# CCL: Dipole moment calculation from non-zero charge distribution

*From*: "Patrick Senet"
<Patrick.Senet]^[u-bourgogne.fr>
*Subject*: CCL: Dipole moment calculation from non-zero charge
distribution
*Date*: Fri, 4 Nov 2005 18:17:05 +0100

Sent to CCL by: "Patrick Senet" [Patrick.Senet]=[u-bourgogne.fr]
> I guess the second moment definition as integral over charge times
position
> 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
psenet(0)u-bourgogne.fr
http://www;u-bourgogne.fr/LPUB