Physics Book - User contributions [en]

Hall Effect

2019-11-25T03:05:30Z

Aboswell7:

<h1><strong>Edited by Adeline Boswell Fall 2019</strong></h1>

The Hall Effect is the electric polarization of a block or slab of metal that occurs when a current is run through it while it is subject to a magnetic field perpendicular to the current.

==The Main Idea==

When a mobile charge, either positive or negative, flows through a metal block and is influenced by a magnetic field, the magnetic force on the charges force them to begin concentrating on one side of the block. Thus the block polarizes and has negative charges on one side and positive on the other in order to remain neutral. This grouping of positive charges in one part of the block and negative charges in another part of the block creates an electric field and thus an electric force equal on magnitude to the magnetic force that causes the initial polarization, but opposite in direction. The magnetic and electric forces cancel each other out and after some time, the charges flow normally through the block and do not group on one side or the other of the block. This perpendicular electric field also creates a potential difference known as the "Hall Voltage."

===Part 1: Normal circuit (No Magnetic Field Yet)===
(For simplicity, the mobile charges in this example have already been determined to be negatively charged electrons. This will not always be the case and it should not be assumed that the mobile charges are electrons)

Mobile electrons flow through a wire due to a parallel electric field inside the wire. This electric field is caused by an energy source, most commonly a battery. The parallel electric field flows from an area of high potential (i.e. the positive end of the battery) to an area of low potential (i.e. the negative end of the battery). This is the same direction as the conventional current. Since electrons are negatively charged, they flow in the opposite direction of the parallel electric field.

=== Part 2: Initial Transient State (Magnetic Field Present) ===

Mobile electrons are subjected to a magnetic field perpendicular to their motion as they flow through the wire. This results in the mobile charges being forced onto one side of the block by the magnetic force. This grouping of mobile charges on one side of the block creates an electric force. As time passes, more mobile charges are deposited on the side of the block and the electric force increases in magnitude.

===Part 3: Steady State (Magnetic Field Still Present, but abated)===

Over time massive quantities of charges are concentrated on one side of the block. As the charges build up, they will begin to create a charged area on one surface of the conductor. The charged surface will create an electric force to oppose the magnetic force that is pushing new electrons onto this charged surface. This opposing electric force is called the transverse electric force. When enough mobile charges have collected, their combined transverse electric force will be equal in magnitude to the magnetic force that is holding them. At this point, there is no net vertical force pushing more electrons against the surface of the conductor and these electrons will flow normally again, as they would if there was no magnetic field present. This is called the steady state.

==A Mathematical Model==

===Part 1: Normal circuit (No Magnetic Field Yet)===

<math> F_{electric, parallel} = qE_{parallel} </math>

Where q is the electric charge of the mobile charge. As F and E are vectors, a negative charge results in an electric force in the opposite direction of the electric field.

=== Part 2: Initial Transient State (Magnetic Field Present) ===

<math> F_{magnetic} = q(v\; Χ \;B)</math>

Where v is the velocity of the mobile charge and B is the magnetic field. For help calculating the cross product, including an example using the Hall Effect, see [[Right-Hand_Rule]]. REMEMBER, the mobile charge will move in the opposite direction of the cross product if it is negative, similar to how it behaves in an electric field.

===Part 3: Steady State (Magnetic Field Still Present, but abated)===

<math> F_{electric, perpendicular} = qE_{perpendicular} </math>

<math> |F_{electric, perpendicular}| = |F_{magnetic}| </math>

==Computational Model==
In this diagram, it is assumed the charge carrier is a negatively charged electron. THIS IS NOT A SAFE ASSUMPTION on a real question, experiment, or exam but was done for the purpose of simplifying explanations.

===Part 1: Normal circuit (No Magnetic Field Yet)===

[[File: Hall_Effect_part_1.png]]

In this diagram a solid conductive metal block is connected to two ends of a battery by wires. At this time there is no magnetic field present and electrons flow through the block in a straight line from wire to wire without interference or interruption.

=== Part 2: Initial Transient State (Magnetic Field Present) ===

[[File: Hall_effect_part_2.png]]

In this diagram the circles containing x's represent a magnetic field (NOT a magnetic force) into the page. When the electrons begin to move across the block their initial velocity interacts with the magnetic field to create a magnetic force downward. This causes electrons to begin pooling on the bottom face of the slab. This polarizes the block and creates a vertical potential difference across the block. It also creates an electric force that opposes the magnetic force, but in this state it is smaller than the magnetic force, resulting in continued pooling of electrons.

===Part 3: Steady State (Magnetic Field Still Present, but abated)===

[[File: Hall_effect_part_3.png]]

As time passes eventually sufficient quantities of electrons build up to create an electric force equal in magnitude to the magnetic force but opposite in direction. This allows the electrons to continue flow across the block as they did in part 1, however now the vertical voltage difference which was created in part 2 is not only still present but also at its maximum value. Most practice and exam problems will involve either the calculation or orientation of this voltage difference. It's important to remember that a voltmeter will have a positive reading if the positive node is connected to the end of the block which is positively charged and vice versa.

==Examples==

===Simple===
[[File:Hall Effect 1.jpg]]
[[File:Hall Effect 2.jpg]]
[[File:Hall effect cenceptual 1.png]]

A metal block is connected to a battery by two wires. Conventional current flows clockwise and the mobile charge in the block is positive. The block also experiences a magnetic field out of the page denoted by concentric circles. The block is also connected to a voltmeter. The positive end of the voltmeter is connected to the bottom of the block and the negative end of the voltmeter is connected to the top of the block. See attached photo for a diagram. What sign will the voltmeter display?

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

'''''Click for Solution'''''
<div class="mw-collapsible-content">
In this case, since magnetic force is q(v X B) and we know the charges are positive and thus follow the conventional current which moves across the block from left to right, the magnetic force points up. This means that the mobile charges (positive) will be pushed towards the bottom of the block. Remember: a voltmeter will have a positive reading if the positive end is connected to the positively charged side of the block. In this case, the bottom of the block is positively charged and the positive end of the voltmeter is connected there. The voltmeter will have a positive reading.

</div>
</div>

[[File:Hall effect cenceptual 2.png]]

A battery and metal block are connected by 2 wires. Conventional current flows clockwise. A magnetic field points out of the page, denoted by concentric circles. A voltmeter is attached to the block with its positive lead at the top of the block and its negative lead at the bottom of the block. The voltmeter has a positive reading. What sign does the mobile charge have?

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

'''''Click for Solution'''''
<div class="mw-collapsible-content">
From the voltmeter reading we can deduce that the top of the block is positively charged and the bottom negatively charged. Thus, we check if positive mobile charge carriers satisfy this requirement. A positive charge moves with the conventional current, which in this case is from left to right, meaning its velocity would be in the positive x direction. When taking the cross product of the charge's velocity and the magnetic field (out of the page) we get a magnetic force pointing downward, thus meaning the positive charges would be forced downward as well. This is in conflict with the positive voltmeter reading and thus cannot be true. Next we check if negative charge carriers agree with the voltmeter readings. A negatively charged mobile charge carrier moves counter to the conventional current, in this case meaning it moves across the block from right to left resulting in a velocity in the negative x direction. When we take the cross product of this velocity and the magnetic field out of the page multiplied by the charge of the carrier we get a magnetic force pointing downwards (using F = q(v X B). This would result in the block's bottom being negatively charged and the top being positively charged. This result agrees with the given voltmeter reading. The mobile charge carriers are negative.
</div>
</div>

===Middling===

[[File:Hall Effect Middling problem 1.png]]

<math>B = 1.8 T </math> out of the page (denoted by concentric circles)

<math> n = 7*10^{25} /m^3 </math>

<math> u = 3*10^{-5} </math>

# What does reading does the voltmeter display (both magnitude and sign)?
# What does reading does the Ammeter display(both magnitude and sign?

