CCL: Dipole moment calculation from non-zero charge distribution

 Sent to CCL by: "Patrick Senet" [Patrick.Senet]=[]
 > I guess the second moment definition as integral over charge times
 > vector would be a better/more general definition. But what makes
 > these definitions equivalent or allows to expand from one to the other ?
 > (The first definition a priori breaking down for charged species)
 Dear Marc Baaden,
 Yes indeed, the most general definition of multipole moments came from the
 expansion of the electric potential of a charge density (confined in a
 sphere of large radius) in spherical harmonics. The dipole moment is defined
 by the integral of r*density in all cases. For two opposite point charges
 represented by Dirac Delta functions you recover the > pair of electric
 charges of equal magnitude but opposite polarity [..]" An electrostatic
 theorem tells you that the lowest nonvanishing multipole moment of any
 charge distribution is independent of the choice of the coordinates but all
 higher multipole moments are not in general translationaly invariant. In
 other words, a charged system has a dipole depending on the choice of
 coordinates. For two opposite charges, the monopole vanishes and the dipole
 is invariant.
 Best regards,
 Patrick Senet
 Prof. Patrick Senet
 Théorie de la matière condensée
 CNRS-UMR 5027, LPUB, Univ. de Bourgogne
 9 Avenue Alain Savary - BP 47870
 F-21078 Dijon Cedex
 Tel: 03 80 39 5922
 Fax:03 80 39 6024