# 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 ${\displaystyle {\mathbf {E} }}$ induced in a loop equals the negative time derivative of the magnetic flux ${\displaystyle \phi }$ cutting the loop (${\displaystyle d{\mathbf {l} }}$ is a length element of the loop):

${\displaystyle \oint {\mathbf {E} }\cdot d{\mathbf {l} }=-{\frac {\partial \phi }{\partial t}}.}$

It is also expressed in terms of the change in the magnetic induction ${\displaystyle {\mathbf {B} }}$ with time ${\displaystyle t}$:

${\displaystyle \nabla \times {\mathbf {E} }=-{\frac {\partial {\mathbf {B} }}{\partial t}}.}$

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

## References

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