Non-Coulomb Electric Field - Revision history

Gmckelvey3 at 03:25, 6 December 2015

2015-12-06T03:25:25Z

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	Claimed by Geoffrey McKelvey~~, Work in Progress~~		Claimed by Geoffrey McKelvey

	The non-Coulomb electric field, often represented by the variable <math> \vec{E}_{NC}</math>, is an electric field, which does not result from a stationary point charge.		The non-Coulomb electric field, often represented by the variable <math> \vec{E}_{NC}</math>, is an electric field, which does not result from a stationary point charge.

Gmckelvey3: /* Examples */

2015-12-06T03:24:58Z

Examples

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 ===Simple===
-===Middling===
+Problem:
-===Difficult===
+On a circular path of radius 8 cm in air around a solenoid with increasing magnetic field, the emf is 32 volts. What is the magnitude of the non-Coulomb electric field on this path?
 ==Connectedness==

Gmckelvey3: /* Connectedness */

2015-12-06T02:49:50Z

Connectedness

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	MRI and functional MRI (fMRI) are two very useful imaging techniques, being on of the highest resolution imaging techniques available, with none of the accompanying radiative dangers, which accompany computerized tomography (CT) scans. Eddy currents, product of the non-Coulomb fields, which accompany the induced, opposing magnetic field, present a significant complication to the use of MRI, via the creation of artifact within the image, heat within current loops induced in tissue, among others.		MRI and functional MRI (fMRI) are two very useful imaging techniques, being on of the highest resolution imaging techniques available, with none of the accompanying radiative dangers, which accompany computerized tomography (CT) scans. Eddy currents, product of the non-Coulomb fields, which accompany the induced, opposing magnetic field, present a significant complication to the use of MRI, via the creation of artifact within the image, heat within current loops induced in tissue, among others.

			A step-by-step explanation of Eddy current can be found [https://www.youtube.com/watch?v=zJ23gmS3KHY here]

	==History==		==History==

Gmckelvey3: /* A Mathematical Model */

2015-12-06T02:47:12Z

A Mathematical Model

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	===A Mathematical Model===		===A Mathematical Model===

	Along a closed path, the general equation, from which the magnitude of the non-Coulomb electric field can be obtained, is <math> \|emf\| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = \|\frac{d\Phi_{mag}}{dt}\|</math>. The direction of this can be found by using <math> emf =- \frac{dB}{dt}</math>.		Along a closed path, the general equation, from which the magnitude of the non-Coulomb electric field can be obtained, is <math> \|emf\| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = \|\frac{d\Phi_{mag}}{dt}\|</math>. The direction of this can be found by using <math> emf =- \frac{dB}{dt}</math>, followed by the used of the above integral in order to determine the direction of the field.

	===A Computational Model===		===A Computational Model===

Gmckelvey3: /* References */

2015-12-06T02:46:30Z

References

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	==References==		==References==

	~~This section contains the the references you used while writing this page~~		Vpython Code Simulations, Written by Ruth Chabay and Bruce Sherwood, licensed under Creative Commons 4.0.

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

Gmckelvey3: /* A Computational Model */

2015-12-06T02:43:27Z

A Computational Model

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	===A Computational Model===		===A Computational Model===

	~~How do we visualize or predict using~~ this ~~topic~~. ~~Consider embedding some~~ vpython ~~code here~~ [~~https~~://~~trinket~~.io/~~glowscript~~/~~31d0f9ad9e Teach hands~~-on with ~~GlowScript]~~		In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-magnet vpython simulation], the effects of the motion of the magnet on a conductor can be observed, with the curly electric field shown in orange, while the induced magnetic field is shown in blue

			In this [http://www.glowscript.org/#/user/matterandinteractions/folder/matterandinteractions/program/22-Faraday-coil vpython simulation], the curly magnetic field associated with the alternating magnetic field of a coil of wire can be seen, along with the measured induced current.

	==Examples==		==Examples==

Gmckelvey3: /* See also */

2015-12-06T02:23:30Z

Gmckelvey3: /* Lenz's Law */

2015-12-06T02:16:23Z

Lenz's Law

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	The concept of the non-Coulomb electric field arises from the discovery of electric fields, which cannot be created as a result of Coulomb's law. Due to the involvement of motion, the resulting potential difference is often referred to as motional emf. The non-Coulomb electric field is also know as the curly electric field, due to it's directionality of curling around the conductor, which in turn will induce voltage, which in turn will induce the current to flow.		The concept of the non-Coulomb electric field arises from the discovery of electric fields, which cannot be created as a result of Coulomb's law. Due to the involvement of motion, the resulting potential difference is often referred to as motional emf. The non-Coulomb electric field is also know as the curly electric field, due to it's directionality of curling around the conductor, which in turn will induce voltage, which in turn will induce the current to flow.

