Michel Jullian wrote:
a violation of energy conservation? No. Electric potential
energy is decreasing somewhere, I'll let you find where :)
...
...We want to know, lol! :-)
Oops I have found in the meantime that my initial explanation was
wrong, so it's just as well I kept it to myself ;-)
Electric potential energy has nothing to do with the matter as I
realized (my apologies for the misleading hint). Still it seemed
obvious to me that _some_ potential energy had to be decreasing,
since it takes work to bring the dipoles back to their non-aligned
initial state. Same reasoning as in the non-rotating case where
magnets are just attracted to each other, similar to a mass falling
off a table as previously mentioned by Stephen. This led me to
Googling "magnetic potential energy", and bingo, there is such a
thing, and it decreases all right when magnetic dipoles align!
Yes, I knew that. In fact the formula which you quoted below,
-mu <dot> B
applies to linear potential energy as well, which the authors apparently
didn't mention. A dipole in a nonuniform field feels a linear force
which is equal to
gradient(mu <dot> B)
and in any field it feels a torque which is
mu <cross> B
and these are easily seen to be the negatives of the gradient of the
potential and partial of the potential with respect to the dipole angle,
respectively.
I actually said this 'way back before the beginning of this discussion,
and again part way through...
