Subject: Dipole moment origin and electrostatics

From: Steven M Risser <[email-masked]>
Date: Tue, 26 Mar 1996 12:42:47 -0600 (CST)

Patrick Bultinck recently asked about the choice of the origin for the 
dipole moment.

The choice of origin will not matter if the net charge on the system is 
zero.  The dipole moment of a neutral system is independent of the 
origin.  The higher order terms, however, will depend on the choice of 
the origin.

______________________________________________________________________________
Dr. Steven M. Risser
Department of Physics
East Texas State University 
Commerce, TX 75429  USA
EML   : [email-masked]
______________________________________________________________________________

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From: [email-masked] (Konrad HINSEN)
Date: Tue, 26 Mar 1996 14:59:09 -0500

> origin.  The higher order terms, however, will depend on the choice of 

More generally, the lowest non-vanishing multipole moment is independent
of the choice of the origin. But if I have understood the original
question correctly, this is not the point. The question was about
the choice of an origin for a multipole expansion, not about
the origin dependence of one group of its coefficients.

When you use multipole expansions, you choose an origin, calculate
multipole moments up to a certain order for this origin, and
calculate energies, forces, or whatever using a set of point
multipoles located at this origin. And even if the multipole
moments for two origins happen to be the same, the potential
of the point multipoles can be quite different.

As an example, take a multipole expansion for a set of two opposite
charges up to the dipole. The dipole moment will be the same for each
origin, even for an origin 10 meters away from the charges, but the
potential of a point dipole with this moment will nevertheless depend
very much on this. It will represent the potential of the original
charges best if the origin is right between the two charges. The
reason is that for this position the combined potential of the
neglected higher-order multipoles is smallest.

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