One of the fundamentally important things in the study of electric fields is Gauss’s Law. It is one of four equations that form electromagnetic theory. Gauss’s Law describes the relationship between the net electric flux through a closed or Gaussian surface and the charge enclosed by the surface.

** It can be represented in differential form

where Φ is the electric flux, is the electric field, is a differential area on the closed surface S with an outward facing surface normal defining its direction, Q_A is the charge enclosed by the surface, ρ is the charge density at a point in V, is the permittivity of free space and is the integral over the surface S enclosing volume V.

**Differential form of Gauss’s Law and description directly from Wikipedia description of Gauss’s Law at http://en.wikipedia.org/wiki/Gauss's_law