<div class="toccolours mw-collapsible mw-collapsed">
'''''Click for Solution to #1'''''
<div class="mw-collapsible-content">
;Step 1 Find <math> E_{Hall} </math>
: <math> ΣF_y = q(v\; Χ \;B) + q|E_{Hall}| </math>
: <math> 0 = q(v\; Χ \;B) + q|E_{Hall}| </math>
: <math> q(v\; Χ \;B) = q|E_{Hall}| </math>
: <math> |E_{Hall}| = (v\; Χ \;B) </math>
: <math> |E_{Hall}| = |v| * |B| </math>

;Step 2 Find v
: <math> I = q*n*A*v </math>
: <math> v = \frac{I}{q*n*A} </math>

;Step 3 Substitute v into our formula for <math> E_{Hall} </math>
: <math> |E_{Hall}| = \frac{I * |B|}{q*n*A} </math>

;Step 4
: <math> σ = q*n*u </math>

;Step 5
: <math> R = \frac{L}{σA} </math>

;Step 6 Substitute σ
: <math> R = \frac{L}{q*n*u*A} </math>

;Step 7
: <math> Emf = I*R </math>

;Step 8 Substitute R
: <math> Emf = \frac{I*L}{q*n*u*A} </math>

;Step 9 Solve for I
: <math> I = \frac{Emf*q*n*u*A}{L} </math>

;Step 10 Substitute I in our formula for <math> E_{Hall} </math>
: <math> |E_{Hall}| = \frac{Emf * u * |B|}{L} </math>

;Step 11
: <math> ∆V = E * d </math>

;Step 12 Substitute <math> E_{Hall} </math>
: <math> ∆V = \frac{Emf * u * |B|* h}{L} </math>

;Step 13 Plug in given values and solve for<math> ∆V </math>
: <math> ∆V = -1.767*10^{-5} </math>

Explanation:
The voltmeter reads the voltage of the bar between the given distance. Since this voltmeter is attached along the height of the bar, the distance is going to be the 3cm. We write out the Lorentz Force formula and set it equal to zero, which makes the magnetic force and electric force equal to each other. After manipulating the equation, the Hall Electric Field is drift sped times the magnetic field. The drift speed is found by manipulating the Current formula, Area density formula, and the Resistance Formula. After I is found, you plug it into the I in the drift speed formula, and plug drift speed v into the Hall electric field formula. Since Hall voltage is Hall electric times the distance, you multiply the calculated Hall electric field with 3 cm in order to get the final Hall voltage.
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
'''''Click for Solution to #2'''''
<div class="mw-collapsible-content">
<math> I = \frac{Emf*q*n*u*A}{L} </math>

<math> I = 2.19927 A </math>

Explanation:
You use the derivation of I from first portion of the question and plug in the values to calculate the conventional current. The Area here is the width times the height because the Ammeter is connected through the face created by the area of width and height.
</div>
</div>

===Difficult===

[[File:Hall Effect difficult problem.png]]

<math> B = 1.5</math> T out of the page (denoted by concentric circles)

# Calculate the drift speed v of the mobile charges
# Calculate the charge density n of the mobile charges
# ∆V = 13 V along the length of the bar, calculate the mobility u of the mobile charge carrier in the metal

<div class="toccolours mw-collapsible mw-collapsed">
'''''Click for Solution to #1'''''
<div class="mw-collapsible-content">

;Step 1 Find <math> E_{Hall} </math>
: <math> ΣF_y = q(v\; Χ \;B) + q*E_{Hall} </math>
: <math> 0 = q(v\; Χ \;B) + q*E_{Hall}</math>
: <math> q(v\; Χ \;B) = q*E_{Hall} </math>
: <math> E_{Hall} = (v\; Χ \;B) </math>
: <math> E_{Hall} = v * B </math>

;Step 2
: <math> E_{Hall} = \frac{∆V_H}{h} </math>

;Step 3 Substitute <math> E_{Hall} </math>
: <math> v * B = \frac{∆V_H}{h} </math>

;Step 4 Solve for v
: <math> v = \frac{∆V_H}{h*B} </math>

;Step 5 Plug in given values
: <math> v = 1.367 </math> m/s

Explanation:
First, set the Lorentz Force Equation equal to zero. After a couple of algebraic manipulations similar to the middling question, the Hall electric field equals to the product of the drift speed and magnetic field. Since, the hall electric field is not given but hall voltage is, you have to substitute the hall electric field with hall voltage divided by the height of the bar (distance that voltmeter calculated). Afterwards, plug in all the given values, and calculate for the drift speed.
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
'''''Click for Solution to #2'''''
<div class="mw-collapsible-content">
;Step 1
: <math> I = |q|*n*A*v </math>

;Step 2
: <math> n = \frac{I}{|q|*A*v} </math>

;Step 3 Plug in given values and solve
: <math> n = 9.971 * 10^{23} /m^3</math>

Explanation:
In order to find the charge density of the mobile charge carriers use the conventional current formula. Manipulate the conventional current formula to find a formula for charge density and plug in all the values.
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
'''''Click for Solution to #3'''''
<div class="mw-collapsible-content">
;Step 1
: <math> v = u*E </math>

;Step 2 Find a formula for u
: <math> u = \frac{v}{E} </math>

;Step 3 Substitute for E using <math> ∆V = E*L </math>
: <math> u = \frac{v*L}{∆V} </math>

;Step 4 Plug in known and calculated values
: <math> u = 2.41*10^{-3} </math>

Explanation:
The drift speed of the charge carriers is the product of the electric field and mobility of the charge carriers. Since electric field is not given, but the voltage along the length of the bar is, you have to substitute the electric field with the given voltage divided by the length of the bar. Afterwards, plug in all the values given in the problem and the value calculated for the drift speed.
</div>
</div>

==Applications==
Hall effect is all about seeing the relationship between magnetic and electric forces while also remembering how metals polarize. This means that it has a lot of mechanical and machine applications. It can sense when a magnetic field or electric field changes, so it can control many machines, apply pressures, and report many values. All of these skills are very important for Mechanical Engineering, so this topic has a lot of relevance to my major. Moreover, a lot of engineering, in general, is about analyzing concepts before calculating values. The idea of the Hall Effect gives a lot of important data without the use of any numbers (of course it gives more info on the calculation of numbers). This reasoning process required for the Hall Effect is a very helpful skill for engineers to have.

[[File:Hall sensor tach.gif|thumb|left|Hall Effect Sensor with a magnet]]
Another field that takes advantage of the Hall Effect is Electrical Engineering thanks to the Hall Effect Sensor. Electrical engineers can use the hall effect sensor to record movement. As seen in the picture to the left, the sensor will increase its voltage the closer the magnet is to the sensor. In fact, a VIP group here at Georgia Tech, the VIP Hands-on Learning team, researched the possibility of using the sensor to measure the movement of a two-degree of freedom spring-mass system.
Links to the VIP Research: https://vip.gatech.edu/wiki/index.php/Vibrations https://vip.gatech.edu/wiki/index.php/Hall_Effect_Sensor

===Industrial===

Hall Effects are used in industry to aid in the control of Hydraulic systems such as moving cranes and backhoes. It is also used to help sense a car wheel's motion to aid in the use of anti-skid/anti-lock brakes. Every smartphone today uses a hall effect sensor as well. This is how the digital compass of a cell phone works. The hall effect senses the change in magnetic field to approximate direction. Another great way of using the hall effect in smartphones is to lock the screen when a case cover is flipped. The cover has a magnet that the smartphone senses, so it locks the screen automatically when the cover is on the screen. A test for this feature can be seen in the following video: https://www.youtube.com/watch?v=ITbT5vrvhX8 .

===Laboratory===

Hall effect is also taken into consideration when hall probes are used as magnetometers.

A Hall probe is used to measure the difference of magnetic flux perpendicular to its sensor. This information is then fed to magnetometers to help read the difference in magnetic fields.

Hall effect sensor:
http://www.ebay.com/sch/i.html?_nkw=hall+effect+sensor

Magnetometer:
http://www.ebay.com/itm/EM2-EARTH-MAGNETOMETER-MAP-MAGNETIC-FIELDS-SURVEY-TOOL-/251324557405?hash=item3a841c685d:m:m8gnViuidubx7vMbMejiNNA

To use this idea in a lab, simply create a circuit through a conductive material, like a piece of foil, and calculate the direction of the magnetic field using right-hand rule. Use this information to then properly add the hall probes to the foil so they are perpendicular to the magnetic field, and then BOOM! You will have information to read to a magnetometer.

==History==
[[File:HALL3.jpg|thumb|right|Edwin Herbert Hall]]

The Hall Effect was discovered in 1879 by [[Edwin Hall]] while attending Johns Hopkins University for his Doctoral Degree. While a solid mathematical groundwork for electric and magnetic phenomenon had already been discovered by James Clark Maxwell, many of the physical implications and practical uses for these theories was still being explored. The interaction of magnetic and electric fields was a particularly hot topic. Hall exposed a gold leaf (metal slab) to a magnetic field perpendicular to its surface and had current flow through the slab. He observed a potential difference perpendicular to the current and also the magnetic field. This means that potential is observed not only in the direction of current flow as usual. This is what led to Hall's discovery of the Hall Effect, originally published in his paper [https://www.jstor.org/stable/2369245?seq=1#metadata_info_tab_contents|"On a New Action of the Magnet on Electric Currents"].

==Conclusion: Tips to remember==

1. When a current carrying metal/conductor is placed in a magnetic field, a voltage is formed perpendicular to both current and magnetic field

2. The Hall effect is made when the charges create almost a polarized metal, as a result of being subject to a magnetic field perpendicular to the flow of electrons.

3. Right-hand rule whenever in doubt.

Hall effect can only be tested so many ways. There are a few tricks to keep in mind.

[[File:HALL1.png]]

In the diagram above a voltmeter connected to a sheet of metal. Since the voltmeter reads a negative voltage, you can automatically assume that the side connected to the negative terminal of the voltmeter is connected to the positive side of the metal due to hall effect, because voltmeter is reading a charge in the opposite direction.

[[File:HALL2.png]]

== 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?