	===Lenz's Law===		===Lenz-Faraday Law===

	[[File:Direction_of_E_NC_with_Changing_B.png\|thumb\|alt=dB/dt with ENC relationship \|Relationship of <math> -\frac{dB}{dt}</math> and the non-Coulomb electric field]] While Faradays law tells us the magnitude of motional emf, which is equivalent to the change in magnetic flux over time, Lenz's law gives us the direction, and states that the direction of the motional emf can be found by <math> emf =- \frac{dB}{dt}</math>, and the resultant induced electric field can be found by using the associated right-hand rule. This rule states that with the thumb of the right hand pointing in the direction of <math> -\frac{dB}{dt}</math>, then the fingers will curl in the direction of the non-Coulomb electrical field.

			[[File:Direction_of_E_NC_with_Changing_B.png\|thumb\|alt=dB/dt with ENC relationship \|Relationship of <math> -\frac{dB}{dt}</math> and the non-Coulomb electric field]] While Faradays law tells us the magnitude of motional emf, which is equivalent to the change in magnetic flux over time, Lenz's law gives us the direction, and states that the direction of the motional emf can be found by <math> emf =- \frac{dB}{dt}</math>, and the resultant induced electric field can be found by using the associated right-hand rule. This rule states that with the thumb of the right hand pointing in the direction of <math> -\frac{dB}{dt}</math>, then the fingers will curl in the direction of the non-Coulomb electrical field. The combination of these two laws is known as the Lenz-Faraday law, and in its entirety appears as such <math> \|emf\| = \oint \vec{E}_{NC} \cdot \Delta \vec{l} = \|\frac{d\Phi_{mag}}{dt}\|</math>. These tell us that the flux of the time-varying magnetic field is what creates the non-Coulomb electric field, which is the source of voltage (emf) and ultimately, the induced current which follows.

	===A Mathematical Model===		===A Mathematical Model===

Gmckelvey3: /* Connectedness */

2015-12-06T02:14:20Z

Connectedness

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	1. How is this topic connected to something that you are interested in?		1. How is this topic connected to something that you are interested in?

	Non-Coulomb electrical fields are a possible complication involved in magnetic resonance imaging (MRI), as they ~~accompany~~ Eddy currents, ~~which are induced currents~~ from the alternating magnetic fields that oppose the magnetic force that created them, which may cause such complications as heating tissue or creating an artifact within the image.		Non-Coulomb electrical fields are a possible complication involved in magnetic resonance imaging (MRI), as they are what creates the induced voltage and ultimately, current, known as Eddy currents, , from the alternating magnetic fields that oppose the magnetic force that created them, which may cause such complications as heating tissue or creating an artifact within the image.

	2. How is it connected to your major?		2. How is it connected to your major?

	MRI and functional MRI (fMRI) are two very useful imaging techniques, being on of the highest resolution imaging techniques available, with none of the accompanying radiative dangers, which accompany computerized tomography (CT) scans. Eddy currents, ~~along with their accompanying~~ non-Coulomb fields, which ~~oppose~~ the magnetic field~~, that created them~~, present a significant complication to the use of MRI, via the creation of artifact within the image, heat within current loops induced in tissue, among others.		MRI and functional MRI (fMRI) are two very useful imaging techniques, being on of the highest resolution imaging techniques available, with none of the accompanying radiative dangers, which accompany computerized tomography (CT) scans. Eddy currents, product of the non-Coulomb fields, which accompany the induced, opposing magnetic field, present a significant complication to the use of MRI, via the creation of artifact within the image, heat within current loops induced in tissue, among others.

	==History==		==History==

Gmckelvey3: /* External links */

2015-12-06T02:09:27Z

External links

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	===External links===		===External links===

	~~Internet resources on this topic~~		This [https://youtu.be/2DH7ufrkeHM video] provides a video walkthrough of the process of motional emf form a time-varying magnetic field

	==References==		==References==

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	== See also ==		== 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?~~		[[Transformers (Circuits)]]: This page investigates the use of these concepts in the transmission of electricity from power plants to the home.

	~~===Further reading===~~

	~~Books, Articles or other print media on this topic~~

	===External links===		===External links===