摘要：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 words Gauss coefficients magnetic field magnetic scalar potential multipole moments spherical harmonics vector potential vector spherical harmonics.
