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Methodological notes


Multipole expansions in magnetostatics


National University of ‘Kyiv-Mohyla Academy’, ul. G. Skovorody 2, Kyiv, 04655, Ukraine

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.

Fulltext pdf (275 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0181.201102d.0173
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)
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Îðèãèíàë: Àãðå Ì ß «Ìóëüòèïîëüíûå ðàçëîæåíèÿ â ìàãíèòîñòàòèêå» ÓÔÍ 181 173–186 (2011); DOI: 10.3367/UFNr.0181.201102d.0173

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