Lower a small magnet near the surface of
a superconducting disk and
it will reach a point where the magnetic force on the magnet equals
the gravitational force causing the magnet to levitate - a
demonstration of the Meissner effect, the exclusion of the magnetic
field from the interior of the superconductor. But often the magnet
is quite unstable if the magnet is lowered in such a way that the
magnetic field at the disk's surface is never allowed to exceed the
lower critical field of the Type II cuprate superconductor used in
these demonstrations. That is, if the magnetic field is excluded by
the superconductor so that the flux density is zero in the interior -
a condition called the Meissner state, the levitating magnet appears
to ride on an imaginary "bubble" and any small displacement will
result in the magnet quickly falling to the side.
However, if the magnet is forced close
to the superconducting
surface, the lower critical field can be exceeded resulting in the
superconductor being in the intermediate or vortex state - with some
magnet flux penetrating the sample through normal filaments or flux
tubes (in single flux quanta according to the theory of
superconductivity). These flux lines become pinned on impurities in
the sample resulting in much enhanced stability. When released, the
magnet then rises from the superconducting surface - but not to as
great a height as when lowered slowly and it is "on the bubble".
Furthermore, the magnet will actually resist being displaced and even
oscillate about an equilibrium position because of the flux pinning.
If the magnet is placed on the surface
of the superconducting disk
prior to its being cooled below the transition temperature, magnetic
field penetrates the disk as it will any non-magnetic material. When
cooled below the transition temperature, the strong Meissner effect
expels the magnetic field (as opposed to simply excluding it as when
the magnet is lowered toward the disk) and the magnet levitates. But
since the field inside the superconductor exceeded the lower critical
field prior to cooling, the expulsion of magnetic flux is not
complete and the superconductor is in the intermediate state with
field lines from the magnet being pinned on impurities giving the
magnet great stability (and, again, a lower ride height than when the
field is completely excluded).
Persistent Current - Zero Resistance
Extending this demonstration to also
show the persistent currents
associated with zero resistance in a superconductor simply requires
lifting the magnet from the surface of the superconducting disk. The
magnetic field that had penetrated the superconductor and become
pinned to impurities will remain after the magnet is removed. That
is, according to Faraday's law the changing magnetic flux as the
magnet is lifted induces surface currents in order to oppose the
change within the superconductor. These induced surface currents
thus maintain the magnetic field lines that had penetrated the disk.
But since the superconductor has zero resistance, these currents do
not diminish with time - hence persistent current and the field lines
remain.
The effect can be observed by placing a
small compass above the
superconducting disk and noticing that the compass needle will align
in the direction of the polarity of the magnet which had been used to
imbed the pinned field lines. Rotating the superconducting disk
results in the compass needle rotating with it.
To demonstrate the persistence of the
surface currents, the
demonstration can be done at the beginning of a lecture - and then
submerging the disk in liquid nitrogen without letting it return to
the normal state. If the superconductor is kept below its transition
temperature, the currents will flow forever. Although that might be
difficult to demonstrate, the disk can be removed from the liquid
nitrogen at the end of the lecture and the "compass effect" is
undiminished. This shows that the currents remained for at least a
micro-century - ie, a standard 50 minute lecture period - rather than
the fraction of a picosecond relaxation time typical of the normal
state. Watching the compass realign with earth's magnetic field as
the sample warms above its transition temperature is then a
compelling demonstration that the currents had persisted.
[Text of note published in the March 2000 issue of The Physics
Teacher.]