[[Combining Electric and Magnetic Forces]]

[[Biot-Savart Law for Currents]]

[[Lorentz Force]]
===Further reading===

Books, Articles or other print media on this topic

Matter and Interactions: Volume 2 by Ruth Chabay and Bruce Sherwood (4th Edition)

http://www.phys.utk.edu/labs/modphys/Hall%20Effect.pdf

===External links===

Internet resources on this topic

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/hall.html

https://www.youtube.com/watch?v=_ATDraCQtpQ

==References==

https://en.wikipedia.org/wiki/Hall_effect

http://www.nobelprize.org/nobel_prizes/physics/laureates/1998/press.html

https://en.wikipedia.org/wiki/Edwin_Hall

Matter and Interactions: Volume 2 by Ruth Chabay and Bruce Sherwood (4th Edition)

http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/hall-edwin.pdf

http://www.electronics-tutorials.ws/electromagnetism/hall-effect.html

https://www.quora.com/What-is-the-use-of-Hall-effect-sensors-in-smartphones

[[Category: Hall Effect]]

Hall Effect

2019-11-25T03:04:05Z

Aboswell7: /* Simple */

The Hall Effect is the electric polarization of a block or slab of metal that occurs when a current is run through it while it is subject to a magnetic field perpendicular to the current.

==The Main Idea==

When a mobile charge, either positive or negative, flows through a metal block and is influenced by a magnetic field, the magnetic force on the charges force them to begin concentrating on one side of the block. Thus the block polarizes and has negative charges on one side and positive on the other in order to remain neutral. This grouping of positive charges in one part of the block and negative charges in another part of the block creates an electric field and thus an electric force equal on magnitude to the magnetic force that causes the initial polarization, but opposite in direction. The magnetic and electric forces cancel each other out and after some time, the charges flow normally through the block and do not group on one side or the other of the block. This perpendicular electric field also creates a potential difference known as the "Hall Voltage."

===Part 1: Normal circuit (No Magnetic Field Yet)===
(For simplicity, the mobile charges in this example have already been determined to be negatively charged electrons. This will not always be the case and it should not be assumed that the mobile charges are electrons)

Mobile electrons flow through a wire due to a parallel electric field inside the wire. This electric field is caused by an energy source, most commonly a battery. The parallel electric field flows from an area of high potential (i.e. the positive end of the battery) to an area of low potential (i.e. the negative end of the battery). This is the same direction as the conventional current. Since electrons are negatively charged, they flow in the opposite direction of the parallel electric field.

=== Part 2: Initial Transient State (Magnetic Field Present) ===

Mobile electrons are subjected to a magnetic field perpendicular to their motion as they flow through the wire. This results in the mobile charges being forced onto one side of the block by the magnetic force. This grouping of mobile charges on one side of the block creates an electric force. As time passes, more mobile charges are deposited on the side of the block and the electric force increases in magnitude.

===Part 3: Steady State (Magnetic Field Still Present, but abated)===

Over time massive quantities of charges are concentrated on one side of the block. As the charges build up, they will begin to create a charged area on one surface of the conductor. The charged surface will create an electric force to oppose the magnetic force that is pushing new electrons onto this charged surface. This opposing electric force is called the transverse electric force. When enough mobile charges have collected, their combined transverse electric force will be equal in magnitude to the magnetic force that is holding them. At this point, there is no net vertical force pushing more electrons against the surface of the conductor and these electrons will flow normally again, as they would if there was no magnetic field present. This is called the steady state.

==A Mathematical Model==

===Part 1: Normal circuit (No Magnetic Field Yet)===

<math> F_{electric, parallel} = qE_{parallel} </math>

Where q is the electric charge of the mobile charge. As F and E are vectors, a negative charge results in an electric force in the opposite direction of the electric field.

=== Part 2: Initial Transient State (Magnetic Field Present) ===

<math> F_{magnetic} = q(v\; Χ \;B)</math>

Where v is the velocity of the mobile charge and B is the magnetic field. For help calculating the cross product, including an example using the Hall Effect, see [[Right-Hand_Rule]]. REMEMBER, the mobile charge will move in the opposite direction of the cross product if it is negative, similar to how it behaves in an electric field.

===Part 3: Steady State (Magnetic Field Still Present, but abated)===

<math> F_{electric, perpendicular} = qE_{perpendicular} </math>

<math> |F_{electric, perpendicular}| = |F_{magnetic}| </math>

==Computational Model==
In this diagram, it is assumed the charge carrier is a negatively charged electron. THIS IS NOT A SAFE ASSUMPTION on a real question, experiment, or exam but was done for the purpose of simplifying explanations.

===Part 1: Normal circuit (No Magnetic Field Yet)===

[[File: Hall_Effect_part_1.png]]

In this diagram a solid conductive metal block is connected to two ends of a battery by wires. At this time there is no magnetic field present and electrons flow through the block in a straight line from wire to wire without interference or interruption.

=== Part 2: Initial Transient State (Magnetic Field Present) ===

[[File: Hall_effect_part_2.png]]

In this diagram the circles containing x's represent a magnetic field (NOT a magnetic force) into the page. When the electrons begin to move across the block their initial velocity interacts with the magnetic field to create a magnetic force downward. This causes electrons to begin pooling on the bottom face of the slab. This polarizes the block and creates a vertical potential difference across the block. It also creates an electric force that opposes the magnetic force, but in this state it is smaller than the magnetic force, resulting in continued pooling of electrons.

===Part 3: Steady State (Magnetic Field Still Present, but abated)===

[[File: Hall_effect_part_3.png]]

As time passes eventually sufficient quantities of electrons build up to create an electric force equal in magnitude to the magnetic force but opposite in direction. This allows the electrons to continue flow across the block as they did in part 1, however now the vertical voltage difference which was created in part 2 is not only still present but also at its maximum value. Most practice and exam problems will involve either the calculation or orientation of this voltage difference. It's important to remember that a voltmeter will have a positive reading if the positive node is connected to the end of the block which is positively charged and vice versa.

==Examples==

===Simple===
[[File:Hall Effect 1.jpg]]
[[File:Hall Effect 2.jpg]]
[[File:Hall effect cenceptual 1.png]]

A metal block is connected to a battery by two wires. Conventional current flows clockwise and the mobile charge in the block is positive. The block also experiences a magnetic field out of the page denoted by concentric circles. The block is also connected to a voltmeter. The positive end of the voltmeter is connected to the bottom of the block and the negative end of the voltmeter is connected to the top of the block. See attached photo for a diagram. What sign will the voltmeter display?

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

'''''Click for Solution'''''
<div class="mw-collapsible-content">
In this case, since magnetic force is q(v X B) and we know the charges are positive and thus follow the conventional current which moves across the block from left to right, the magnetic force points up. This means that the mobile charges (positive) will be pushed towards the bottom of the block. Remember: a voltmeter will have a positive reading if the positive end is connected to the positively charged side of the block. In this case, the bottom of the block is positively charged and the positive end of the voltmeter is connected there. The voltmeter will have a positive reading.

</div>
</div>

[[File:Hall effect cenceptual 2.png]]

A battery and metal block are connected by 2 wires. Conventional current flows clockwise. A magnetic field points out of the page, denoted by concentric circles. A voltmeter is attached to the block with its positive lead at the top of the block and its negative lead at the bottom of the block. The voltmeter has a positive reading. What sign does the mobile charge have?

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

'''''Click for Solution'''''
<div class="mw-collapsible-content">
From the voltmeter reading we can deduce that the top of the block is positively charged and the bottom negatively charged. Thus, we check if positive mobile charge carriers satisfy this requirement. A positive charge moves with the conventional current, which in this case is from left to right, meaning its velocity would be in the positive x direction. When taking the cross product of the charge's velocity and the magnetic field (out of the page) we get a magnetic force pointing downward, thus meaning the positive charges would be forced downward as well. This is in conflict with the positive voltmeter reading and thus cannot be true. Next we check if negative charge carriers agree with the voltmeter readings. A negatively charged mobile charge carrier moves counter to the conventional current, in this case meaning it moves across the block from right to left resulting in a velocity in the negative x direction. When we take the cross product of this velocity and the magnetic field out of the page multiplied by the charge of the carrier we get a magnetic force pointing downwards (using F = q(v X B). This would result in the block's bottom being negatively charged and the top being positively charged. This result agrees with the given voltmeter reading. The mobile charge carriers are negative.
</div>
</div>

===Middling===

[[File:Hall Effect Middling problem 1.png]]

<math>B = 1.8 T </math> out of the page (denoted by concentric circles)

<math> n = 7*10^{25} /m^3 </math>

<math> u = 3*10^{-5} </math>

# What does reading does the voltmeter display (both magnitude and sign)?
# What does reading does the Ammeter display(both magnitude and sign?

