How do you calculate the Force of Attraction of two magnets?

[ryccoh]

I just took physics 2. We learned how to calculate the force of a magnetic field on a current or moving charges. What we didn't learn is how to calculate the force of attraction of two bar magnets or electromagnets for that matter. I'm building a coilgun and having a set of equations for this would come in really handy.

 

[DrDu]

You could imagine the bar magnet to be made up of small magnetic dipoles, i.e. the magnetization M is the dipole moment density. So you could derive first the magnetic moment of a dipole and the force it experiences in a homogeneous magnetic field (e.g. you can model it as an arbitrary small current loop) and then you can obtain the force between extended magnets integrating over the magnetizations.