Re: excluding B fields

[Leigh Palmer <palmer@SFU.CA>]

> Does the Meissner effect imply that there are no transparent (to any
> wavelength) superconductors?

No. The Meissner effect is a DC effect anyway. Do you suppose
that superconductors can thwart Superman's x-ray vision?!
(Before you ask, Kryptonite is not superconducting.)

The Meissner effect is only seen to varying degrees in the zoo
(perhaps I should say "bestiary") of superconducting materials.
In most it does not imply that magnetic fields are strictly
excluded from the interior of superconductors. The "true"
Meissner effect is misrepresented being the exclusion of
magnetic fields from the interior of a superconductor anyway.
The effect, best seen in Type I superconductors, is more
dramatic. It is the *expulsion* of a magnetic field from the
interior of a superconductor when its temperature is lowered
through the critical temperature at that field. If the sole
result of cooling the material was the vanishing of electrical
resistance the magnetic field would not be expelled; it would
be frozen in, and a persistent magnetic moment would be seen
when the source of the field is switched off. Instead, a Type
I superconductor becomes a perfect diamagnet. This effect was
not noted by Onnes when he discovered the effect in mercury,
and it should be emphasized more strongly.

It is now possible to demonstrate an incomplete Meissner
effect using a pill of 1-2-3 nitrogen temperature
superconductor. A small magnet placed on the pill will be seen
to lift off its surface when the pill is cooled. The expulsion
of magnetic flux from this sort-of-Type-II superconductor is
not complete, however, and the magnet remains suspended in
place above a horizontal superconducting surface. It would not
do so if the expulsion of flux was complete; it would not be
in stable equilibrium in that case. It remains stationary (or
can be made to spin attractively) above the pill because it is
pinned to trapped flux bundles in the pill.

What would be seen if only zero resistance was present? Well,
that too is demonstrable in principle. If one places the
small magnet on a horizontal aluminum surface and tries to
lift it rapidly, a force greater than its weight plus *vis
inertiae* will be seen to be necessary to lift it. That is
because the induced currents attending the removal of magnetic
flux from the bulk of the aluminum will, in their Lenzian
perversity, resist you efforts to remove the magnet. The
effect is in the opposite direction; the magnet is attracted
to the aluminum while it is being pulled away. The degree of
attraction is proportional to the product of the conductivity
and a monotonically increasing function of the velocity of
the magnet, but the attraction decays in time, and when the
velocity reaches zero at any distance. If the conductivity
goes to infinity the attraction never abates. There is,
effectively, a virtual image of the magnet seen inside the
conductor. (Being a virtual image the magnet still seems to
be at its original position outside the conductor.)

That's probably more than you wanted to know. I didn't
understand the metaquestion you asked, perhaps, but wouldn't
the absence of an electric field inside the superconductor
lead you to the same speculation? Why did you specify the
Meissner effect?

Leigh