<div class="toccolours mw-collapsible mw-collapsed">
'''''Click for Solution to #1'''''
<div class="mw-collapsible-content">
;Step 1 Find <math> E_{Hall} </math>
: <math> ΣF_y = q(v\; Χ \;B) + q|E_{Hall}| </math>
: <math> 0 = q(v\; Χ \;B) + q|E_{Hall}| </math>
: <math> q(v\; Χ \;B) = q|E_{Hall}| </math>
: <math> |E_{Hall}| = (v\; Χ \;B) </math>
: <math> |E_{Hall}| = |v| * |B| </math>

;Step 2 Find v
: <math> I = q*n*A*v </math>
: <math> v = \frac{I}{q*n*A} </math>

;Step 3 Substitute v into our formula for <math> E_{Hall} </math>
: <math> |E_{Hall}| = \frac{I * |B|}{q*n*A} </math>

;Step 4
: <math> σ = q*n*u </math>

;Step 5
: <math> R = \frac{L}{σA} </math>

;Step 6 Substitute σ
: <math> R = \frac{L}{q*n*u*A} </math>

;Step 7
: <math> Emf = I*R </math>

;Step 8 Substitute R
: <math> Emf = \frac{I*L}{q*n*u*A} </math>

;Step 9 Solve for I
: <math> I = \frac{Emf*q*n*u*A}{L} </math>

;Step 10 Substitute I in our formula for <math> E_{Hall} </math>
: <math> |E_{Hall}| = \frac{Emf * u * |B|}{L} </math>

;Step 11
: <math> ∆V = E * d </math>

;Step 12 Substitute <math> E_{Hall} </math>
: <math> ∆V = \frac{Emf * u * |B|* h}{L} </math>

;Step 13 Plug in given values and solve for<math> ∆V </math>
: <math> ∆V = -1.767*10^{-5} </math>

Explanation:
The voltmeter reads the voltage of the bar between the given distance. Since this voltmeter is attached along the height of the bar, the distance is going to be the 3cm. We write out the Lorentz Force formula and set it equal to zero, which makes the magnetic force and electric force equal to each other. After manipulating the equation, the Hall Electric Field is drift sped times the magnetic field. The drift speed is found by manipulating the Current formula, Area density formula, and the Resistance Formula. After I is found, you plug it into the I in the drift speed formula, and plug drift speed v into the Hall electric field formula. Since Hall voltage is Hall electric times the distance, you multiply the calculated Hall electric field with 3 cm in order to get the final Hall voltage.
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
'''''Click for Solution to #2'''''
<div class="mw-collapsible-content">
<math> I = \frac{Emf*q*n*u*A}{L} </math>

<math> I = 2.19927 A </math>

Explanation:
You use the derivation of I from first portion of the question and plug in the values to calculate the conventional current. The Area here is the width times the height because the Ammeter is connected through the face created by the area of width and height.
</div>
</div>

===Difficult===

[[File:Hall Effect difficult problem.png]]

<math> B = 1.5</math> T out of the page (denoted by concentric circles)

# Calculate the drift speed v of the mobile charges
# Calculate the charge density n of the mobile charges
# ∆V = 13 V along the length of the bar, calculate the mobility u of the mobile charge carrier in the metal

<div class="toccolours mw-collapsible mw-collapsed">
'''''Click for Solution to #1'''''
<div class="mw-collapsible-content">

;Step 1 Find <math> E_{Hall} </math>
: <math> ΣF_y = q(v\; Χ \;B) + q*E_{Hall} </math>
: <math> 0 = q(v\; Χ \;B) + q*E_{Hall}</math>
: <math> q(v\; Χ \;B) = q*E_{Hall} </math>
: <math> E_{Hall} = (v\; Χ \;B) </math>
: <math> E_{Hall} = v * B </math>

;Step 2
: <math> E_{Hall} = \frac{∆V_H}{h} </math>

;Step 3 Substitute <math> E_{Hall} </math>
: <math> v * B = \frac{∆V_H}{h} </math>

;Step 4 Solve for v
: <math> v = \frac{∆V_H}{h*B} </math>

;Step 5 Plug in given values
: <math> v = 1.367 </math> m/s

Explanation:
First, set the Lorentz Force Equation equal to zero. After a couple of algebraic manipulations similar to the middling question, the Hall electric field equals to the product of the drift speed and magnetic field. Since, the hall electric field is not given but hall voltage is, you have to substitute the hall electric field with hall voltage divided by the height of the bar (distance that voltmeter calculated). Afterwards, plug in all the given values, and calculate for the drift speed.
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
'''''Click for Solution to #2'''''
<div class="mw-collapsible-content">
;Step 1
: <math> I = |q|*n*A*v </math>

;Step 2
: <math> n = \frac{I}{|q|*A*v} </math>

;Step 3 Plug in given values and solve
: <math> n = 9.971 * 10^{23} /m^3</math>

Explanation:
In order to find the charge density of the mobile charge carriers use the conventional current formula. Manipulate the conventional current formula to find a formula for charge density and plug in all the values.
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
'''''Click for Solution to #3'''''
<div class="mw-collapsible-content">
;Step 1
: <math> v = u*E </math>

;Step 2 Find a formula for u
: <math> u = \frac{v}{E} </math>

;Step 3 Substitute for E using <math> ∆V = E*L </math>
: <math> u = \frac{v*L}{∆V} </math>

;Step 4 Plug in known and calculated values
: <math> u = 2.41*10^{-3} </math>

Explanation:
The drift speed of the charge carriers is the product of the electric field and mobility of the charge carriers. Since electric field is not given, but the voltage along the length of the bar is, you have to substitute the electric field with the given voltage divided by the length of the bar. Afterwards, plug in all the values given in the problem and the value calculated for the drift speed.
</div>
</div>

==Applications==
Hall effect is all about seeing the relationship between magnetic and electric forces while also remembering how metals polarize. This means that it has a lot of mechanical and machine applications. It can sense when a magnetic field or electric field changes, so it can control many machines, apply pressures, and report many values. All of these skills are very important for Mechanical Engineering, so this topic has a lot of relevance to my major. Moreover, a lot of engineering, in general, is about analyzing concepts before calculating values. The idea of the Hall Effect gives a lot of important data without the use of any numbers (of course it gives more info on the calculation of numbers). This reasoning process required for the Hall Effect is a very helpful skill for engineers to have.

[[File:Hall sensor tach.gif|thumb|left|Hall Effect Sensor with a magnet]]
Another field that takes advantage of the Hall Effect is Electrical Engineering thanks to the Hall Effect Sensor. Electrical engineers can use the hall effect sensor to record movement. As seen in the picture to the left, the sensor will increase its voltage the closer the magnet is to the sensor. In fact, a VIP group here at Georgia Tech, the VIP Hands-on Learning team, researched the possibility of using the sensor to measure the movement of a two-degree of freedom spring-mass system.
Links to the VIP Research: https://vip.gatech.edu/wiki/index.php/Vibrations https://vip.gatech.edu/wiki/index.php/Hall_Effect_Sensor

===Industrial===

Hall Effects are used in industry to aid in the control of Hydraulic systems such as moving cranes and backhoes. It is also used to help sense a car wheel's motion to aid in the use of anti-skid/anti-lock brakes. Every smartphone today uses a hall effect sensor as well. This is how the digital compass of a cell phone works. The hall effect senses the change in magnetic field to approximate direction. Another great way of using the hall effect in smartphones is to lock the screen when a case cover is flipped. The cover has a magnet that the smartphone senses, so it locks the screen automatically when the cover is on the screen. A test for this feature can be seen in the following video: https://www.youtube.com/watch?v=ITbT5vrvhX8 .

===Laboratory===

Hall effect is also taken into consideration when hall probes are used as magnetometers.

A Hall probe is used to measure the difference of magnetic flux perpendicular to its sensor. This information is then fed to magnetometers to help read the difference in magnetic fields.

Hall effect sensor:
http://www.ebay.com/sch/i.html?_nkw=hall+effect+sensor

Magnetometer:
http://www.ebay.com/itm/EM2-EARTH-MAGNETOMETER-MAP-MAGNETIC-FIELDS-SURVEY-TOOL-/251324557405?hash=item3a841c685d:m:m8gnViuidubx7vMbMejiNNA

To use this idea in a lab, simply create a circuit through a conductive material, like a piece of foil, and calculate the direction of the magnetic field using right-hand rule. Use this information to then properly add the hall probes to the foil so they are perpendicular to the magnetic field, and then BOOM! You will have information to read to a magnetometer.

==History==
[[File:HALL3.jpg|thumb|right|Edwin Herbert Hall]]

The Hall Effect was discovered in 1879 by [[Edwin Hall]] while attending Johns Hopkins University for his Doctoral Degree. While a solid mathematical groundwork for electric and magnetic phenomenon had already been discovered by James Clark Maxwell, many of the physical implications and practical uses for these theories was still being explored. The interaction of magnetic and electric fields was a particularly hot topic. Hall exposed a gold leaf (metal slab) to a magnetic field perpendicular to its surface and had current flow through the slab. He observed a potential difference perpendicular to the current and also the magnetic field. This means that potential is observed not only in the direction of current flow as usual. This is what led to Hall's discovery of the Hall Effect, originally published in his paper [https://www.jstor.org/stable/2369245?seq=1#metadata_info_tab_contents|"On a New Action of the Magnet on Electric Currents"].

==Conclusion: Tips to remember==

1. When a current carrying metal/conductor is placed in a magnetic field, a voltage is formed perpendicular to both current and magnetic field

2. The Hall effect is made when the charges create almost a polarized metal, as a result of being subject to a magnetic field perpendicular to the flow of electrons.

