# Can permanent magnets be modeled as set of magnetic charges ?

1. Jun 23, 2011

### Kahlua

Can permanent magnets be modeled as set of "magnetic charges"?

Computing the full magnetic field of a permanent magnet and what forces two permenant magnets exert on eachother is obviously a field theoretic problem that requires a solve using e.g. a FEA method or simular.
For two idealized magnetic poles the force is proportional to ~ 1/r^2.
See e.g. http://en.wikipedia.org/wiki/Magnet#Force_between_two_magnetic_poles

I was wondering if one to a good approximation can model a magnet as a set of magnetic "charges" distributed over the geometry of the magnet. Then positive charges would be placed on one pole and negative charges on the other pole and one would simply use the 1/r^2 law and sum up forces from this. What would be the limitations of such a model?
It looks like an electric dipole to me, and then I suppose it isn't ideal as a magnetic dipole...

Obviously, we know that two magnetic dipoles do not have 1/r^2 interaction, but more like 1/r^4 interaction.
http://en.wikipedia.org/wiki/Magnetic_moment#Forces_between_two_magnetic_dipoles
Is this obtained approximately by integrating (summing) over "magnetic charges" like above with a 1/r^2 force law?

I guess one limitation is that the charge model goes all wrong for the magnetic field of magnet A inside magnet B (becuase of permeability) so I suppose force summations for "magnetic charges" inside the magnet also goes wrong because of this?

I thought the discrete magnetic charge approach would be alot easier to use in a simulation compared to solving for the magnetic field on a background mesh, but need to understand if the model makes any sense, and before refreshing myself with Jackson, I wanted to ask for advice since I'm sure someone's got answers for me ;-)

2. Jun 24, 2011

### granpa

Re: Can permanent magnets be modeled as set of "magnetic charges"?

yes.
a magnets external magnetic field can be thought of as arising from a distribution of monopoles within the magnet

some situations are easier to solve that way.
Some arent