Electric field

In physics, an electric field E is a vector field in which each point is associated with a vector representing a force F acting on an electric charge q,

\mathbf{F} = q \mathbf{E}. $$ The direction of the force is such that a positive charge q is pushed in the direction of the field vector (F and E parallel) and a negative charge q is pulled by F against the direction of E (F and E antiparallel).

Often E is due to the presence in its neighborhood of one or more other electric charges, but E may also be caused by a  magnetic field that varies in time, or by a combination of the two causes.

The length |E| of the field vector E at a certain point is the strength of the electric field in that point, also known as the field intensity. The strength |E| &equiv; E may be defined as the magnitude  F &equiv; |F| of the electric force  exerted on a unit positive electric test charge q, or for arbitrary q by

$$ The strength of the electric field does not depend on the test charge q. Strictly speaking, the introduction of a small test charge, which itself causes an electric field, slightly modifies the existing field. The electric field may therefore be defined as the force per positive charge &Delta;q that is so small that the field can be assumed undisturbed by the presence of &Delta;q.
 * \mathbf{F}| = q |\mathbf{E}|\quad\Longrightarrow\quad E = \frac{F}{q}.

The strength of the electric field due to a single point charge is given by Coulomb's law.

An electric field may be time-dependent, as in the case of a field caused by charges accelerating up and down the transmitting antenna of a television station. Such a field is always accompanied by a magnetic field. The electric field with an accompanying magnetic field is propagated through space as an electromagnetic wave at the same speed as that of light.

The electric field has dimension force per charge or, equivalently, voltage per length. In the SI system, the appropriate units are newton per coulomb, equivalent to volt per meter. In Gaussian units, the electric field is expressed in units of dyne per statcoulomb (formerly known as esu), equivalent to statvolt per centimeter.

Mathematical description
An electric field E may be due to the presence of charges by Gauss's law, which in differential form is one of Maxwell's equations

\boldsymbol{\nabla} \cdot \mathbf{E} = \frac{\rho(\mathbf{r})}{\epsilon_0}, $$ where &epsilon;0 is the electric constant, &rho;(r) is a charge distribution, and &nabla;· stands for the divergence of E.

(To be continued)