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.

PACS: 41.20.Cv, 41.20.Gz (all) DOI: 10.3367/UFNe.0182.201209d.0987 URL: https://ufn.ru/en/articles/2012/9/c/ 000312382200003 2-s2.0-84872100326 Citation: Muratov R Z "Some useful correspondences in classical magnetostatics, and the multipole representations of the magnetic potential of an ellipsoid" Phys. Usp. 55 919–928 (2012) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 21st, March 2011, accepted: 8th, June 2011 Оригинал: Муратов Р З «О некоторых полезных соответствиях в классической магнитостатике и o мультипольных представлениях магнитного потенциала эллипсоида» УФН 182 987–997 (2012); DOI: 10.3367/UFNr.0182.201209d.0987