I am aware of (and believe, even though I can't myself derive the conclusion) the Earnshaw's theorem that says that true levitation using only permanent magnets is impossible, I'm more like looking for an explanation in what ways would a particular setup be unstable (by true levitation I mean that the levitating object is not being mechanically supported or restrained in any way, and also not requiring any active control or motion of any part of the system, like spin-stabilization. Obviously, no superconductors too, just permanent magnets). The idea is as follows:
I was thinking about a sphere completely covered in small magnets all pointing with like poles outwards (sort of magnetic disco-ball), and a flat floor also covered with magnets facing the same poles up - would such a ball float above the floor? At least in theory, ignoring manufacturing imperfections? I. e., would it be stable in the vertical direction?
If the floor had a circular shape with the edges curved upwards (creating a hollow "bowl"), could it prevent the ball from rolling off of it? That is, if it would float above the surface in the first place.
On the face of it, it looks like the disco-ball would always present like poles closest to the magnets in the floor, so should produce a net repulsive force. But I can't work out all the forces as many of the magnets on the ball would be oriented at various different angles relative to the floor, and I suspect this would be the bane of the setup.
What do you think? I would be quite surprised if this hasn't been demonstrated in some experiment already.
