Faraday's Law - Revision history

Lwall9: /* Computational Model of Faraday's Law */

2025-11-26T20:12:42Z

Computational Model of Faraday's Law

← Older revision		Revision as of 16:12, 26 November 2025
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	The model shows a loop of wire with a magnetic field that oscillates in time, producing a changing magnetic flux.		The model shows a loop of wire with a magnetic field that oscillates in time, producing a changing magnetic flux.
	According to Faraday’s law, this changing flux induces a non-Coulomb electric field which drives a circulating current in the loop.		According to Faraday’s law, this changing flux induces a non-Coulomb electric field which drives a circulating current in the loop.

			<div style="float:right; margin-left:15px; margin-bottom:10px;">
			[[File:ComputationalModel.png\|link=]]
			</div>

	You can open and run the simulation using the link below:		You can open and run the simulation using the link below:

	[https://www.glowscript.org/#/user/lily.wall/folder/MyPrograms/program/Faraday'sLaw Faraday’s Law Interactive Simulation]		[https://www.glowscript.org/#/user/lily.wall/folder/MyPrograms/program/Faraday'sLaw Faraday’s Law Interactive Simulation]


	The visualization includes:		The visualization includes:

Lwall9: /* Computational Model of Faraday's Law */

2025-11-26T20:02:09Z

Computational Model of Faraday's Law

← Older revision		Revision as of 16:02, 26 November 2025
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	* Flux <math>\Phi(t)</math> and induced emf <math>\mathcal{E}(t)</math> graphs		* Flux <math>\Phi(t)</math> and induced emf <math>\mathcal{E}(t)</math> graphs
	* A rotating arrow showing the direction of the induced current according to Lenz’s law		* A rotating arrow showing the direction of the induced current according to Lenz’s law

			From the graphs, you can clearly see that the emf curve is the negative time derivative of the flux curve, matching the relationship <math>\mathcal{E}(t) = -\,\frac{d\Phi(t)}{dt}</math> in Faraday’s law.

	This model provides a clear, dynamic illustration of how a changing magnetic field induces an emf in a loop.		This model provides a clear, dynamic illustration of how a changing magnetic field induces an emf in a loop.


	==More on Faraday's Law==		==More on Faraday's Law==

Lwall9: /* Fiding the direction of the induced conventional current */

2025-11-26T19:59:53Z

Fiding the direction of the induced conventional current

← Older revision		Revision as of 15:59, 26 November 2025
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	Pointing the thumb of your right hand in the direction of <math> \frac{-dB}{dt} </math> allows you to curl your fingers in the direction of <math> \mathbf{E_{NC}} </math>.		Pointing the thumb of your right hand in the direction of <math> \frac{-dB}{dt} </math> allows you to curl your fingers in the direction of <math> \mathbf{E_{NC}} </math>.


			The negative sign in Faraday’s law expresses Lenz’s law: nature resists sudden changes in flux.
			*If the magnetic field through a loop increases, the induced current produces a field that reduces it.
			*If the magnetic field decreases, the induced current produces a field that increases it.
			This opposition maintains consistency with energy conservation.


	In this chapter we have seen that a changing magnetic flux induces an emf:		In this chapter we have seen that a changing magnetic flux induces an emf:

Lwall9 at 19:56, 26 November 2025

2025-11-26T19:56:42Z

@@ Line 76: / Line 76: @@
 . 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).
 ==Computational Model of Faraday's Law==

Lwall9 at 19:48, 26 November 2025

2025-11-26T19:48:15Z

← Older revision		Revision as of 15:48, 26 November 2025
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	The external magnetic field induces the Non-Coulomb electric field which drives the current which in turn creates a new magnetic field which we will call the induced magnetic field. This is the magnetic field whose direction we can deduce which in turn will help us find the direction of the current.		The external magnetic field induces the Non-Coulomb electric field which drives the current which in turn creates a new magnetic field which we will call the induced magnetic field. This is the magnetic field whose direction we can deduce which in turn will help us find the direction of the current.
	The easiest way to do this is to imagine a loop of wire with and an external magnetic field perpendicular to the surface of the plane of the loop. There is a change in magnetic flux generated by the change in the magnitude of the magnetic field. vector for the initial external magnetic field and a vector for the final magnetic field. Then, draw the change in magnetic field vector, <math> \Delta \mathbf{B} </math>, and then the negative vector of that change in magnetic field gives <math> \frac{-dB}{dt} </math>:		The easiest way to do this is to imagine a loop of wire with and an external magnetic field perpendicular to the surface of the plane of the loop. There is a change in magnetic flux generated by the change in the magnitude of the magnetic field. vector for the initial external magnetic field and a vector for the final magnetic field. Then, draw the change in magnetic field vector, <math> \Delta \mathbf{B} </math>, and then the negative vector of that change in magnetic field gives <math> \frac{-dB}{dt} </math>:

			[[File:RightHandRule.png\|right\|350px]]

	[[File:neg_change_B_dt.jpg]]		[[File:neg_change_B_dt.jpg]]

	Pointing the thumb of your right hand in the direction of <math> \frac{-dB}{dt} </math> allows you to curl your fingers in the direction of <math> \mathbf{E_{NC}} </math>.		Pointing the thumb of your right hand in the direction of <math> \frac{-dB}{dt} </math> allows you to curl your fingers in the direction of <math> \mathbf{E_{NC}} </math>.

