Some useful correspondences in classical magnetostatics, and the multipole representations of the magnetic potential of an ellipsoid
Moscow State Mining University, Leninskii 6, Moscow, 119991, Russian Federation
It is shown that for a given geometric body, the Ferrers theorem not only relates the potentials of volume- and surface-distributed scalar (charge or mass) sources (which it is known to do) but also relates the vector (scalar) magnetic field potentials produced by the volume- and surface-distributed densities of a stationary current (i.e., vector sources). For a body with a given magnetization, the magnetic multipole moments calculated from expressions for polarization magnetic charges are shown to be equal to those of AmpÉre currents. Using these results and noting the universality of the multipole expressions, multipole representations of the scalar magnetic potential of an ellipsoid can be (and, indeed, have been) obtained rather straightforwardly.