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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    $\begingroup$ 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. $\endgroup$ – user4552 Aug 12 '14 at 22:47
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    $\begingroup$ Possible duplicate of What is the magnetic field inside hollow ball of magnets? $\endgroup$ – sammy gerbil Apr 1 '17 at 4:43
  • $\begingroup$ @sammygerbil It is the other way round. That question is a duplicate of this question. $\endgroup$ – Yashas Apr 1 '17 at 7:01
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    $\begingroup$ @YashasSamaga When there are 2 posts asking the same question, it is not necessarily the later post which should be closed. See Which duplicated question should be closed? In this case, neither question is superior in clarity or research, but the other question is more popular and has more answers. So any further answers should be posted on the other question, I think. $\endgroup$ – sammy gerbil Apr 1 '17 at 15:07

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.

  • $\begingroup$ I don't understand the concentric circle thing though. $\endgroup$ – Tnelsond Oct 13 '11 at 4:07
  • $\begingroup$ 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. $\endgroup$ – Ron Maimon Oct 13 '11 at 6:19

I don't think it would work with ordinary magnets, but if the magnets were solenoids it might work. Ampere's Law applies to solenoids. The way contour integrals work with Ampere's Law, there should not be a way for the magnetic field lines from inside the sphere to escape since the returning magnetic field is zero (since the maximum capacity of the contour integral is used up with the concentration of field traveling to the center of the sphere). If the field lines cannot connect to the opposite pole a monopole should be created. I have not been able to find evidence of an experiment having been done that would contradict this.


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