Claimed by Cristina Guruceaga (cguruceaga3)

==Faraday's Law of Induction==

This topics focuses on the electric field associated with a time-varying magnetic field. Faraday's Law makes the connection between electric and magnetic field.
'''Faraday's Law''' summarizes the ways voltage can be generated.
Faraday's law is a fundamental relationship which comes from Maxwell's equations. It serves as a succinct summary of the ways a voltage (or emf) may be generated by a changing magnetic environment. The induced emf in a coil is equal to the negative of the rate of change of magnetic flux times the number of turns in the coil. It involves the interaction of charge with magnetic field.

===Faraday's Law Experiment ===

[[File:experiment.png]]

Faraday showed that no current is registered in the galvanometer when bar magnet is
stationary with respect to the loop. However, a current is induced in the loop when a
relative motion exists between the bar magnet and the loop. In particular, the
galvanometer deflects in one direction as the magnet approaches the loop, and the
opposite direction as it moves away.

Faraday’s experiment demonstrates that an electric current is induced in the loop by
changing the magnetic field. The coil behaves as if it were connected to an emf source.
Experimentally it is found that the induced emf depends on the rate of change of
magnetic flux through the coil.

===Mathematical Equation===

'''Faraday's Law Equation'''
[[File:Law.png]]

In other words: The emf along a round-trip is equal to the rate of change of the magnetic flux on the area encircled by the path.

Direction: With the thumb of your right hand pointing in the direction of the ''-dB/dt'', your fingers curl around in the direction of Enc.

The meaning of the minus sign: If the thumb of your right hand points in the direction of ''-dB/dt'' (that is, the opposite of the direction in which the magnetic field is increasing), your fingers curl around in the direction along which the path integral of electric field is positive. Similarly it can be explained using Lenz's Law. The direction of the induced current is determined by Lenz’s law which states that the induced current produces magnetic fields which tend to oppose the changes in magnetic flux that induces such currents.

'''Formal Version of Faraday's Law'''
[[File:FormalLaw.png]]

==Problem Solving Tips==
In this chapter we have seen that a changing magnetic flux induces an emf:

[[File:tips5.png]]

according to Faraday’s law of induction. For a conductor which forms a closed loop, the
emf sets up an induced current ''I =|ε|/R'' , where ''R'' is the resistance of the loop. To
compute the induced current and its direction, we follow the procedure below:

1. For the closed loop of area on a plane, define an area vector A and let it point in
the direction of your thumb, for the convenience of applying the right-hand rule later.
Compute the magnetic flux through the loop using

[[File:tips4.png]]

Determine the sign of the magnetic flux [[File:tips3.png]]

2. Evaluate the rate of change of magnetic flux [[File:tips2.png]] . Keep in mind that the change
could be caused by

[[File:tips.png]]

Determine the sign of [[File:tips2.png]]

3. The sign of the induced emf is the opposite of that of [[File:tips2.png]]. The direction of the
induced current can be found by using Lenz’s law or right hand rule (discussed previously).

==Conceptual Questions ==

'''Falling Loop'''

A rectangular loop of wire with mass m, width w, vertical length l, and resistance R falls
out of a magnetic field under the influence of gravity. The magnetic field is uniform and out of the paper [[File:con3.png]] within the area shown and zero outside of that area. At the time shown in the sketch, the loop is exiting the magnetic field at speed [[File:con2.png]]

[[File:con1.png]]

1) What is the direction of the current flowing in the circuit at the time shown, clockwise
or counterclockwise? Why did you pick this direction?

2) Using Faraday's law, find an expression for the magnitude of the emf in this circuit in
terms of the quantities given. What is the magnitude of the current flowing in the circuit
at the time shown?

3) Besides gravity, what other force acts on the loop in the ±k direction? Give its
magnitude and direction in terms of the quantities given.

4) Assume that the loop has reached a “terminal velocity” and is no longer accelerating.
What is the magnitude of that terminal velocity in terms of given quantities?

5) Show that at terminal velocity, the rate at which gravity is doing work on the loop is
equal to the rate at which energy is being dissipated in the loop through Joule heating.

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

==History==

Michael Faraday was an English physicist working in the early 1800's. He worked with another scientist named Sir Humphrey Davy. Faraday's big discovery happened in 1831 when he found that when you change a magnetic field, you can create an electric current. He did a lot of other work with electricity such as making generators and experimenting with electrochemistry and electrolysis.

