**Statement
of Gauss's law**

Gauss's law allows one to solve some problems involving charge distributions on conductors, and to calculate the electric field of several simple charge configurations. It is a mathematically equivalent form of Coulomb's law.

Gauss's law relates the *flux*
*F*
of electric field that "leaves"
through a closed surface, to the total charge interior to that surface.
The formula is

*F*
= (E)(A)(*cos*
*q*) = 4
*p*
*k Q*

where *E* is the electric field, *A* is the
surface area, and *Q* is the charge enclosed by the surface.
The angle
*q*
is the angle between E and the normal to the surface. In all of our
applications of Gauss's law, the electric field will be perpendicular to the
surface, so
*q* will be
equal to *0* and therefore the factor
*cos*
*q*
will simply be equal to *1*.

We have to live with a perverse tradition that the constant *k*
is frequently written as
*1/(4*
*p e*_{0}*)*, where
*e*_{0} = *1/(4*
*p*
*k)* = 8.85e-12. So Gauss's law also
may be seen written in the form
*F*
* = Q / *
*e*_{0}
.