I have a question, where I would like to hear how you would answer the
following conundrum.
In a typical introductory books treatment of magnetic forces and magnetic
dipoles, the following occurs.
a) You introduce magnetic forces on moving charges and then on currents. If
you are like me you pound the table and make loud noises regarding the fact
that the magnetic forces *do zero mechanical work*.
b) Then we segue a few sections down the road in the textbook where we see
the discussion of the magnetic force and torque on a small current loop in a
*constant* uniform magnetic field. Naturally we calculate that the net
force is zero and that there is a net torque. Thus arriving at the "mu
cross B" formula for torque and then introducing a potential energy for the
work done by the "magnetic" torque we get the famous "- mu dot B" for the
potential energy of the current loop in the magnetic field.
If the magnetic forces do no work, how do we arrive at a potential energy
for the current loop in the magnetic field?
I have an idea which I won't mention now, so as to not prejudice the
responses.