3. Right-hand rule whenever in doubt.

Hall effect can only be tested so many ways. There are a few tricks to keep in mind.

[[File:HALL1.png]]

In the diagram above a voltmeter connected to a sheet of metal. Since the voltmeter reads a negative voltage, you can automatically assume that the side connected to the negative terminal of the voltmeter is connected to the positive side of the metal due to hall effect, because voltmeter is reading a charge in the opposite direction.

[[File:HALL2.png]]

== 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?

[[Combining Electric and Magnetic Forces]]

[[Biot-Savart Law for Currents]]

[[Lorentz Force]]
===Further reading===

Books, Articles or other print media on this topic

Matter and Interactions: Volume 2 by Ruth Chabay and Bruce Sherwood (4th Edition)

http://www.phys.utk.edu/labs/modphys/Hall%20Effect.pdf

===External links===

Internet resources on this topic

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/hall.html

https://www.youtube.com/watch?v=_ATDraCQtpQ

==References==

https://en.wikipedia.org/wiki/Hall_effect

http://www.nobelprize.org/nobel_prizes/physics/laureates/1998/press.html

https://en.wikipedia.org/wiki/Edwin_Hall

Matter and Interactions: Volume 2 by Ruth Chabay and Bruce Sherwood (4th Edition)

http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/hall-edwin.pdf

http://www.electronics-tutorials.ws/electromagnetism/hall-effect.html

https://www.quora.com/What-is-the-use-of-Hall-effect-sensors-in-smartphones

[[Category: Hall Effect]]

Motional Emf

2019-11-25T02:57:05Z

Aboswell7:

<h1><strong>Edited by Adeline Boswell Fall 2019</strong></h1>

'''Motional emf''' is an electromagnetic field caused by current that is produced through the motion of a conductor in a magnetic field. Polarization of the bar occurs which is similar to the Hall effect except that the Hall effect involves polarization through the force of a magnetic field on charged particles that are already moving inside a motionless conductor. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small.

Note: This page does involve the use of Faraday's Law.

==The Main Idea==

Moving a metal bar (or similar conductive material) will naturally also move the mobile charges within the metal bar. if this is done in a magnetic field it will create a magnetic force, which acts on the charged particles inside the bar polarizing it (charge separation). This makes the bar similar to a battery which means that If the bar is part of a circuit, the magnetic force produced causes a current to run through it.

Additionally, when the metal bar is polarized, because of the charge separation, an electric force is created in the bar opposite to the magnetic force on charged particles.

===Polarization and Steady State===
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]

Polarization occurs due to the shift of the mobile electron sea in one direction caused by the magnetic force. Eventually, the shifting will stop when enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity, assuming it moves in a frictionless environment.
<br />
<br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.

===Driving Current===
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]

[[File:electromagnetforce.png|thumb|alt=sssa|The x and y components of the magnetic force on a mobile electron in the bar]]

If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the bar's polarization in the bar mimics a battery and can drive a current through the bar and the rails it slides on, given the bars are connected at some other point.
<br />
<br />
Once the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. There will be a magnetic force in the direction of the length of the bar on the electrons which will cause the electrons to have a small velocity through the bar. This is in addition to the velocity caused by the moving bar. In the diagram shown on the left the velocity vector of the electrons would be <math> < V_{bar}, V, 0 > </math>. Magnetic force on the electrons is <math> <-e*V*B,-e*V_{bar}*B, 0> </math>. B is the magnetic field being applied. It is clear that there is a magnetic force on the electrons that is opposite to the horizontal force of the moving bar. This means that the horizontal net force for the bar is <math> F_{net} = F_{applied} - N*V*B*e </math> with N being the number of mobile electrons. If the bar moves at higher speeds, the vertical magnetic force on the electrons becomes greater along with the vertical velocity of the electrons. This in turn, increases the magnetic force to the left of the bar. If the bar continues to accelerate, the horizontal net force will get smaller and smaller until it reaches zero at which point the bar will move at a constant velocity with one force pulling it in one direction and the magnetic force pulling it in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.
<br />
<br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip for the entire circuit is zero.

===Ideal Conditions===
Motional emf is difficult to observe with light bulbs and batteries because it is relatively small. In order to obtain a sizeable emf, a large magnetic field (B) needs to be applied over large regions (L) all the while the bar is moving at great velocities (V) through the region. If dealing with a wire, adding multiple turns will also help. Even then if you have a large emf, it only lasts for a little amount of time. Also detectors like lightbulbs and compasses are not very sensitive, so in order to actually detect motional emf more sensitive equipment is needed.

==A Mathematical Model==
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]

The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.
<br />
<br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.
<br />
<br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.

===Equations to remember===
'''1.''' <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.
<br />
<br />
'''2.''' During steady state, the electric force balances with the magnetic force(<math>qvB=qE</math>), so <math>E=vB</math>.
<br />
<br />
'''3.'''We know <math>\Delta V=emf</math>, <br /> <math>\Delta V=EL</math>, <br /> and <math>E=vB</math>, <br /> so <math>\Delta V=v_{bar}BL</math>.
<br />
<br />
'''4.''' Power <math>P=I\Delta V</math> so <math>P=I(IR)=I^{2}R</math>.
<br />
<br />
'''5.'''<math> emf = {\frac{q(\vec{v} \times \vec{B})L}{q}} = v*B*L </math> where v is the velocity of the bar and L is the bar length

==A Computational Model==
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].

==Examples==

===Simple===
[[File:Motional EMF Example.jpg]]
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]

''Taken from the'' Matter & Interactions ''textbook, variation of P60''.

A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?
<br />
<br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.
<br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.
<br />

===Middling===
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''

A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?
<br />
<br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.
<br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.
<br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.
<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.
<br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.
<br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.
<br />

===Difficult===
[[File:Middlemotionalemf.png|center|alt=Picture for difficult example]]

''Taken from the'' Matter & Interactions ''textbook, P64''.
<br />

A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar. '''(d)''' What is the direction of the electric force acting on a positive mobile charge? '''(e)''' What is the direction of the magnetic force acting on the bar?
<br />
<br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.
<br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.
<br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.
<br />
<br />
Note: We can also find the speed of the falling bar with <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>. Using the loop rule, <math>0=IR - {emf}</math>. So <math>\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |=IR</math>. We can transform that to <math>IR=\frac{\mathrm{d} (BA)}{\mathrm{d} t}</math>. Since B is constant, <math>IR=B(\frac{\mathrm{d} (A)}{\mathrm{d} t})</math>. We can transform that to <math>IR=B(\frac{\mathrm{d} (Lh)}{\mathrm{d} t})</math>, where h is the distance of the bar above the bottom rod. Since L is constant, <math>IR=BL(\frac{\mathrm{d} (h)}{\mathrm{d} t})</math>. <math>\frac{\mathrm{d} (h)}{\mathrm{d} t})</math> is the velocity of the bar, so <math>IR=BLv</math>. Solving for v, <math>v={MgR}/{L^{2}B^{2}}</math>.
<br />
'''(d)''' The electric force acting on a positive mobile charge points towards the ''right'' in the bar. Using the right hand rule, with B pointing out of the page, v pointing downwards, we know that the magnetic force points to the right. This means that the bar is polarized with positive charges on the left side of the bar and negative charges on the right side. The electric force points from positive charges to negative charges, so the electric force points towards the right.
<br />
'''(e)''' The magnetic force acting on the bar points ''upwards''. We know that current flows from left to right in the bar because positive charges are polarized on the left side of the bar and negative charges are on the right side of the bar. Using the right hand rule, with B pointing out of the page and current pointing to the right, we find that the magnetic force points upwards.

==Connectedness==
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.
<br />
Motional emf is also applied in the DC motors of airplanes, when mechanical energy is transformed into electrical energy. Additionally, motional emf is applied in breaking systems. When an object moves through a magnetic field, it resists the change(movement) by converting the mechanical energy into electrical energy. So if an object moves with a sufficient amount of force to move, through a magnetic field, it can convert enough mechanical energy to stop a system. This concept is applied in, for example, roller coasters.

==History==
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]][[File:James Clerk Maxwell.png|thumb|left|James Clerk Maxwell]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and the Maxwell equations.
<br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.

== See also ==
*[[Motional Emf using Faraday's Law]]: An expansion of this concept
*[[Lorentz Force]]: Combining electric and magnetic forces
*[[Generator]]: Real-world application
*[[Right-Hand Rule]]: How it works and other RHRs
===Further reading===
*''Matter & Interactions, Vol 2''
*''The Feynman Lectures on Physics, Vol 2'', Ch 16

===External links===
*[http://web.mit.edu/8.02t/www/materials/StudyGuide/guide10.pdf Guide from MIT]

==References==

*''Matter & Interactions Vol 2''
*MIT OpenCourseWare
*[http://web.hep.uiuc.edu/home/serrede/P435/Lecture_Notes/A_Brief_History_of_Electromagnetism.pdf A Brief History of The Development of Classical Electrodynamics]

[[Category:Fields]]

Motional Emf

2019-11-25T02:56:15Z

Aboswell7: Added an image file titled "Motional EMF Example.jpg" to Examples (simple)

Edited by Adeline Boswell Fall 2019

'''Motional emf''' is an electromagnetic field caused by current that is produced through the motion of a conductor in a magnetic field. Polarization of the bar occurs which is similar to the Hall effect except that the Hall effect involves polarization through the force of a magnetic field on charged particles that are already moving inside a motionless conductor. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small.

