ABSTRACT
Figure 45.1. Temperature dependence of resistivity σρ /1= for a superconducting metal The condition of perfect conductivity can be described in terms of a finite current density j
G which flows indefinitely in the superconducting state, such that Ohm's law
(12.10) gives
( ) 0/1 === jjE GGG ρσ (45.1) Substituting this result, