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[Phys-L] Re: Lenz's law



On 04/11/05 22:01, Herbert H Gottlieb wrote:
However I was wondering
if the ring could possibly contain a material that is usually
repelled by a strong magnet

Sure it could. Diamagnetic materials exist ... and
so do paramagnetic materials. Copper in particular
is known to be weakly (very weakly) paramagnetic.

The built-in diamagnetism or paramagnetism is in
addition to (not instead of) the eddy-current
phenomenon.

You can easily sort out which is which based on
the time dependence.
-- The diamagnetism of the material always produces
a force away from the high-field region.
-- The paramagnetism of the material always produces
a force toward the high-field region.
-- Eddy currents in an ordinary conductor produce a
force away from or toward the magnet, according to
whether the field is increasing or decreasing.

The total force will be the sum of the relevant
contributions.

(I say "ordinary conductor" to exclude superconductors,
which have their own weird and beautiful special
properties. They are not simply like metals in the
limit of exceedingly good conductivity.)

I've spent a fair amount of time around serious magnets
(ten tesla and up). These critters will pull steel
tools out of your hand from three feet away. For
high-conductivity copper, with ordinary sizes, shapes,
and velocities, the paramagnetism is unobservably
small compared to the eddy-current effects.

I made a toy that is very popular at the physics
open-house: it is a short length of OFHC copper
pipe on a long insulating handle. You soak the
copper in liquid nitrogen (to increase the
conductivity) and then stick it into the gap of
a big magnet. You can wave it around all day,
freely, so long as you keep the pipe at the same
angle, i.e. so that it is threaded by an unchanging
amount of flux. But if you try to re-orient the
pipe, by twisting the handle, you almost can't do
it, because the eddy current forces are so large.

(It's a one-on-one demo, not good for a large
audience, because you have to feel the forces
on the handle to really appreciate them.)

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

Here's an amusing riddle for you: Suppose you want
to build an adiabatic-demagnetization stage for your
cryostat, to obtain temperatures well below one
millikelvin. You've got many moles of copper in
a changing magnetic field. You must make sure there
are no eddy currents, because the V^2 / R heating
would wipe you out. (At these temperatures, the
heat capacity of everything is very very very
small, so it doesn't take much heat to ruin
everything.) So what do you do?

Answer: build the demag stage out of a bundle of
fine wires ... electrically insulated from one
another. The induced voltage around the circumference
of a given wire goes like size squared, while the
resistance goes like size or better, so the heating
goes like size cubed or better. Meanwhile the
required number of wires goes like size squared.
Put it all together and the scaling definitely
favors small wires.
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