Note: This page does involve the use of Faraday's Law.

==The Main Idea==

Moving a metal bar (or similar conductive material) will naturally also move the mobile charges within the metal bar. if this is done in a magnetic field it will create a magnetic force, which acts on the charged particles inside the bar polarizing it (charge separation). This makes the bar similar to a battery which means that If the bar is part of a circuit, the magnetic force produced causes a current to run through it.

Additionally, when the metal bar is polarized, because of the charge separation, an electric force is created in the bar opposite to the magnetic force on charged particles.

===Polarization and Steady State===
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]

Polarization occurs due to the shift of the mobile electron sea in one direction caused by the magnetic force. Eventually, the shifting will stop when enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity, assuming it moves in a frictionless environment.
<br />
<br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.

===Driving Current===
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]

[[File:electromagnetforce.png|thumb|alt=sssa|The x and y components of the magnetic force on a mobile electron in the bar]]

If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the bar's polarization in the bar mimics a battery and can drive a current through the bar and the rails it slides on, given the bars are connected at some other point.
<br />
<br />
Once the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. There will be a magnetic force in the direction of the length of the bar on the electrons which will cause the electrons to have a small velocity through the bar. This is in addition to the velocity caused by the moving bar. In the diagram shown on the left the velocity vector of the electrons would be <math> < V_{bar}, V, 0 > </math>. Magnetic force on the electrons is <math> <-e*V*B,-e*V_{bar}*B, 0> </math>. B is the magnetic field being applied. It is clear that there is a magnetic force on the electrons that is opposite to the horizontal force of the moving bar. This means that the horizontal net force for the bar is <math> F_{net} = F_{applied} - N*V*B*e </math> with N being the number of mobile electrons. If the bar moves at higher speeds, the vertical magnetic force on the electrons becomes greater along with the vertical velocity of the electrons. This in turn, increases the magnetic force to the left of the bar. If the bar continues to accelerate, the horizontal net force will get smaller and smaller until it reaches zero at which point the bar will move at a constant velocity with one force pulling it in one direction and the magnetic force pulling it in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.
<br />
<br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip for the entire circuit is zero.

===Ideal Conditions===
Motional emf is difficult to observe with light bulbs and batteries because it is relatively small. In order to obtain a sizeable emf, a large magnetic field (B) needs to be applied over large regions (L) all the while the bar is moving at great velocities (V) through the region. If dealing with a wire, adding multiple turns will also help. Even then if you have a large emf, it only lasts for a little amount of time. Also detectors like lightbulbs and compasses are not very sensitive, so in order to actually detect motional emf more sensitive equipment is needed.

==A Mathematical Model==
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]

The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.
<br />
<br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.
<br />
<br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.

===Equations to remember===
'''1.''' <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.
<br />
<br />
'''2.''' During steady state, the electric force balances with the magnetic force(<math>qvB=qE</math>), so <math>E=vB</math>.
<br />
<br />
'''3.'''We know <math>\Delta V=emf</math>, <br /> <math>\Delta V=EL</math>, <br /> and <math>E=vB</math>, <br /> so <math>\Delta V=v_{bar}BL</math>.
<br />
<br />
'''4.''' Power <math>P=I\Delta V</math> so <math>P=I(IR)=I^{2}R</math>.
<br />
<br />
'''5.'''<math> emf = {\frac{q(\vec{v} \times \vec{B})L}{q}} = v*B*L </math> where v is the velocity of the bar and L is the bar length

==A Computational Model==
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].

==Examples==

===Simple===
[[File:Motional EMF Example.jpg]]
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]

''Taken from the'' Matter & Interactions ''textbook, variation of P60''.

A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?
<br />
<br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.
<br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.
<br />

===Middling===
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''

A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?
<br />
<br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.
<br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.
<br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.
<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.
<br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.
<br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.
<br />

===Difficult===
[[File:Middlemotionalemf.png|center|alt=Picture for difficult example]]

''Taken from the'' Matter & Interactions ''textbook, P64''.
<br />

A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar. '''(d)''' What is the direction of the electric force acting on a positive mobile charge? '''(e)''' What is the direction of the magnetic force acting on the bar?
<br />
<br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.
<br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.
<br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.
<br />
<br />
Note: We can also find the speed of the falling bar with <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>. Using the loop rule, <math>0=IR - {emf}</math>. So <math>\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |=IR</math>. We can transform that to <math>IR=\frac{\mathrm{d} (BA)}{\mathrm{d} t}</math>. Since B is constant, <math>IR=B(\frac{\mathrm{d} (A)}{\mathrm{d} t})</math>. We can transform that to <math>IR=B(\frac{\mathrm{d} (Lh)}{\mathrm{d} t})</math>, where h is the distance of the bar above the bottom rod. Since L is constant, <math>IR=BL(\frac{\mathrm{d} (h)}{\mathrm{d} t})</math>. <math>\frac{\mathrm{d} (h)}{\mathrm{d} t})</math> is the velocity of the bar, so <math>IR=BLv</math>. Solving for v, <math>v={MgR}/{L^{2}B^{2}}</math>.
<br />
'''(d)''' The electric force acting on a positive mobile charge points towards the ''right'' in the bar. Using the right hand rule, with B pointing out of the page, v pointing downwards, we know that the magnetic force points to the right. This means that the bar is polarized with positive charges on the left side of the bar and negative charges on the right side. The electric force points from positive charges to negative charges, so the electric force points towards the right.
<br />
'''(e)''' The magnetic force acting on the bar points ''upwards''. We know that current flows from left to right in the bar because positive charges are polarized on the left side of the bar and negative charges are on the right side of the bar. Using the right hand rule, with B pointing out of the page and current pointing to the right, we find that the magnetic force points upwards.

==Connectedness==
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.
<br />
Motional emf is also applied in the DC motors of airplanes, when mechanical energy is transformed into electrical energy. Additionally, motional emf is applied in breaking systems. When an object moves through a magnetic field, it resists the change(movement) by converting the mechanical energy into electrical energy. So if an object moves with a sufficient amount of force to move, through a magnetic field, it can convert enough mechanical energy to stop a system. This concept is applied in, for example, roller coasters.

==History==
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]][[File:James Clerk Maxwell.png|thumb|left|James Clerk Maxwell]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and the Maxwell equations.
<br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.

== See also ==
*[[Motional Emf using Faraday's Law]]: An expansion of this concept
*[[Lorentz Force]]: Combining electric and magnetic forces
*[[Generator]]: Real-world application
*[[Right-Hand Rule]]: How it works and other RHRs
===Further reading===
*''Matter & Interactions, Vol 2''
*''The Feynman Lectures on Physics, Vol 2'', Ch 16

===External links===
*[http://web.mit.edu/8.02t/www/materials/StudyGuide/guide10.pdf Guide from MIT]

==References==

*''Matter & Interactions Vol 2''
*MIT OpenCourseWare
*[http://web.hep.uiuc.edu/home/serrede/P435/Lecture_Notes/A_Brief_History_of_Electromagnetism.pdf A Brief History of The Development of Classical Electrodynamics]

[[Category:Fields]]

Main Page

2019-11-25T02:33:13Z

Aboswell7: /* Motional EMF */

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==Physics 1==
===Week 1===
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====GlowScript 101====
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====Velocity and Momentum====
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===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
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</div>
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====Iterative Prediction with a Constant Force====
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===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

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

*[[Kinematics]]
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====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
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*[[Iterative Prediction of Spring-Mass System]]
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</div>
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===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
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*[[Gravitational Force]]
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*[[Electric Force]]
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====Properties of Matter====
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====Identifying Forces====
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====Curving Motion====
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====Energy Principle====
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<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
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====Potential Energy====
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<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
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**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
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===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
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*[[System & Surroundings]]
</div>
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<div class="mw-collapsible-content">
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====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
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===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
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</div>
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====Friction====
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<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
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*[[Newton's Third Law of Motion]]
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*[[Scattering: Collisions in 2D and 3D]]
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</div>
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===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
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*[[Rotational Kinematics]]
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====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
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</div>
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<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
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*[[Torque vs Work]]
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</div>
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===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
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</div>
</div>
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==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>Adeline Boswell Fall 2019</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>
</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

2019-11-25T02:27:16Z

Aboswell7: /* Hall Effect */

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

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

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

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

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

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

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

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

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

====VPython====

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

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

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

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

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

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

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

</div>
</div>

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
<h1><strong>Adeline Boswell Fall 2019</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====
<h1><strong>Adeline Boswell Fall 2019</strong></h1>
<div class="mw-collapsible-content">
*[[Motional Emf]]

[[File:Motional EMF Example.jpg]]

*[[Motional Emf using Faraday's Law]]
</div>
</div>

<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>
</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

2019-11-25T00:04:34Z

Aboswell7: /* Motional EMF */

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

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

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

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

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

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

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

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

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

====VPython====

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

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

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

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

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

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

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

</div>
</div>

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]

[[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====
<h1><strong>Adeline Boswell Fall 2019</strong></h1>
<div class="mw-collapsible-content">
*[[Motional Emf]]

[[File:Motional EMF Example.jpg]]

*[[Motional Emf using Faraday's Law]]
</div>
</div>

<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>
</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>

Motional Emf

2019-11-25T00:02:50Z

Aboswell7:

'''Motional emf''' is an electromagnetic field caused by current that is produced through the motion of a conductor in a magnetic field. Polarization of the bar occurs which is similar to the Hall effect except that the Hall effect involves polarization through the force of a magnetic field on charged particles that are already moving inside a motionless conductor. Motional emf is difficult to observe visually using batteries, light bulbs, and compasses because it is so small.

