>\frac{\mu}{L} = \frac{\frac{1}{2} Q \omega R^2}{m R^2 \omega} = \frac{Q}{2m}</math>

:'''b) What is the torque experienced by the ring if an external magnetic field described by <math>\mathbf{B} = (2, 4, -5)</math> is applied to the ring?'''

::We know the torque experienced by a current carrying loop is described by:

:::<math>\boldsymbol{\tau} = \boldsymbol{\mu} \times \mathbf{B} \ \mathbf{(1)}</math>

::The magnitude of <math>\boldsymbol{\mu}</math> was found to be <math>\frac{1}{2} Q \omega R^2</math> in the previous part. To find the direction of <math>\boldsymbol{\mu}</math>, we consider the direction of the current and where the ring lies. Since the ring is lying in the xy-plane and rotating clockwise, using the right-hand rule shows <math>\boldsymbol{\mu}</math> must point in the <math>-z</math> direction. A unit vector in this direction can be described as <math>\mathbf{\hat n} = (0, 0, -1)</math>.

::Thus, <math>\boldsymbol{\mu}</math> can be described by:

:::<math>\boldsymbol{\mu} = \mu \mathbf{\hat n}</math>

::Plugging this into '''1''' shows:

:::<math>\begin{align}
\boldsymbol{\tau} & = \mu \bigr[ \mathbf{\hat n} \times \mathbf{B} \bigr] \\
& = \mu \bigr[(0, 0, -1) \times (2, 4, -5) \bigr] \\
& = \mu \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 0 & 0 & -1 \\ 2 & 4 & -5 \end{vmatrix} \\
& = \mu \biggr[ \ \mathbf{i} \begin{vmatrix} 0 & -1 \\ 4 & -5 \end{vmatrix} - \mathbf{j} \begin{vmatrix} 0 & -1 \\ 2 & -5 \end{vmatrix} + \mathbf{k} \begin{vmatrix} 0 & 0 \\ 2 & 4 \end{vmatrix} \biggr] \\
& = \mu \biggr[\mathbf{i} \bigr[(0) - (-4) \bigr] - \mathbf{j} \bigr[(0) - (-2) \bigr] + \mathbf{k} \bigr[(0) - (0) \bigr] \biggr] \\
& = \mu \bigr[4 \mathbf{i} - 2 \mathbf{j} + 0 \mathbf{k} \bigr] \\
& = \frac{1}{2} Q \omega R^2 \cdot (4, -2, 0) \\
& = Q \omega R^2 \cdot (2, -1, 0) \\
\boldsymbol{\tau} & = \sqrt{5} \cdot Q \omega R^2 \left(\frac{2}{\sqrt{5}}, -\frac{1}{\sqrt{5}}, 0 \right)
\end{align}</math>

==Connectedness==
::'''Insert Connectedness Section here'''

==History==

The study of magnetism dates far back in time, but it was not until 1825 that Andre Ampere showed that magnetism is due to perpetually flowing current through loops of wire. He then went on to derive Ampere's Law, which connected magnetic fields to electric currents. This equation was then further adapted to simplify the on axis magnetic field generated by a loop of current to use the magnetic dipole moment.

At first, people thought magnets, both natural and man-made, are made up of countless magnetic dipoles, each consisting of positive and negative magnetic charges separated by a small distance. This consequently defined the concept of magnetic dipole moment, a vector, pointing from the negative magnetic charge to the positive magnetic charge. When scientists discovered that magnetic charges, or "magnetic monopoles" do not exist, the magnetic properties of matter were believed to be generated by the alignment of molecular currents. Since then, magnetic dipole moment has been redefined using current <math>I</math>, allowing the idea of magnetic dipole to remain.

== See also ==

Here are some more resources with extra information on magnetic dipole moments.

