Gaussian Surface - Common Gaussian Surfaces

Common Gaussian Surfaces

When performing the closed surface integral, the Gaussian surface (commonly abbreviated G.S. or g.s.) does not necessarily encompass all the charge; i.e., there can be arbitrary charges outside the volume: as mentioned, Q(V) only counts the interior contribution. Furthermore: it is not necessary to choose a Gaussian surface that utilises the symmetry of a situation (as in the examples below) but, obviously the calculations are much less laborious if an appropriate surface is chosen.

Most calculations using Gaussian surfaces begin by implementing Gauss' law (for electricity):

Thereby Q(V) is the electrical charge contained in the interior, V, of the closed surface.

This is Gauss's law, combining both the divergence theorem and Coulomb's law.