Back on 6/20/06, after I had baldly asserted that "magnetic fields do no
work", George Holz wrote, regarding the fields of permanent magnets,
The currents are almost entirely electron spin dipoles aligned
within in changing domains which reorient to aid the applied field.
And I responded, regarding the energy gained by such a dipole as moves
due to the force on it from a nonuniform magnetic field,
Where'd the energy come from? I have no idea.
And after that I said nothing much at all about magnetic motors or
permanent magnets for a good long time.
Since then I've given it some thought and I finally worked through a
classical (non-quantum, just magnetostatics) analysis of the forces and
torques on a dipole, which I put on a web page. The upshot is that, for
a permanent dipole in a nonuniform but fixed magnetic field, the forces
are conservative (and, _yes_, the magnetic field certainly does "do
work" on the dipole). The page is here:
http://www.physicsinsights.org/force_on_dipole_1.html
and the conclusion that the forces are conservative is found here:
http://www.physicsinsights.org/force_on_dipole_1.html#conservative
For electromagnets, as opposed to permanent (spin) dipoles, the force is
due to q(E+vxB) and the work done comes from the currents. There's more
to be said about that, however, and I will be writing up a companion
page on electromagnetic dipoles and their interactions with each other
and with permanent dipoles, in which I'll also say a little more about
the consequences of the force on a permanent dipole being conservative.
The upshot is that magnetic motors which gain energy from permanent
magnets do, indeed, violate the classical model of magnetism. So,
before you invest a lot of money in such a device, you should give some
thought to how accurate you think the classical models of magnets and
magnetostatics really are.