===Further reading===

*[http://www.phys.ufl.edu/~acosta/phy2061/lectures/MagneticDipoles.pdf Lecture PDF on Magnetic Dipole Moment]
*[https://en.wikipedia.org/wiki/Magnetic_dipole Wikipedia Magnetic dipole]
*[http://mriquestions.com/magnetic-dipole-moment.html MRI Questions Magnetic Moment]
*http://web.mit.edu/8.02t/www/mitxmaterials/Presentations/Presentation_W07D2.pdf MIT PDF Magnetic Moment]

===External links===

*[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html HyperPhysics Magnetic Moment]
*[https://www.youtube.com/watch?v=H1I9-VjCc-Y Bozeman Science Magnetic Dipole Moment]

==References==

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

[[Category:Fields]]

Magnetic Dipole Moment

2020-11-17T15:27:25Z

Ssahetiya6:

'''Claimed by Sonica Sahetiya Fall 2020'''

==Main Idea==
The magnetic dipole moment of a loop of current may be considered to be a measure of the strength of the magnetic field. The magnetic field generated by a magnet points from south to north and is proportional to its magnetic dipole moment. In a loop of current, the magnetic dipole moment is a vector that is perpendicular to the loop and can be found using the right-hand-rule. The magnetic dipole moment is a measure of the strength of the magnetic dipole.

The main idea for this topic is to define the magnetic dipole moment and distinguish from the magnetic moment. The magnetic moment is a vector quantity that is used to calculate the torque generated by a magnetic field while the magnetic dipole moment is a value used to define the current of a loop to find the magnetic field on axis.

===Mathematical Model===
[[File:Magnetic dipole copy.jpg|right|400px]]

The magnetic dipole moment is represented by a vector <math>\mathbf{µ}</math>. The magnitude of this is set equal to the current running through the wire multiplied by the area of the circular loop the current runs through. Here the area of the circular loop is defined as <math>\pi R^2</math>. Its direction is determined by the right hand rule. The units for the magnetic dipole moment are amperes times meters squared:

::<math>|\boldsymbol{ \mu }| = \mu = I A = I \cdot \pi R^2</math>

A '''coil of <math>N</math> current loops''' would thus have a magnetic moment of:

:::<math> |\boldsymbol{\mu}| = \mu = N I A</math>

*The equation for the '''magnitude of the magnetic field at the center of a current loop''' simplifies as (See [[Magnetic Field of a Loop]]):

:::<math>\begin{align}
B & = \frac{\mu_0}{4 \pi} \frac{2 \pi I R^2}{(z^2 + R^2)^{3/2}} \text{, where } z = 0 \\
& = \frac{\mu_0}{4 \pi} \frac{2 \pi I R^2}{R^3} \text{, and the } R^2 \text{ cancels} \\
& = \frac{\mu_0}{4 \pi} \frac{2 \pi I}{R} \\
& = \frac{\mu_0}{4 \pi} \frac{2 \pi \frac{\mu}{\pi R^2}}{R} \text{, where } I = \frac{\mu}{\pi R^2} \\
B & = \frac{\mu_0}{4 \pi} \frac{2 \mu}{R^3} \ \mathbf{(2)}\\
\end{align}</math>

*The '''magnitude of the magnetic moment <math>\mu</math> of an electron in circular orbit''' is given by:

:::<math> |\boldsymbol{\mu}| = \mu = I A = - \frac{e}{2m_{e}} L</math>

::::<math>L</math> is the magnitude of the angular momentum of the electron

*The '''torque experienced by a current loop''' due to an external magnetic field is defined as the cross product of the magnetic dipole moment of the loop and the external magnetic field applied to the loop:

:::<math>\boldsymbol{\tau} = \boldsymbol{\mu} \times \boldsymbol{B}</math>

*The '''magnetic potential energy of the loop''' is also defined as the negated dot product between the magnetic dipole moment of the loop and the external magnetic field applied to the loop:

[[File:MagneticMomentEnergy.gif|right|300px]]

:::<math>U(\theta) = - \boldsymbol{\mu} \bullet \mathbf{B} = - [\mu B] \ \text{cos}(\theta)</math>

::::<math>\theta</math> is the angle between the magnetic moment and the external magnetic field

:*For example, if <math>\theta = 0°</math>, then we see:

:::<math>U(0°) = -[\mu B] \ \text{cos}(0°) = -\mu B</math>

:*For <math>\theta = 180°</math>, we get:

:::<math>U(180°) = -[\mu B] \ \text{cos}(180°) = \mu B</math>

:::From this we see that, when there is no separation between the magnetic field's direction and the magnetic moment's direction, the loop is at its lowest possible magnetic potential energy state, and when the directions are anti-parallel, the loop is at its highest possible magnetic potential energy state, as shown in the figure.

