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?
 A: 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.
A: 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.
