# Force on an iron ball due to a dipole magnet

1. Apr 11, 2012

### cereal9

1. The problem statement, all variables and given/known data
A soft iron ball is fixed a distance d above the pole of a rectangular dipole magnet which is permanently magnetized. What is the force the iron ball feels due to the magnetic field?

The dimensions of the dipole magnet are a x a x b, where a < b

2. Relevant equations

$$B= \frac{μ_0}{4π}\frac{m}{d^3}$$

Dipole Moment:
$$m = pl$$
p = magnetic dipole strength (how is this even calculated?)
l = displacement vector between poles

3. The attempt at a solution

I know the following:

$$F = qv x B$$

But I don't think I can use that because there's no velocity as the iron ball is fixed.

The ball has to feel some kind of force, though that formula suggests it isn't possible. It seems to me that if I hung a ball from a string, the tension in the string would increase if a magnet was placed below the iron ball. Is there some concept I'm not understanding, here?

2. Apr 14, 2012

### cereal9

After thinking about it, I think that with the magnetic field from the dipole magnet pulling charge to one spot in the soft iron, that too would act like a dipole so I'd be looking for dipole-dipole forces.

$$F_{mag}=\frac{-3μ_0m_1m_2}{4πr^4}$$

Where m1 and m2 are the masses of the soft iron ball and the aforementioned dipole magnet?

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