===Computational Model===
::'''Insert Computational Model here'''

==Examples==

===Simple===
A <math>1,200</math> turn circular coil of radius <math>10 \text{ cm}</math> carries <math>2 \text{ Amps}</math>.

:'''a) What is the magnitude of the magnetic dipole moment of the coil. What direction does it point?'''

::We can use our [[Magnetic Dipole Moment#Mathematical Model| Mathematical Model]] to answer this:

:::<math>\mu = N I A = N I \cdot \pi R^2</math>

::In this problem, the following values have been specified for us:

:::<math>N = 1,200 \text{ turns or loops}</math>

:::<math>R = 0.1 \text{ m}</math>

:::<math>I = 2 \text{ Amps}</math>

::Therefore, <math>\mu</math> is:

:::<math>\mu = 1,200 \times 2 \times \pi \times (0.1)^2 = 75.4 \text{ A} \cdot \text{m}^2</math>

===Middling===
A current loop with a radius of <math>2 \text{ m}</math> and a current of <math>5 \text{ Amps}</math> is in an external magnetic field. This magnetic field is given by:

::<math>\mathbf{B_{ext}} = (x, y, z) = (1, 1, 1) = \sqrt{3} \left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \right)</math>

A unit vector normal to the area of the current loop (and has a direction consistent with the right-hand rule) is given by:

::<math>\mathbf{\hat n} = (x, y, z) = \left(-\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}\right)</math>

:'''a) What is the magnetic potential energy of the current loop?'''

::The magnetic potential energy of a current loop is defined as:

:::<math>U(\theta) = - \boldsymbol{\mu} \bullet \mathbf{B_{ext}} = - [\mu B_{ext}] \ \text{cos}(\theta) \ \mathbf{(1)}</math>

::Since <math>\mathbf{\hat n}</math> is consistent with the direction of <math>\boldsymbol{\mu}</math> and has a magnitude of <math>1</math>, we can define <math>\boldsymbol{\mu}</math> as the its magnitude times its unit direction:

:::<math>\boldsymbol{\mu} = \mu \mathbf{\hat n} \ \mathbf{(2)}</math>

::We know <math>\mu</math> is:

:::<math>\mu = I A = I \cdot \pi R^2 \ \mathbf{(3)}</math>

::Putting '''2''' and '''3''' together shows:

:::<math>\boldsymbol{\mu} = \left( I \cdot \pi R^2 \right) \mathbf{\hat n}</math>

::Plugging this into '''1''' gives:

:::<math>U(\theta) = - \left( I \cdot \pi R^2 \right) \mathbf{\hat n} \bullet \mathbf{B_{ext}}</math>

::The dot product is calculated as:

:::<math>\begin{align}
\mathbf{\hat n} \bullet \mathbf{B_{ext}} & = \left(-\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}\right) \bullet \sqrt{3} \left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \right) \\
& = \sqrt{3} \left(-\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}\right) \bullet \left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \right) \\
& = \sqrt{3} \Biggr[ \left(-\frac{1}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}} \right) + \left(-\frac{1}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}} \right) + \left(-\frac{1}{\sqrt{3}} \cdot \frac{1}{\sqrt{3}} \right) \Biggr] \\
& = \sqrt{3} \Biggr[ -\frac{1}{3} -\frac{1}{3} -\frac{1}{3} \Biggr] \\
& = \sqrt{3} \Bigr[- 1 \Bigr] \\
\mathbf{\hat n} \bullet \mathbf{B_{ext}} & = -\sqrt{3} \\
\end{align}</math>

::We can now find the magnetic potential energy of the loop:

:::<math>U(\theta) = \sqrt{3} \times 5 \times \pi \times (2)^2 = 20 \sqrt{3} \pi \approx 108.83 \text{ J}</math>

::Keep in mind we could have found the angle between <math>\mathbf{\hat n}</math> and <math>\mathbf{B_{ext}}</math> and used

:::<math>U(\theta) = - [\mu B_{ext}] \ \text{cos}(\theta)</math>

::to find the magnetic potential energy. The angle found would be <math>\pm 180°</math>, corresponding to an anti-parallel relation between the magnetic field and the magnetic moment, and therefore a max potential energy.

