Multipole expansions of the magnetic field of a spatially restricted system of stationary currents and those for the potential function of such currents in an external magnetic field are studied using angular momentum algebraic techniques. It is found that the expansion for the magnetic induction vector is made identical to that for the electric field strength of a neutral system of charges by substituting electric for magnetic multipole moments. The toroidal part of the multipole expansion for the magnetic field vector potential can, due to its potential nature, be omitted in the static case. Also, the potential function of a system of currents in an external magnetic field and the potential energy of a neutral system of charges in an external electric field have identical multipole expansions. For axisymmetric systems, the expressions for the field and those for the potential energy of electric and magnetic multipoles are reduced to simple forms, with symmetry axis orientation dependence separated out.

PACS: 41.20.Cv, 41.20.Gz (all) DOI: 10.3367/UFNe.0181.201102d.0173 URL: https://ufn.ru/en/articles/2011/2/c/ 000294812700003 2-s2.0-79960002753 2011PhyU...54..167A Citation: Agre M Ya "Multipole expansions in magnetostatics" Phys. Usp. 54 167–180 (2011) BibTexBibNote ® (generic)BibNote ® (RIS) MedlineRefWorks PT Journal Article TI Multipole expansions in magnetostatics AU Agre M Ya FAU Agre MY DP 10 Feb, 2011 TA Phys. Usp. VI 54 IP 2 PG 167-180 RX 10.3367/UFNe.0181.201102d.0173 URL https://ufn.ru/en/articles/2011/2/c/ SO Phys. Usp. 2011 Feb 10;54(2):167-180 Оригинал: Агре М Я «Мультипольные разложения в магнитостатике» УФН 181 173–186 (2011); DOI: 10.3367/UFNr.0181.201102d.0173