Gauss' law states that "the total electric flux through a closed surface is proportional to the total electric charge enclosed within the surface". The constant of proportionality is the permittivity of free space.

Mathematically, Gauss's law takes the form of an integral equation:

Alternatively, in differential form, the equation becomes

 

 

The definition of electrostatic potential, combined with the differential form of Gauss's law (above), provides a relationship between the potential ? and the charge density ?:

This relationship is a form of Poisson's equation.

 

 

In the absence of unpaired electric charge, the equation becomes

which is Laplace's equation.