Faraday's experiments started with magnetic fields that stayed the same. That setup did not induce current. It was only when he started to change the magnetic fields that the current and voltage were induced (created). He discovered that the changes in the magnetic field and the size of the field were related to the amount of current created. Scientists also use the term magnetic flux. Magnetic flux is a value that is the strength of the magnetic field multiplied by the surface area of the device.

== See also ==

To fully understand this topic, you need to have an understanding on Maxwell's equations and Lenz's Law.
===Further reading===

Books, Articles or other print media on this topic

===External links===

Faraday's Law Simulation: https://phet.colorado.edu/en/simulation/faradays-law

==References==

Encyclopedia.com: http://www.encyclopedia.com/topic/Faradays_law.aspx
Wikipedia (Electromagnetic Induction): http://en.wikipedia.org/wiki/Electromagnetic_induction
Encyclopædia Britannica (Faraday's Law of Induction): http://www.britannica.com/EBchecked/topic/201744/Faradays-law-of-induction

[[Category: Maxwell's equations]]

File:Con3.png

2015-11-30T22:36:18Z

Cguruceaga3:

File:Con2.png

2015-11-30T22:35:45Z

Cguruceaga3:

File:Con1.png

2015-11-30T22:35:29Z

Cguruceaga3:

Faraday's Law

2015-11-30T22:33:48Z

Cguruceaga3:

Claimed by Cristina Guruceaga (cguruceaga3)

==Faraday's Law of Induction==

This topics focuses on the electric field associated with a time-varying magnetic field. Faraday's Law makes the connection between electric and magnetic field.
'''Faraday's Law''' summarizes the ways voltage can be generated.
Faraday's law is a fundamental relationship which comes from Maxwell's equations. It serves as a succinct summary of the ways a voltage (or emf) may be generated by a changing magnetic environment. The induced emf in a coil is equal to the negative of the rate of change of magnetic flux times the number of turns in the coil. It involves the interaction of charge with magnetic field.

===Faraday's Law Experiment ===

[[File:experiment.png]]

Faraday showed that no current is registered in the galvanometer when bar magnet is
stationary with respect to the loop. However, a current is induced in the loop when a
relative motion exists between the bar magnet and the loop. In particular, the
galvanometer deflects in one direction as the magnet approaches the loop, and the
opposite direction as it moves away.

Faraday’s experiment demonstrates that an electric current is induced in the loop by
changing the magnetic field. The coil behaves as if it were connected to an emf source.
Experimentally it is found that the induced emf depends on the rate of change of
magnetic flux through the coil.

===Mathematical Equation===

'''Faraday's Law Equation'''
[[File:Law.png]]

In other words: The emf along a round-trip is equal to the rate of change of the magnetic flux on the area encircled by the path.

Direction: With the thumb of your right hand pointing in the direction of the ''-dB/dt'', your fingers curl around in the direction of Enc.

The meaning of the minus sign: If the thumb of your right hand points in the direction of ''-dB/dt'' (that is, the opposite of the direction in which the magnetic field is increasing), your fingers curl around in the direction along which the path integral of electric field is positive. Similarly it can be explained using Lenz's Law. The direction of the induced current is determined by Lenz’s law which states that the induced current produces magnetic fields which tend to oppose the changes in magnetic flux that induces such currents.

'''Formal Version of Faraday's Law'''
[[File:FormalLaw.png]]

==Problem Solving Tips==
In this chapter we have seen that a changing magnetic flux induces an emf:

[[File:tips5.png]]

according to Faraday’s law of induction. For a conductor which forms a closed loop, the
emf sets up an induced current ''I =|ε|/R'' , where ''R'' is the resistance of the loop. To
compute the induced current and its direction, we follow the procedure below:

1. For the closed loop of area on a plane, define an area vector A and let it point in
the direction of your thumb, for the convenience of applying the right-hand rule later.
Compute the magnetic flux through the loop using

[[File:tips4.png]]

Determine the sign of the magnetic flux [[File:tips3.png]]

2. Evaluate the rate of change of magnetic flux [[File:tips2.png]] . Keep in mind that the change
could be caused by

[[File:tips.png]]

Determine the sign of [[File:tips2.png]]

3. The sign of the induced emf is the opposite of that of [[File:tips2.png]]. The direction of the
induced current can be found by using Lenz’s law or right hand rule (discussed previously).

==Conceptual Questions ==

'''Falling Loop'''

A rectangular loop of wire with mass m, width w, vertical length l, and resistance R falls
out of a magnetic field under the influence of gravity. The
magnetic field is uniform and out of the paper within the area shown and zero
outside of that area. At the time shown in the sketch, the loop is exiting the magnetic
field at speed

1) What is the direction of the current flowing in the circuit at the time shown, clockwise
or counterclockwise? Why did you pick this direction?

