Multipole expansion of electrostatic and magnetostatic fields

Abstract

The multipole moments of an electrostatic or magnetostatic field and the components of the field itself are expressed in terms of two-component spinor and of spin-weighted spherical harmonics, obtaining the correspondence between the Cartesian and spherical components. It is shown that the $2^{l}$-pole moment of a charge or current distribution defines $l$, not necessarily distinct, directions which determine the angular dependence of the multipole field.