Re: [Phys-l] Magnetic force and work

[John Denker <jsd@av8n.com>]

Rauber, Joel wrote:

> I'm curious as to how some of the experienced veterans on the list would
> respond.  I just finished deriving the fact that the magnetic force law
> on a charge implies that magnetic forces do no work.
>  
> After class a thinking student came up and started fiddling with the two
> bar magnets I had and asked me (I'm changing the question a bit)
>  
> If I take the two magnets up into outer space (no other influences) and
> align them co-linearly so the South pole of one is near the north pole
> of the other and let go, they'll accelerate toward each other.  Does
> this contradict the idea that magnetic forces do no work.

Well, look again at the details of the proof.

You presumably have not proved that "magnetic forces do no work",
because that's not true.

More likely, you proved that a _static_ magnetic field does no
work on a _test charge_.

1) If the field is in any way time-dependent, all bets are off.
 -- Betatron.
 -- Dynamo (aka electrical generator).
 -- et cetera.

2) An electron is not a test charge.  An electron has a built-in
magnetic moment.  This means real electrons are not entirely
covered by the aforementioned theorem.

For clarity, suppose ferrogmagnetic bar magnet "A" is static,
and magnetic object "B" (either ferromagnetic or just paramagnetic)
is attracted towards it.  Object "B" cannot be modeled as just a
bunch of test charges (i.e. Amperian currents).  Ferromagnetism
and paramagnetism are totally dependent on the alignment of the
spin (and built-in dipole moment) of individual electrons.  Spin
is nonclassical.  Really, really, nonclassical.  If you moved a
classical Amperian current loop in an external field (i.e. the
field produced by magnet "A"), there would be eddy currents (or
whatever you want to call them) that would change the amount of
current in the loop.  Instead, there is some nonclassical mechanism
that keeps the dipole moment of the electron constant, no matter
how you move it around in the external field.  So in some sense,
you are doing work against this mechanism.


==================

FWIW a more general version of issue (1) arises when people misquote
the theorem about forces of constraint, and leap to the conclusion that
forces of constraint never do any work.  A moment's thought should make
it clear that although a _static_ constraint does no work, you can do
all sorts of work using moving contraints.  Example: water is held in
a ladle by forces of constraint, yet you can easily lift water from
a lower bucket to a higher bucket, by moving the ladle.