Lior M Burko 2007 Eur. J. Phys. 28 593 doi:10.1088/0143-0807/28/3/021
Lior M Burko
Show affiliationsMultipole expansions depend on the coordinate system, so that coefficients of multipole moments can be set equal to zero by an appropriate choice of coordinates. Therefore, it is meaningless to say that a physical system has a nonvanishing quadrupole moment, say, without specifying which coordinate system is used. (Except if this moment is the lowest non-vanishing one.) This result is demonstrated for the case of two equal like electric charges. Specifically, an adapted coordinate system in which the potential is given by a monopole term only is explicitly found, the coefficients of all higher multipoles vanish identically. It is suggested that this result can be generalized to other potential problems, by making equal coordinate surfaces adapt to the potential problem's equipotential surfaces.
41.20.Cv Electrostatics; Poisson and Laplace equations, boundary-value problems
Issue 3 (May 2007)
Received 20 February 2007
Published 1 May 2007
Lior M Burko 2007 Eur. J. Phys. 28 593
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