2) Using Faraday's law, find an expression for the magnitude of the emf in this circuit in
terms of the quantities given. What is the magnitude of the current flowing in the circuit
at the time shown?

3) Besides gravity, what other force acts on the loop in the ±k direction? Give its
magnitude and direction in terms of the quantities given.

4) Assume that the loop has reached a “terminal velocity” and is no longer accelerating.
What is the magnitude of that terminal velocity in terms of given quantities?

5) Show that at terminal velocity, the rate at which gravity is doing work on the loop is
equal to the rate at which energy is being dissipated in the loop through Joule heating.

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

==History==

Michael Faraday was an English physicist working in the early 1800's. He worked with another scientist named Sir Humphrey Davy. Faraday's big discovery happened in 1831 when he found that when you change a magnetic field, you can create an electric current. He did a lot of other work with electricity such as making generators and experimenting with electrochemistry and electrolysis.

Faraday's experiments started with magnetic fields that stayed the same. That setup did not induce current. It was only when he started to change the magnetic fields that the current and voltage were induced (created). He discovered that the changes in the magnetic field and the size of the field were related to the amount of current created. Scientists also use the term magnetic flux. Magnetic flux is a value that is the strength of the magnetic field multiplied by the surface area of the device.

== See also ==

To fully understand this topic, you need to have an understanding on Maxwell's equations and Lenz's Law.
===Further reading===

Books, Articles or other print media on this topic

===External links===

Faraday's Law Simulation: https://phet.colorado.edu/en/simulation/faradays-law

==References==

Encyclopedia.com: http://www.encyclopedia.com/topic/Faradays_law.aspx
Wikipedia (Electromagnetic Induction): http://en.wikipedia.org/wiki/Electromagnetic_induction
Encyclopædia Britannica (Faraday's Law of Induction): http://www.britannica.com/EBchecked/topic/201744/Faradays-law-of-induction

[[Category: Maxwell's equations]]

2015-11-30T21:54:02Z

Cguruceaga3:

Faraday's Law

2015-11-30T21:52:12Z

Cguruceaga3:

Claimed by Cristina Guruceaga (cguruceaga3)

==Faraday's Law==

This topics focuses on the electric field associated with a time-varying magnetic field. Faraday's Law makes the connection between electric and magnetic field.
'''Faraday's Law''' summarizes the ways voltage can be generated.
Faraday's law is a fundamental relationship which comes from Maxwell's equations. It serves as a succinct summary of the ways a voltage (or emf) may be generated by a changing magnetic environment. The induced emf in a coil is equal to the negative of the rate of change of magnetic flux times the number of turns in the coil. It involves the interaction of charge with magnetic field.

===Mathematical Equation===

Formal Version of Faraday's Law

[[File:FormalLaw.png]]

===Mathematical Models===

delta S = delta Q/T
Sf = Si (reversible process)
Sf > Si (irreversible process)

===Examples===

'''Reversible process''': Ideally forcing a flow through a constricted pipe, where there are no boundary layers. As the flow moves through the constriction, the pressure, volume and temperature change, but they return to their normal values once they hit the downstream. This return to the variables' original values allows there to be no change in entropy. It is often known as an isentropic process.

'''Irreversible process''': When a hot object and cold object are put in contact with each other, eventually the heat from the hot object will transfer to the cold object and the two will reach the same temperature and stay constant at that temperature, reaching equilibrium. However, once those objects are separated, they will remain at that equilibrium temperature until something else acts upon it. The objects do not go back to their original temperatures so there is a change in entropy.

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

==History==

Michael Faraday was an English physicist working in the early 1800's. He worked with another scientist named Sir Humphrey Davy. Faraday's big discovery happened in 1831 when he found that when you change a magnetic field, you can create an electric current. He did a lot of other work with electricity such as making generators and experimenting with electrochemistry and electrolysis.

Faraday's experiments started with magnetic fields that stayed the same. That setup did not induce current. It was only when he started to change the magnetic fields that the current and voltage were induced (created). He discovered that the changes in the magnetic field and the size of the field were related to the amount of current created. Scientists also use the term magnetic flux. Magnetic flux is a value that is the strength of the magnetic field multiplied by the surface area of the device.

