Magnetic empty sphere

Question

Suppose I have a large supply of small rods that are magnetized, each extremity of the cylinder with the usual N or S magnetic pole. I assemble those small rods into the shell of a hollow sphere, say all S poles pointing towards the center of the sphere. What happens to the magnetic field lines inside and outside the sphere?

Answer 1

In the suggested orientation, the magnets do not make any preferred direction. By symmetry, only a B-field in a radial direction can be created. And, for external or internal field, that is impossible (because it would be a magnetic monoopole if there were any nonzero field value).

So, you'd get zero field, except for the small gaps between the rods, and short distances compared to the gap spacing. If the 'rods' are allowed to become microscopic, an interesting thing happens: permanent magnets (like the rods) are effectively created by a sheet current running around their cylindrical surfaces (it's electron orbitals and spins, on the atomic level). Those currents, if you make a bundle of rods, cancel everywhere inside the bundle, and only leave a sheet current running around the outer bundle surface.

So, fusing magnetized atoms into the sphere as described would cancel the sheet currents, and demagnetize all the 'rod' elements. The complete spherical shell has no 'outer' boundary where a net uncancelled current could flow.