===Difficult===
[[File:MagneticMoment.png|right|400px]]

A thin uniform ring of radius <math>R</math> and mass <math>M</math>, carrying a uniformly distributed charge <math>+Q</math>, rotates clockwise (as seen from above) about its axis with a constant angular speed <math>\omega</math>. It lies in the xy-plane.

:'''a) Find the ratio of the magnitude of the ring's magnetic dipole moment <math>(\mu)</math> to its angular momentum <math>(L)</math>.'''

::The current in the ring can be calculated using the period of the rotation <math>(T)</math> and the charge on the ring as:

:::<math>I = \frac{dQ}{dt} = \frac{\Delta Q}{\Delta t} = \frac{Q}{T} = \frac{Q \omega}{2 \pi}</math>

::The magnetic moment is:

:::<math>\mu = I A = \frac{Q \omega}{2 \pi} \cdot \pi R^2 = \frac{1}{2} QωR^2</math>

::The angular momentum is calculated as the loops rotational inertia (moment of inertia) times its angular speed. The rotational inertia of a ring is given by <math>m R^2</math>:

:::<math> L = I \omega = m R^2 \omega</math>

::Therefore, the ratio is:

:::<math>\frac{\mu}{L} = \frac{\frac{1}{2} Q \omega R^2}{m R^2 \omega} = \frac{Q}{2m}</math>

:'''b) What is the torque experienced by the ring if an external magnetic field described by <math>\mathbf{B} = (2, 4, -5)</math> is applied to the ring?'''

::We know the torque experienced by a current carrying loop is described by:

:::<math>\boldsymbol{\tau} = \boldsymbol{\mu} \times \mathbf{B} \ \mathbf{(1)}</math>

::The magnitude of <math>\boldsymbol{\mu}</math> was found to be <math>\frac{1}{2} Q \omega R^2</math> in the previous part. To find the direction of <math>\boldsymbol{\mu}</math>, we consider the direction of the current and where the ring lies. Since the ring is lying in the xy-plane and rotating clockwise, using the right-hand rule shows <math>\boldsymbol{\mu}</math> must point in the <math>-z</math> direction. A unit vector in this direction can be described as <math>\mathbf{\hat n} = (0, 0, -1)</math>.

::Thus, <math>\boldsymbol{\mu}</math> can be described by:

:::<math>\boldsymbol{\mu} = \mu \mathbf{\hat n}</math>

::Plugging this into '''1''' shows:

:::<math>\begin{align}
\boldsymbol{\tau} & = \mu \bigr[ \mathbf{\hat n} \times \mathbf{B} \bigr] \\
& = \mu \bigr[(0, 0, -1) \times (2, 4, -5) \bigr] \\
& = \mu \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 0 & 0 & -1 \\ 2 & 4 & -5 \end{vmatrix} \\
& = \mu \biggr[ \ \mathbf{i} \begin{vmatrix} 0 & -1 \\ 4 & -5 \end{vmatrix} - \mathbf{j} \begin{vmatrix} 0 & -1 \\ 2 & -5 \end{vmatrix} + \mathbf{k} \begin{vmatrix} 0 & 0 \\ 2 & 4 \end{vmatrix} \biggr] \\
& = \mu \biggr[\mathbf{i} \bigr[(0) - (-4) \bigr] - \mathbf{j} \bigr[(0) - (-2) \bigr] + \mathbf{k} \bigr[(0) - (0) \bigr] \biggr] \\
& = \mu \bigr[4 \mathbf{i} - 2 \mathbf{j} + 0 \mathbf{k} \bigr] \\
& = \frac{1}{2} Q \omega R^2 \cdot (4, -2, 0) \\
& = Q \omega R^2 \cdot (2, -1, 0) \\
\boldsymbol{\tau} & = \sqrt{5} \cdot Q \omega R^2 \left(\frac{2}{\sqrt{5}}, -\frac{1}{\sqrt{5}}, 0 \right)
\end{align}</math>

==Connectedness==
::'''Insert Connectedness Section here'''

==History==

The study of magnetism dates far back in time, but it was not until 1825 that Andre Ampere showed that magnetism is due to perpetually flowing current through loops of wire. He then went on to derive Ampere's Law, which connected magnetic fields to electric currents. This equation was then further adapted to simplify the on axis magnetic field generated by a loop of current to use the magnetic dipole moment.

