An electric multipole expansion is a determination of the voltage V due to a collection of charges obtained by performing a multipole expansion. This corresponds to a series expansion of the charge density in terms of its moments, normalized by the distance to a point R far from the charge distribution. In cgs, the electric multipole expansion is given by
where is a Legendre polynomial Eric Weisstein's World of Math and is the polar angle, defined such that
In MKS, the corresponding formula has the following normalization
where is the permittivity of free space.
