Dipole interaction potential for mixed species

1. shehry1

44
1. The problem statement, all variables and given/known data
Not a homework question. I need the solution to this to model another problem.

We all know the potential for the electromagnetic dipole dipole interaction (e.g. see Jackson)

I want to know if there is a solution to the problem in which there are several replicas of the two dipoles all mixed up together (as in the case of polarized gases) and were occupying the same volume. e.g. we might have a 1000000 p1 and say 100000 p2 with p1 and p2 being the two dipole moments.

Obviously I would have to make some kind of an integration over all the particles. But this is where I am somewhat unsure. Since the two species are mixed up hence I do not think an integration over the entire volume would do the trick.

As an approximation - I am thinking about ignoring the shielding effect altogether

2. Relevant equations
Only the dipole interaction potentials
http://en.wikipedia.org/wiki/Magnetic_dipole-dipole_interaction

EDIT: To make matters simple the two gases are polarized parallel to each other

3. The attempt at a solution

Last edited: Jun 19, 2009