How Do Magnetic Dipole Moments Interact at a Distance?

[kylie14]

Say you have two magnetic dipole moments, say p1 and p2, which are separated by a distance r, with no external magnetic fields.

If you want to figure out the energy of their magnetic interaction, is it valid to figure out the energy of p1 in the magnetic field generated by p2, or vice versa? Or will this not work?

 

[kylie14]

Actually, sorry, I think I was being stupid!
Do I consider it both ways round, so treat p1 as being in an external mag field (from p2), then p2 in an external field (from p1) and then sum the energies together?

 

[kylie14]

I have an answer:
(-mu_0 / 2 pi r^3) p1 ∙ p2

I have a problem with this answer though; while it takes into account the orientation of the two with respect to each other, shouldn't it also take into account the orientation of each with the vector joining them?

My equation seems to agree with a general one I found, but only when assuming that p1 and p2 are parallel to to the vector joining them!