Stephen A. Lawrence wrote:
> A "successful" exchange in a science group is, IMHO, one in which I
> learn something.
>
> This one's been successful ;-)
Ditto!
> > > Remember, E and B fields (apparently!) follow the law of
> > > superposition, which means overlapping fields themselves don't
> > > interact; they just sum.
> >
> > They really don't just sum, it's more complex than that in real
> > geometries with real materials, mu and saturation. Thats why we need
> > finite element programs.
>
> Um ... As I learned E&M ... and this is just quoting from Griffiths, I
> sure can't claim to have proved this experimentally -- both E and B
> fields obey superposition perfectly, and the "pure" form of Maxwell's
> equations holds everywhere, inside matter as well as outside. The
> _apparently_ different equations we get in matter -- with D vs E and H
> vs B and with funky values for mu and strange saturation effects --
> _just_ result from the superposition of E and B fields induced in the
> matter as a result of the effect of the externally applied fields. They
> can come from tiny current loops, or from rotated/stretched electric
> dipoles, but either way it's actually an additional field associated
> with the matter which is added to the applied field. Or so say the
> textbooks I've read.
Ok, I agree that superposition holds as long as all the materials
present are operating in linear ranges. We should keep in mind however
that if any material in the system is significantly nonlinear then
the entire problem should be considered nonlinear and superposition
no longer holds. Fortunately, the small nonlinear effects in
diamagnetic and paramagnetic materials can normally be ignored.
Unfortunately, most of the useful magnetic materials are highly
nonlinear at fields where they are commonly used. Nonlinear
materials also cause interactions between orthogonal fields.
The separation of the magnetic field into B and H components as
is done in all of the texts can also be misleading. There is really only
one field that is measurable at any point in space. We have no way
to separate out that part which is due to material dipoles from that
part which is caused by current carrying coils.
Standard texts only consider what I call the "available
magnetic energy" which corresponds to the energy which can
be recovered by a coil from an excited soft magnetic material.
The energy inside high mu materials is however just as real
even though it is mostly due to internal dipoles. Remember
that essentially all of the space inside materials has mu equal
to mu_zero and that this real energy can be 10^6 times larger
than the applied exciting energy.
>
> An electron in a B field has a magnetic dipole field, and unless
> Wikipedia got it totally wrong, the strength of the electron's dipole is
> independent of the strength of the external field.
Correct as far as we can measure and suggestive of some
form of energy source within electrons. ZPE?
>
> If my mental picture is right, then a free electron's dipole must be
> aligned with the external field (parallel or antiparallel).
This is experimentally observed but is something that I find
extremely strange. Although one of the orientations is a true
stable equilibrium the other should be an unstable equlibrium and
the dipole should flip with any pertubation. Spin must come in
here somehow but I don't see quite how.
>
> But in that case an electron in a non-uniform B field must feel a force,
> proportional to the gradient of the field ('cause that's what magnetic
> dipoles _do_, and besides, if the electron sourced a dipole field but
> didn't feel a force as a result of being immersed in somebody else's
> dipole field we'd violate conservation of linear momentum which would be
> unfortunate).
>
> But then if we let the electron go in a non-uniform B field it'll
> accelerate, which means something did work on it; it gained kinetic
energy.
>
> Where'd the energy come from? I have no idea. Since the force on the
> electron depends on whether it's spin-up or spin-down there's certainly
> no simple "potential-gradient" model one can use here, either.
>
> Interesting. There must be something wrong with this picture, but I
> don't know what. :-)
The electrons in macroscopic magnets source and sink energy so I
don't have any problem with that here. Perhaps the spin of the electrons
needs to be considered to apply the relativistic model of magnetics here.
I always find it more intuitive to apply magnetic energy considerations
in calculating magnetic forces. The answers always seem to come out
right even though the relativistic model holds that magnetic fields do
no work on charged particles.
George Holz
