Some useful correspondences in classical magnetostatics and multipole representations of the magnetic potential of an ellipsoid

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 Amp$\rm \acute e$re 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.