Magnetic multipole moments Gauss coefficients and vector potential given by an arbitrary current distributionReport as inadecuate




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Earth, Planets and Space

, Volume 63, Issue 12, pp i–vi

First Online: 21 February 2012Received: 25 November 2009Revised: 17 December 2010Accepted: 04 August 2011

Abstract

Until recently there has been nothing in the geomagnetic literature giving the Gauss coefficients equivalent to magnetic multipole moments for the magnetic scalar potential produced outside a finite-sized region of electric current. Nor has there been an expression for the corresponding magnetic vector potential. This paper presents a simple expression for the Gauss coefficients in terms of a volume integral over the current, and also a series expansion of the vector potential in terms of these coefficients. We show how our result is related to the classical expressions for the scalar potential given by a spherical current sheet, and to the results of the recent papers by Engels and Olsen 1998, Stump and Pollack 1998 and Kazantsev 1999.

Key wordsGauss coefficients magnetic field magnetic scalar potential multipole moments spherical harmonics vector potential vector spherical harmonics  Download fulltext PDF



Author: F. J. Lowes - B. Duka

Source: https://link.springer.com/







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