Dictionary:Electric field

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

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

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

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

See a classic text, such as Jackson (1962)