# Flux between two magnets?

## Main Question or Discussion Point

I know that when there's a magnet next to a piece of iron, the former's flux density just travels across the air gap between them provided it's small enough. But what happens when there's two magnets next to each other? I know B follows the superposition principle, so do their flux densities just add up? Then, for two equally strong magnets separated by a small space, would the flux density in the air gap be ~2B? And is it different for attraction and repulsion? Because flux line diagrams make it seem so.

On another question, if two magnets of different strength are put next to each other, do they remain unchanged, or their flux intensities eventually even out?

EDIT: Sorry, this probably goes in the Classical Physics forum, doesn't it?

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To clarify: I'm confused by the fact that given the same parameters, I would expect attraction and repulsion forces between two magnets to have the same magnitude. But the formulas for force between two magnets are directly proportional to the square of the flux density (in particular, for nearby magnets F = (A*B^2)/2μ0, according to wikipedia), and by superposition principle, the flux between attracting equal magnets would be ~2B, whereas for repelling magnets it'd be near 0.

So how does that work? Is the formula for attraction only or something?

BruceW
Homework Helper

It gives a couple of links which give a rough derivation of the F=AB^2/2μ0 law. The basic idea is to start off with the standard law for the energy density stored in the magnetic field:
$$\epsilon = \frac{B^2}{2 \mu_0}$$
(Where $\epsilon$ is the energy per volume stored in the magnetic field).
And so assuming the magnetic field is roughly constant in the small space between magnets, we can say the energy stored is:
$$E = A d \frac{B^2}{2 \mu_0}$$
(Where d is the distance between the two magnets). And since the magnetic field is roughly constant, then energy is just force times distance, so the force is:
$$F= \frac{AB^2}{2 \mu_0}$$
Which is the law we were looking for :) So looking back at what we started with, B is the total magnetic field from both magnets, not just from one. I hope this has helped.

So looking back at what we started with, B is the total magnetic field from both magnets
So, for two equal magnets each with a B field, would the total between them be 2B? And is it different for attraction and repulsion?

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BruceW
Homework Helper
um. good question. If the B field from each magnet (in the space between the magnets) were pointing in the same direction, then yes, the total would be 2B. And this is attraction, because the force is negative of the gradient of potential energy. I think a different derivation would be required for repulsion.