I know this is a bit late, like years, but I've been wondering about this, too.
So, back to the OP's second question, which was never answered that I saw. Has anyone actually built one? If not, why not? Isn't one of the purposes of experimentation to check whether what we expect to happen really does happen? I would think it would be relatively straightforward, if not necessarily simple to do a first approximation, possibly enough to see if Maxwell has the last word or not. Alas, I don't have the youth, money, math, machining skills, or knowledge of magnetism to pursue this, but if I did, I'd start with perhaps steel as the material of choice since we don't need or want a super strong magnet for the experiment and steel would be easy to work with. I'd make it of multiple components; in short a geodesic sphere.
If you would, imagine a geodesic sphere inside a larger geodesic sphere and in alignment with it. If you imagine it as a skeletal structure then it is easy to see that the planes that connect the skeleton of the outside sphere's structural components to the matching ones on the inside sphere would define the shapes of the individual components of our magnet. They would then be magnetized with one pole on the surface of the smaller sphere and the other pole on the surface of the outer sphere, and then glued together, perhaps with superglue, to form the magnetic sphere. Control of the individual parts would be a bit challenging since they would try to squirm out of position. Of course the individual components could be designed to go all the way to the center of the sphere, but I would imagine it would be easier to make it hollow. The higher the frequency of the geodesic, the better your control of the the magnetism of the individual components, but that could get out of hand real fast for the number of individual components involved.
So, what would really happen, without guessing or resorting to unproven theories? Would the lines "force" their way through to make multiple poles? Would the whole field just collapse, and if so would the components resume their magnetic properties if it was disassembled or would the field collapse be permanent? Would you actually have a single pole surface that radiated its lines out into space? if this is what would occur, then what is happening inside might be the most interesting of all. Might make a dandy plasma containment field. Imagine, if you are at the center of the sphere, then every direction is North. Or South. Who knows, maybe it would even trigger a Big Bang in a different dimension. Just kidding. I think.
No matter what happens, except total field collapse, of course, this would likely be a very interesting toy to play with. Has it been done? Anyone want to try? I'm hoping for some totally unexpected result that redefines physics, but that's just me.
Thanks for taking the time to read this silly proposal!
Jerry
