A Levitron and Earnshaw’s theorem.

[andresB]

The Earnshaw’s theorem comes directly from Maxwell equation so it should be unavoidable in any classical situation. The theorem usually disallows magnetic levitation. However, there are loopholes. Quoting wikipedia "Earnshaw's theorem has no exceptions for non-moving permanent ferromagnets. However, Earnshaw's theorem does not necessarily apply to moving ferromagnets".

The usual counterexample to the impossibility of an equilibrium situation for magnetic levitation is given by the levitron
Open article on the subject: https://iopscience.iop.org/article/10.1088/1361-6404/abbc2c

I tried the literature on the topic, but I still can't understand what is actually happening with the levitron and the Earnshaw’s theorem. Is the theorem simply not applicable to the levitron? why? how?

 

[A.T.]

The Earnshaw’s theorem comes directly from Maxwell equation so it should be unavoidable in any classical situation. The theorem usually disallows magnetic levitation.

It disallows stable static configurations.

Is the theorem simply not applicable to the levitron? why?

Because it spins, so it's not static.