Note: This page does involve the use of Faraday's Law.

==The Main Idea==

Moving a metal bar (or similar conductive material) will naturally also move the mobile charges within the metal bar. if this is done in a magnetic field it will create a magnetic force, which acts on the charged particles inside the bar polarizing it (charge separation). This makes the bar similar to a battery which means that If the bar is part of a circuit, the magnetic force produced causes a current to run through it.

Additionally, when the metal bar is polarized, because of the charge separation, an electric force is created in the bar opposite to the magnetic force on charged particles.

===Polarization and Steady State===
[[File:Polarizationmotionalemf.png|thumb|alt=Picture showing a conducting bar moving in a magnetic field being polarized as a result of magnetic force|A conducting bar moving with velocity ''v'' is polarized as a result of the upwards magnetic force; see section 1.3 for a right-hand rule applicable to the scenario]]

Polarization occurs due to the shift of the mobile electron sea in one direction caused by the magnetic force. Eventually, the shifting will stop when enough electrons will shift in a particular direction so that the electric force, in the opposite direction, balances out the magnetic force (<math>qvB=qE</math>). Consequently, in the steady state, <math>E=vB</math> and there is no net force on the bar, so the bar does not require any additional force to keep it moving at a constant velocity, assuming it moves in a frictionless environment.
<br />
<br />
In the steady state, a nonzero E-field exists inside the metal bar; however, if the bar is not connected in a circuit, there is no current. This is because the electric force is balanced with the magnetic force, resulting in zero net force on the mobile electrons. The potential difference across the metal bar is then the product of the electric field and the length of the bar.

===Driving Current===
[[File:Circuitmotionalemf.png|thumb|left|alt=Picture demonstrating a possible circuit setup involving a moving conducting bar|A circuit formed with a moving conducting bar on conducting, frictionless rails connected by a resistor]]

[[File:electromagnetforce.png|thumb|alt=sssa|The x and y components of the magnetic force on a mobile electron in the bar]]

If the metal bar is used to form a circuit, where the bar is slid along on two frictionless metal rails that are also connected, then the bar's polarization in the bar mimics a battery and can drive a current through the bar and the rails it slides on, given the bars are connected at some other point.
<br />
<br />
Once the bar, moving within the magnetic field, has a velocity, the direction of the magnetic force can be determined through the right-hand rule. There will be a magnetic force in the direction of the length of the bar on the electrons which will cause the electrons to have a small velocity through the bar. This is in addition to the velocity caused by the moving bar. In the diagram shown on the left the velocity vector of the electrons would be <math> < V_{bar}, V, 0 > </math>. Magnetic force on the electrons is <math> <-e*V*B,-e*V_{bar}*B, 0> </math>. B is the magnetic field being applied. It is clear that there is a magnetic force on the electrons that is opposite to the horizontal force of the moving bar. This means that the horizontal net force for the bar is <math> F_{net} = F_{applied} - N*V*B*e </math> with N being the number of mobile electrons. If the bar moves at higher speeds, the vertical magnetic force on the electrons becomes greater along with the vertical velocity of the electrons. This in turn, increases the magnetic force to the left of the bar. If the bar continues to accelerate, the horizontal net force will get smaller and smaller until it reaches zero at which point the bar will move at a constant velocity with one force pulling it in one direction and the magnetic force pulling it in the opposite direction. A current now runs through the bar. The mobile electrons in the bar move toward the negatively charged end, rather than the positively charged end, because the continuous depletion of charge means that the electric field is always slightly less than what is needed to balance out the opposing magnetic field. Therefore, the electrons move to the negative end to maintain charge separation and the electric field.
<br />
<br />
The potential difference across the bar is still the product of the electric field and the length of the bar. If the bar does have some resistance, then it is treated like a battery with internal resistance. In the circuit, the potential difference round-trip for the entire circuit is zero.

===Ideal Conditions===
Motional emf is difficult to observe with light bulbs and batteries because it is relatively small. In order to obtain a sizeable emf, a large magnetic field (B) needs to be applied over large regions (L) all the while the bar is moving at great velocities (V) through the region. If dealing with a wire, adding multiple turns will also help. Even then if you have a large emf, it only lasts for a little amount of time. Also detectors like lightbulbs and compasses are not very sensitive, so in order to actually detect motional emf more sensitive equipment is needed.

==A Mathematical Model==
[[File:RHRmotionalemf.JPG|thumb|alt=Picture showing a right-hand rule applicable to motional emf|A right-hand rule determining the directions of magnetic force, conventional current, and magnetic field]]

The potential difference across the metal bar is <math>\Delta V=emf=EL=v_{bar}BL</math>. If the bar has resistance, then <math>\Delta V=emf-r_{int}I</math>.
<br />
<br />
When the bar in the circuit, in steady state, moves a distance <math>\Delta x</math> over a time <math>\Delta t</math>, the work done is <math>F \Delta x</math> and the power supplied is <math>{F \Delta x}/{\Delta t}</math>, or <math>Fv_{bar}</math>. If the rails in the circuit are connected by a resistor, then the power dissipated in the resistor is <math>ILBv_{bar}=I*emf={emf/R}*emf={emf^{2}}/R=RI^{2}</math>.
<br />
<br />
Motional emf can be calculated in terms of magnetic flux: <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.

===Equations to remember===
'''1.''' <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>.
<br />
<br />
'''2.''' During steady state, the electric force balances with the magnetic force(<math>qvB=qE</math>), so <math>E=vB</math>.
<br />
<br />
'''3.'''We know <math>\Delta V=emf</math>, <br /> <math>\Delta V=EL</math>, <br /> and <math>E=vB</math>, <br /> so <math>\Delta V=v_{bar}BL</math>.
<br />
<br />
'''4.''' Power <math>P=I\Delta V</math> so <math>P=I(IR)=I^{2}R</math>.
<br />
<br />
'''5.'''<math> emf = {\frac{q(\vec{v} \times \vec{B})L}{q}} = v*B*L </math> where v is the velocity of the bar and L is the bar length

==A Computational Model==
A simulation of motional emf can be found [http://www.phy.hk/wiki/englishhtm/Induction.htm here].

==Examples==

===Simple===
[[File:Motional EMF Example.jpg]]
[[File:Motionalemfsimple.png|center|alt=Diagram for simple example]]

''Taken from the'' Matter & Interactions ''textbook, variation of P60''.

A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B that points out of the page, as shown above. '''(a)''' In which direction is the magnetic force? '''(b)''' Which diagram (1–5) best shows the state of the bar?
<br />
<br />
'''(a)''' The magnetic force points ''upwards''. Use the right hand rule.
<br />
'''(b)''' ''Diagram 3'' shows the correct polarization based on the direction of the magnetic force.
<br />

===Middling===
[[File:21.X.091-moving-bar01.gif|center|alt=Diagram for middle example]]
''Taken from the ''Matter & Interactions ''textbook, variation of P63.''