== See also ==

To fully understand this topic, you need to have an understanding on Maxwell's equations and Lenz's Law.
===Further reading===

Books, Articles or other print media on this topic

===External links===

Faraday's Law Simulation: https://phet.colorado.edu/en/simulation/faradays-law

==References==

Encyclopedia.com: http://www.encyclopedia.com/topic/Faradays_law.aspx
Wikipedia (Electromagnetic Induction): http://en.wikipedia.org/wiki/Electromagnetic_induction
Encyclopædia Britannica (Faraday's Law of Induction): http://www.britannica.com/EBchecked/topic/201744/Faradays-law-of-induction

[[Category: Maxwell's equations]]

Faraday's Law

2015-11-30T21:51:29Z

Cguruceaga3:

Claimed by Cristina Guruceaga (cguruceaga3)

==Faraday's Law==

This topics focuses on the electric field associated with a time-varying magnetic field. Faraday's Law makes the connection between electric and magnetic field.
'''Faraday's Law''' summarizes the ways voltage can be generated.
Faraday's law is a fundamental relationship which comes from Maxwell's equations. It serves as a succinct summary of the ways a voltage (or emf) may be generated by a changing magnetic environment. The induced emf in a coil is equal to the negative of the rate of change of magnetic flux times the number of turns in the coil. It involves the interaction of charge with magnetic field.

===Mathematical Equation===

[[File:FormalLaw.png]]

===Mathematical Models===

delta S = delta Q/T
Sf = Si (reversible process)
Sf > Si (irreversible process)

===Examples===

'''Reversible process''': Ideally forcing a flow through a constricted pipe, where there are no boundary layers. As the flow moves through the constriction, the pressure, volume and temperature change, but they return to their normal values once they hit the downstream. This return to the variables' original values allows there to be no change in entropy. It is often known as an isentropic process.

'''Irreversible process''': When a hot object and cold object are put in contact with each other, eventually the heat from the hot object will transfer to the cold object and the two will reach the same temperature and stay constant at that temperature, reaching equilibrium. However, once those objects are separated, they will remain at that equilibrium temperature until something else acts upon it. The objects do not go back to their original temperatures so there is a change in entropy.

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

==History==

Michael Faraday was an English physicist working in the early 1800's. He worked with another scientist named Sir Humphrey Davy. Faraday's big discovery happened in 1831 when he found that when you change a magnetic field, you can create an electric current. He did a lot of other work with electricity such as making generators and experimenting with electrochemistry and electrolysis.

Faraday's experiments started with magnetic fields that stayed the same. That setup did not induce current. It was only when he started to change the magnetic fields that the current and voltage were induced (created). He discovered that the changes in the magnetic field and the size of the field were related to the amount of current created. Scientists also use the term magnetic flux. Magnetic flux is a value that is the strength of the magnetic field multiplied by the surface area of the device.

== See also ==

To fully understand this topic, you need to have an understanding on Maxwell's equations and Lenz's Law.
===Further reading===

Books, Articles or other print media on this topic

===External links===

Faraday's Law Simulation: https://phet.colorado.edu/en/simulation/faradays-law

==References==

Encyclopedia.com: http://www.encyclopedia.com/topic/Faradays_law.aspx
Wikipedia (Electromagnetic Induction): http://en.wikipedia.org/wiki/Electromagnetic_induction
Encyclopædia Britannica (Faraday's Law of Induction): http://www.britannica.com/EBchecked/topic/201744/Faradays-law-of-induction

[[Category: Maxwell's equations]]

2015-11-02T18:56:07Z

Cguruceaga3: Created page with "Claimed by Cristina Guruceaga"

Claimed by Cristina Guruceaga

Main Page

2015-11-02T18:55:49Z

Cguruceaga3: /* Maxwell's Equations */

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

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

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

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
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* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

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

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Fundamental Interactions]]
*[[System & Surroundings]]

</div>
</div>

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

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Relativity]]
</div>
</div>

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

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
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</div>
</div>

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

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
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</div>
</div>

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

===Momentum===
<div class="mw-collapsible-content">
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</div>
</div>

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

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
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* [[Torque]]
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</div>
</div>

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

===Energy===
<div class="mw-collapsible-content">
*Predicting Change
*[[Rest Mass Energy]]
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*[[Potential Energy]]
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</div>
</div>

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

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
*[[Electric Potential]]
**[[Potential Difference in a Uniform Field]]
*[[Magnetic Field]]
**[[Direction of Magnetic Field]]
**[[Bar Magnet]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
</div>
</div>

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

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
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*[[Node Rule]]
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</div>
</div>

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

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Faraday's Law]]
*Ampere-Maxwell Law
</div>
</div>

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

===Radiation===
<div class="mw-collapsible-content">
</div>
</div>

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