Attraction of magnets to ferromagnetic materials with distance?

Magnets, how do they work?

Like this http://en.wikipedia.org/wiki/Magnet

 

Any luck with this?
I'm looking for this answer as well.

 

The force between magnets as a mathematical expression is complicated.

What I have found is the force between magnetic diople moments.

The only source that I remember specifically is wikipedia:

http://en.wikipedia.org/wiki/Magnetic_moment#Forces_between_two_magnetic_dipoles


which gave the force acting on [itex]\vec{m}_{2}[/itex] as being

[itex]\frac{3\mu_{0}}{4\pi \left\|\vec{r} \right\| ^{5}} \left[ (\vec{m}_{1} \cdot \vec{r})\vec{m}_{2} + (\vec{m}_{2} \cdot \vec{r})\vec{m}_{1} + (\vec{m}_{1} \cdot \vec{m}_{2})\vec{r} - \frac {5 ( \vec{m}_{1} \cdot \vec{r} )( \vec{m}_{2} \cdot \vec{r} ) \vec{r} }{ \left\| r \right\| ^{2}} \right] [/itex]

with [itex]\vec{m}_{1}[/itex] and [itex]\vec{m}_{2}[/itex] being the two magnetic dipole moments, and [itex]\vec{r}[/itex] is the displacement vector from the location of m₁ to m₂

 

You may be able to obtain a dipole based representation of each magnet. The permanent magnet would have "bound current", which is which is obtainable from the magnetization.

 

It is complicated to determine the attraction between a magnet and a piece of iron (or other ferromagnetic material). What you can do, if you know exactly how the magnetic field is configured, is to calculate the energy stored in that field and then calculate how much that energy would change when you place a ferromagnetic material around it. This is totally analogous to the problem Feynman analyzed on the Feynman Lectures, volume 2, chapter 10, section 10-5, with the difference Feynman did the math for electric fields and dielectrics. But the reasoning is precisely the same.

Anyways, unless you have a very simple system (such as a uniform magnetic field and a ferromagnetic plate), the math you will need to solve your problem can be quite messy.