Applications of Gauss’s Law

Although it is a powerful theoretical tool, Gauss’s law is difficult to solve for all but the most symmetric situations. When the charge distribution is very symmetric, Gauss’s law becomes easy to apply. The steps to follow when solving Gauss’s law for the electric field due to a symmetric charge distribution are:

Choose a Gaussian surface with the same symmetry as your charge distribution.
Evaluate the scalar product and field magnitude on your surface and pull out any constants within the integrand.
It should now be the case that the surface integral evaluates to the area of a simple geometric surface.
Evaluate the q_in and solve for the explicit form of the field magnitude.

You should be able to follow the above procedure to solve for the electric field in the vicinity of spherical, cylindrical, and plane distributions of charge.