At first, people thought magnets, both natural and man-made, are made up of countless magnetic dipoles, each consisting of positive and negative magnetic charges separated by a small distance. This consequently defined the concept of magnetic dipole moment, a vector, pointing from the negative magnetic charge to the positive magnetic charge. When scientists discovered that magnetic charges, or "magnetic monopoles" do not exist, the magnetic properties of matter were believed to be generated by the alignment of molecular currents. Since then, magnetic dipole moment has been redefined using current <math>I</math>, allowing the idea of magnetic dipole to remain.

== See also ==

Here are some more resources with extra information on magnetic dipole moments.

===Further reading===

*[http://www.phys.ufl.edu/~acosta/phy2061/lectures/MagneticDipoles.pdf Lecture PDF on Magnetic Dipole Moment]
*[https://en.wikipedia.org/wiki/Magnetic_dipole Wikipedia Magnetic dipole]
*[http://mriquestions.com/magnetic-dipole-moment.html MRI Questions Magnetic Moment]
*http://web.mit.edu/8.02t/www/mitxmaterials/Presentations/Presentation_W07D2.pdf MIT PDF Magnetic Moment]

===External links===

*[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html HyperPhysics Magnetic Moment]
*[https://www.youtube.com/watch?v=H1I9-VjCc-Y Bozeman Science Magnetic Dipole Moment]

==References==

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

[[Category:Fields]]

Main Page

2020-11-17T15:18:57Z

Ssahetiya6: /* Magnetic field of a wire */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

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

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

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

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A listing of [[Notable Scientist]] with links to their individual pages

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==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====GlowScript 101====
<div class="mw-collapsible-content">
*[[Python Syntax]]
*[[GlowScript]]
</div>
</div>

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

====VPython====

<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

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

====Vectors and Units====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

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

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

</div>
</div>

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

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

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

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[Energy of a Single Particle]]
*[[Kinetic Energy]]
*[[Work/Energy]]
*[[The Energy Principle]]
*[[Conservation of Energy]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation, and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====

<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

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

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

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

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

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

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

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

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</div>
</div>

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

====Charging and Discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Field of a Charged Rod|Charged Rod]]
</div>
</div>

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

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

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

====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

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

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

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

====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Kirchoff's Laws]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Electric Potential Difference]]
</div>
</div>

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

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

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

====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

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

====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
<h1><strong>Alayna Baker Spring 2020</strong></h1>
[[File:Hall Effect 1.jpg]]
[[File:Hall Effect 2.jpg]]

*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>

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

====Motional EMF====

<div class="mw-collapsible-content">
*[[Motional Emf]]
<h1><strong>Adeline Boswell Fall 2019</strong></h1>
[[File:Motional EMF Example.jpg]]

*[[Motional Emf using Faraday's Law]]
</div>
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page

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

====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

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

====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

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

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
*[[Molecules]]
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>

Main Page

2020-11-17T15:15:40Z

Ssahetiya6: /* Magnetic field of a wire */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

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

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

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

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">

==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====GlowScript 101====
<div class="mw-collapsible-content">
*[[Python Syntax]]
*[[GlowScript]]
</div>
</div>

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

====VPython====

<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

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

====Vectors and Units====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

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

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

</div>
</div>

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

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

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

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[Energy of a Single Particle]]
*[[Kinetic Energy]]
*[[Work/Energy]]
*[[The Energy Principle]]
*[[Conservation of Energy]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation, and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====

<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

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

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

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

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

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

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

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

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</div>
</div>

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

====Charging and Discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Field of a Charged Rod|Charged Rod]]
</div>
</div>

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

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

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

====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

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

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
*[[Magnetic Field of a Short Straight Wire]]
</div>
</div>

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

====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Kirchoff's Laws]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Electric Potential Difference]]
</div>
</div>

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

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

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

====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

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

====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
<h1><strong>Alayna Baker Spring 2020</strong></h1>
[[File:Hall Effect 1.jpg]]
[[File:Hall Effect 2.jpg]]

*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>

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

====Motional EMF====

<div class="mw-collapsible-content">
*[[Motional Emf]]
<h1><strong>Adeline Boswell Fall 2019</strong></h1>
[[File:Motional EMF Example.jpg]]

*[[Motional Emf using Faraday's Law]]
</div>
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page

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

====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

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

====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

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

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
*[[Molecules]]
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>