# Difference between revisions of "Dictionary:Electric field"

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A spatial vector quantity equal to a potential gradient, produced by charged bodies or a time-varying magnetic field. Unit is volts per meter. The electric field <math> {\mathbf E}</math> induced in a loop equals the negative time derivative of the magnetic flux <math> \phi </math> cutting the loop (<math> d{\mathbf l} </math> is a length element of the loop): | A spatial vector quantity equal to a potential gradient, produced by charged bodies or a time-varying magnetic field. Unit is volts per meter. The electric field <math> {\mathbf E}</math> induced in a loop equals the negative time derivative of the magnetic flux <math> \phi </math> cutting the loop (<math> d{\mathbf l} </math> is a length element of the loop): | ||

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<center> <math> \oint {\mathbf E} \cdot d{\mathbf l} = -\frac{\partial \phi}{\partial t} . </math></center> | <center> <math> \oint {\mathbf E} \cdot d{\mathbf l} = -\frac{\partial \phi}{\partial t} . </math></center> | ||

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It is also expressed in terms of the change in the magnetic induction <math> {\mathbf B} </math> with time <math> t </math>: | It is also expressed in terms of the change in the magnetic induction <math> {\mathbf B} </math> with time <math> t </math>: | ||

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<center> <math>\nabla \times {\mathbf E } = - \frac{\partial {\mathbf B }}{\partial t}. </math> </center> | <center> <math>\nabla \times {\mathbf E } = - \frac{\partial {\mathbf B }}{\partial t}. </math> </center> | ||

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See a classic text, such as Jackson (1962) <ref> Jackson, J. D. (1962). Classical electrodynamics (Vol. 3). New York etc.: Wiley.</ref> | See a classic text, such as Jackson (1962) <ref> Jackson, J. D. (1962). Classical electrodynamics (Vol. 3). New York etc.: Wiley.</ref> | ||

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## Latest revision as of 11:37, 31 July 2018

A spatial vector quantity equal to a potential gradient, produced by charged bodies or a time-varying magnetic field. Unit is volts per meter. The electric field induced in a loop equals the negative time derivative of the magnetic flux cutting the loop ( is a length element of the loop):

It is also expressed in terms of the change in the magnetic induction with time :

See a classic text, such as Jackson (1962) ^{[1]}

## References

- ↑ Jackson, J. D. (1962). Classical electrodynamics (Vol. 3). New York etc.: Wiley.