A neutral metal rod of length '''0.21 m''' slides horizontally at a constant speed of '''7 m/s''' on frictionless insulating rails through a region of uniform magnetic field of magnitude '''0.18 tesla''', directed '''out of the page''' as shown in the diagram. '''(a)''' Is the top of the moving rod positive or negative? '''(b)''' After the initial transient, what is the magnitude of the net force on a mobile electron inside the rod? '''(c)''' What is the magnitude of the electric force on a mobile electron inside the rod? '''(d)''' What is the magnitude of the magnetic force on a mobile electron inside the rod? '''(e)''' What is the magnitude of the potential difference across the rod? '''(f)''' In what direction must you exert a force to keep the rod moving at constant speed?
<br />
<br />
'''(a)''' The top of the moving rod is ''negative''. Use the right-hand rule.
<br />
'''(b)''' <math>\left | \overrightarrow{F}_{net} \right |=0 \: N</math> because after the initial transient the system is in steady state and the electric force balances out the magnetic force.
<br />
'''(c)''' First we recognize that the system is in steady state, so <math>E=vB=7 \times 0.18=1.26</math>. Then <math>\left | \overrightarrow{F}_{E} \right |=\left | qE \right |=\left | -1.6 \times 10^{-19}(1.26) \right |=2.016 \times 10^{-19} \: N</math>.
<br />
'''(d)''' In steady state, <math>\left | \overrightarrow{F}_{E} \right |=\left | \overrightarrow{F}_{B} \right |</math>. So, <math>\left | \overrightarrow{F}_{B} \right |=2.016 \times 10^{-19} \: N</math>.
<br />
'''(e)''' <math>\Delta V=EL=v_{bar}BL=7 \times 0.18 \times 0.21=0.2646 \: V</math>.
<br />
'''(f)''' ''No force is needed''. The system is in steady state, so no additional force needs to be applied to keep the rod at constant speed.
<br />

===Difficult===
[[File:Middlemotionalemf.png|center|alt=Picture for difficult example]]

''Taken from the'' Matter & Interactions ''textbook, P64''.
<br />

A metal bar of mass ''M'' and length ''L'' slides with negligible friction but with good electrical contact down between two vertical metal posts, as shown above. The bar falls at a constant speed ''v''. The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance ''R''. Throughout the entire region there is a uniform magnetic field of magnitude ''B'' coming straight out of the page. '''(a)''' Calculate the amount of current ''I'' running through the resistor. '''(b)''' What is the direction of the conventional current ''I''? '''(c)''' Calculate the constant speed ''v'' of the falling bar. '''(d)''' What is the direction of the electric force acting on a positive mobile charge? '''(e)''' What is the direction of the magnetic force acting on the bar?
<br />
<br />
'''(a)''' The bar is already falling at a constant velocity, so <math>\left | \overrightarrow {F}_{net} \right |=0</math> and <math>E=vB</math>. We know that <math>I={emf}/R</math> and <math>{emf}=EL=vBL</math> so it follows that <math>I={vBL}/R</math>.
<br />
'''(b)''' The magnetic force <math>qvB</math> causes positive charges to move left and negative charges to move right. Conventional current flows from the positively charged end of the bar to the negative end, so it runs ''counterclockwise''.
<br />
'''(c)''' The conventional current ''I'' running through the bar causes a magnetic force upwards of magnitude <math>ILB\sin 90^{\circ}=({vBL}/R)LB={vL^{2}B^{2}}/R</math>. This magnitude must balance out the gravitational force <math>Mg</math> because the magnetic and gravitational forces must cancel for <math>\left | \overrightarrow {F}_{net} \right |=0</math> and the bar to have a constant velocity ''v''. So, setting the forces equal to each other, <math>v={MgR}/{L^{2}B^{2}}</math>.
<br />
<br />
Note: We can also find the speed of the falling bar with <math>\left | emf \right |=\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |</math>. Using the loop rule, <math>0=IR - {emf}</math>. So <math>\left | \frac{\mathrm{d} \Phi_ {mag}}{\mathrm{d} t} \right |=IR</math>. We can transform that to <math>IR=\frac{\mathrm{d} (BA)}{\mathrm{d} t}</math>. Since B is constant, <math>IR=B(\frac{\mathrm{d} (A)}{\mathrm{d} t})</math>. We can transform that to <math>IR=B(\frac{\mathrm{d} (Lh)}{\mathrm{d} t})</math>, where h is the distance of the bar above the bottom rod. Since L is constant, <math>IR=BL(\frac{\mathrm{d} (h)}{\mathrm{d} t})</math>. <math>\frac{\mathrm{d} (h)}{\mathrm{d} t})</math> is the velocity of the bar, so <math>IR=BLv</math>. Solving for v, <math>v={MgR}/{L^{2}B^{2}}</math>.
<br />
'''(d)''' The electric force acting on a positive mobile charge points towards the ''right'' in the bar. Using the right hand rule, with B pointing out of the page, v pointing downwards, we know that the magnetic force points to the right. This means that the bar is polarized with positive charges on the left side of the bar and negative charges on the right side. The electric force points from positive charges to negative charges, so the electric force points towards the right.
<br />
'''(e)''' The magnetic force acting on the bar points ''upwards''. We know that current flows from left to right in the bar because positive charges are polarized on the left side of the bar and negative charges are on the right side of the bar. Using the right hand rule, with B pointing out of the page and current pointing to the right, we find that the magnetic force points upwards.

==Connectedness==
The concept of power generated from a mechanical input is how electric generators function. The mechanical energy is commonly supplied by falling water at dams or expanding steam in turbines.
<br />
Motional emf is also applied in the DC motors of airplanes, when mechanical energy is transformed into electrical energy. Additionally, motional emf is applied in breaking systems. When an object moves through a magnetic field, it resists the change(movement) by converting the mechanical energy into electrical energy. So if an object moves with a sufficient amount of force to move, through a magnetic field, it can convert enough mechanical energy to stop a system. This concept is applied in, for example, roller coasters.

==History==
[[File:Faraday-Millikan-Gale-1913.jpg|thumb|alt=Picture of Michael Faraday|Michael Faraday]][[File:James Clerk Maxwell.png|thumb|left|James Clerk Maxwell]] The phenomenon of electromagnetic induction, the emf produced from the interactions between a magnetic field and an electric circuit, was discovered independently in 1831 by Michael Faraday and 1832 by Joseph Henry (Faraday published his results first). Many of Faraday's ideas were rejected by the scientists of the day because they had no mathematical basis, but James Clerk Maxwell used these ideas to formulate his electromagnetic theory and the Maxwell equations.
<br />
At the time, it was not well understood how Maxwell's equations related to moving charged objects. J.J. Thomson was the first to attempt to derive, from Maxwell's equations, an equation describing effects on moving charged particles, and Oliver Heaviside built upon this work and fixed errors in Thomson's derivation. In 1892, Hendrik Lorentz finally derived the correct equation called the Lorentz force. The magnetic force component of the Lorentz force describes motional emf, as the magnetic force pushing electrons in the moving charged object induces the emf.

== See also ==
*[[Motional Emf using Faraday's Law]]: An expansion of this concept
*[[Lorentz Force]]: Combining electric and magnetic forces
*[[Generator]]: Real-world application
*[[Right-Hand Rule]]: How it works and other RHRs
===Further reading===
*''Matter & Interactions, Vol 2''
*''The Feynman Lectures on Physics, Vol 2'', Ch 16

===External links===
*[http://web.mit.edu/8.02t/www/materials/StudyGuide/guide10.pdf Guide from MIT]

==References==

*''Matter & Interactions Vol 2''
*MIT OpenCourseWare
*[http://web.hep.uiuc.edu/home/serrede/P435/Lecture_Notes/A_Brief_History_of_Electromagnetism.pdf A Brief History of The Development of Classical Electrodynamics]

[[Category:Fields]]

Main Page

2019-11-24T23:53:41Z

Aboswell7: /* Motional EMF */

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==Physics 1==
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<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
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</div>
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<div class="toccolours mw-collapsible mw-collapsed">

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
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</div>
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===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

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

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</div>
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====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
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</div>
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===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
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</div>
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<div class="toccolours mw-collapsible mw-collapsed">
====Properties of Matter====
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====Identifying Forces====
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====Curving Motion====
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====Energy Principle====
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<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
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====Potential Energy====
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</div>
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<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
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</div>
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<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
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<div class="mw-collapsible-content">
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====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
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</div>
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<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
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</div>
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====Friction====
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</div>
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<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
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</div>
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*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
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</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
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*[[Rotational Kinematics]]
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</div>
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====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
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*[[Right Hand Rule]]
</div>
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===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
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*[[Torque vs Work]]
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</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
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</div>
</div>
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==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====

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

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

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

====Electric force====
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</div>
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<div class="toccolours mw-collapsible mw-collapsed">

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

[[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]]

[[File:Motional EMF Example.jpg]]

*[[Motional Emf using Faraday's Law]]
</div>
</div>

<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>
</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

2019-11-24T23:50:36Z

Aboswell7: /* Hall Effect */

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

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

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

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

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

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

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

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

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

====VPython====

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

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

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

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

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

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

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

</div>
</div>

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]

[[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]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<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>
</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>

File:Motional EMF Example.jpg

2019-11-24T23:46:59Z

Aboswell7: An example problem of a scenario with a magnet moving towards a loop, where the right hand rule is used to determine the direction of the induced non-Coulombic electric field from the direction of the change in magnetic field

An example problem of a scenario with a magnet moving towards a loop, where the right hand rule is used to determine the direction of the induced non-Coulombic electric field from the direction of the change in magnetic field

File:Hall Effect 2.jpg

2019-11-24T23:44:49Z

Aboswell7: Page 2 of a 2 page example using Hall Effect to determine the type of charge carrier in a circuit

Page 2 of a 2 page example using Hall Effect to determine the type of charge carrier in a circuit

File:Hall Effect 1.jpg

2019-11-24T23:43:58Z

Aboswell7: Page 1 of a 2 page example of using Hall Effect to determine the type of charge carrier in a circuit

Page 1 of a 2 page example of using Hall Effect to determine the type of charge carrier in a circuit