Consider a permanent magnet introducing a magnetic field at some fixed angle to a loop of wire on a spindle. If a fixed current is allowed to run through the wire, the lorentz force introduces a net torque on the system and causes it to rotate. This will increase the KE of the loop, where does this energy come from? Note that the loop has contacts such that when it turns through 180 degrees, it will have its current flowing in the opposite direction.
My initial guess was that it came from the electrons doing work against the magnetic field, but the lorentz force is perpendicular to the current, and so the electrons don't do any work against it.
I've just started the course on magnetostatics and our lecturer hasn't discussed magnetic potential energy, but I think that this is what I am missing from my analysis. Is it the case that by introducing the magnetic field, we have given the system some amount of magnetic potential energy that it then converts to KE?