# Magnets arranged in a sphere

If I was to take a bunch of magnets and arrange them in a sphere (And keep them there with glue or plastic or something) so that the north pole faces the outside of the sphere and the south pole faces the inside, would the magnet have the same pole no matter what way I turn it or would the magnet be neutralized or something.

I'm envisioning a sphere made of magnets so that no matter what way I turn it it is always the same pole and that a bunch of these repelling each other would be really cool, is this possible?

In effect would this create a monopole magnet?

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Funny, as a kid I wondered about exactly the same. :-) thanks for bringing that back. – Kris Van Bael Oct 13 '11 at 21:17
+1: I started to ask precisely this question myself, and your's appeared in the similar titles. – Everyone Dec 27 '11 at 11:07
Other than Gauss's law plus symmetry, another way to see that the field vanishes is to imagine that each magnet is a small current loop. Each loop's current cancels with the current of the adjoining loop along their shared edge, and since there are no edges that aren't shared, the current vanishes everywhere. – Ben Crowell Aug 12 '14 at 22:47

## 1 Answer

The magnetic analog of Gauss's law tells you that

$$\oint B dA = 0$$

This says that he number of magnetic field lines entering and leaving any surface surrounding any configuration of magnets are always equal. So there is no configuration of equal and opposite poles which produces a monopolar field. Your configuration would neutralize the magnetic field of the magnets. All the inner poles would cancel with the outer poles, since the field is spherically symmetric. It's the same as two concentric spheres of equal total charge uniformly distributed on the surface, which also produce no field at long distances.

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Thanks, that was fast. – Tnelsond Oct 13 '11 at 4:01
I don't understand the concentric circle thing though. – Tnelsond Oct 13 '11 at 4:07
If you have two concentric spheres of charge, one small radius sphere of charge Q, one big radius sphere of charge -Q, there is no field outside the bigger sphere. Your magnet configuration has a pole distribution which is the same as the concentric sphere charge distribution. – Ron Maimon Oct 13 '11 at 6:19