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's 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.

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

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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 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.

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.

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

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

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