Non-Coulomb Electric Field

Claimed by Geoffrey McKelvey, Work in Progress

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

Magnetic Field- Induced Electric Field

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-Faraday Law

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Relationship of [math]\displaystyle{ -\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]\displaystyle{ 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]\displaystyle{ -\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]\displaystyle{ |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

Along a closed path, the general equation, from which the magnitude of the non-Coulomb electric field can be obtained, is [math]\displaystyle{ |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]\displaystyle{ emf =- \frac{dB}{dt} }[/math].

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Connectedness

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 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?

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

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Heinrich Lenz

In 1831, Heinrich Lenz, an Estonian physicist, for whom the symbol "L" of inductance is named, discovered the right-hand-rule relationship between a changing magnetic field and the direction of induced electric field, the non-Coulomb field.

This occurrence, however, was preceded by the discovery of the motional electromotive force (emf), resulting from interactions between a non-constant magnetic field and conductor, earlier in same year of 1931 by Michael Faraday, an English physicist and chemist. It is worth noting that this was discovered independently in 1932 by Joseph Henry, an American scientist, however Faraday published first, and is therefore credited with the discovery and contribution to science.

See also

Transformers (Circuits): This page investigates the use of these concepts in the transmission of electricity from power plants to the home.

External links

This video provides a video walkthrough of the process of motional emf form a time-varying magnetic field

References

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