# Attraction of magnets to ferromagnetic materials with distance?

1. Nov 25, 2011

### carmatic

all i can find on the internet are the attractive and repulsive forces between 2 magnets... where can i find the relationship between distance and attractive force , between a magnet and i.e. a piece of iron?

2. Nov 25, 2011

### Dr_Morbius

3. Nov 27, 2011

### carmatic

as i have said, it only contains information on the force between 2 magnets, not between a magnet and a piece of ferromagnetic material

4. Nov 28, 2011

### mmartelli

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

5. Nov 28, 2011

### MisterX

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 $\vec{m}_{2}$ as being

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

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

Last edited: Nov 29, 2011
6. Nov 29, 2011

### MisterX

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.

7. Nov 29, 2011

### Acut

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.