	~~[[File:RightHandRule.png\|right\|350px]]~~

	In this chapter we have seen that a changing magnetic flux induces an emf:		In this chapter we have seen that a changing magnetic flux induces an emf:

Lwall9 at 19:31, 26 November 2025

2025-11-26T19:31:20Z

← Older revision		Revision as of 15:31, 26 November 2025
Line 48:		Line 48:

	Pointing the thumb of your right hand in the direction of <math> \frac{-dB}{dt} </math> allows you to curl your fingers in the direction of <math> \mathbf{E_{NC}} </math>.		Pointing the thumb of your right hand in the direction of <math> \frac{-dB}{dt} </math> allows you to curl your fingers in the direction of <math> \mathbf{E_{NC}} </math>.

			[[File:RightHandRule.png\|right\|350px]]

	In this chapter we have seen that a changing magnetic flux induces an emf:		In this chapter we have seen that a changing magnetic flux induces an emf:

Lwall9 at 19:12, 26 November 2025

2025-11-26T19:12:51Z

@@ Line 1: / Line 1: @@
-'''<u>Claimed by Amelia Mutert Spring 2025</u>'''
+<br>'''<u>Claimed by Lily Wall Fall 2025</u>'''
@@ Line 49: / Line 48: @@
 Pointing the thumb of your right hand in the direction of <math> \frac{-dB}{dt} </math> allows you to curl your fingers in the direction of <math> \mathbf{E_{NC}} </math>.
 In this chapter we have seen that a changing magnetic flux induces an emf:
@@ Line 77: / Line 75: @@
 induced current can be found by using Lenz’s law or right-hand rule (discussed previously).
-==Computational Model==
+==Computational Model of Faraday's Law==
-The following simulations demonstrate Faraday's Law in action.
 ==More on Faraday's Law==

Oshioke.G: /* Faraday's Law */

2025-04-14T04:21:11Z

Faraday's Law

← Older revision		Revision as of 00:21, 14 April 2025
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	Faraday's Law summarizes the ways voltage can be generated as a result of a time-varying magnetic flux. And it gives a way to connect the magnetic and electric fields in a quantifiable way (will elaborate later). Faraday's law is one of four laws in Maxwell's equations. It tells us that in the presence of a time-varying magnetic field or current (which induces a time-varying magnetic field), there is an emf with a magnitude equal to the change in magnetic flux. 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 the magnetic field.		Faraday's Law summarizes the ways voltage can be generated as a result of a time-varying magnetic flux. And it gives a way to connect the magnetic and electric fields in a quantifiable way (will elaborate later). Faraday's law is one of four laws in Maxwell's equations. It tells us that in the presence of a time-varying magnetic field or current (which induces a time-varying magnetic field), there is an emf with a magnitude equal to the change in magnetic flux. 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 the magnetic field.

	Faraday’s experiments demonstrated that the induced ~~EMF~~ from a changing magnetic flux depends on a few key factors. First, the ~~EMF~~ is directly proportional to the change in magnetic flux, ΔΦ. Second, the ~~EMF~~ increases as the time interval Δt over which the change occurs decreases—in other words, it is inversely proportional to Δt. Lastly, if the coil has N turns, the resulting ~~EMF~~ is N times greater than that of a single loop, making ~~EMF~~ directly proportional to N.		Faraday’s experiments demonstrated that the induced emf from a changing magnetic flux depends on a few key factors. First, the emf is directly proportional to the change in magnetic flux, ΔΦ. Second, the emf increases as the time interval Δt over which the change occurs decreases—in other words, it is inversely proportional to Δt. Lastly, if the coil has N turns, the resulting emf is N times greater than that of a single loop, making emf directly proportional to N.

	==Curly Electric Field==		==Curly Electric Field==

Oshioke.G: /* Faraday's Law */

2025-04-14T04:19:39Z

Faraday's Law

← Older revision		Revision as of 00:19, 14 April 2025
Line 9:		Line 9:

	Faraday's Law summarizes the ways voltage can be generated as a result of a time-varying magnetic flux. And it gives a way to connect the magnetic and electric fields in a quantifiable way (will elaborate later). Faraday's law is one of four laws in Maxwell's equations. It tells us that in the presence of a time-varying magnetic field or current (which induces a time-varying magnetic field), there is an emf with a magnitude equal to the change in magnetic flux. 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 the magnetic field.		Faraday's Law summarizes the ways voltage can be generated as a result of a time-varying magnetic flux. And it gives a way to connect the magnetic and electric fields in a quantifiable way (will elaborate later). Faraday's law is one of four laws in Maxwell's equations. It tells us that in the presence of a time-varying magnetic field or current (which induces a time-varying magnetic field), there is an emf with a magnitude equal to the change in magnetic flux. 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 the magnetic field.

			Faraday’s experiments demonstrated that the induced EMF from a changing magnetic flux depends on a few key factors. First, the EMF is directly proportional to the change in magnetic flux, ΔΦ. Second, the EMF increases as the time interval Δt over which the change occurs decreases—in other words, it is inversely proportional to Δt. Lastly, if the coil has N turns, the resulting EMF is N times greater than that of a single loop, making EMF directly proportional to N.

	==Curly Electric Field==		==Curly Electric Field==

Oshioke.G: /* History */

2025-04-14T04:16:10Z

History

← Older revision		Revision as of 00:16, 14 April 2025
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	Test it out yourself [https://phet.colorado.edu/en/simulation/faradays-law here]		Test it out yourself [https://phet.colorado.edu/en/simulation/faradays-law here]


	==See also==		==See also==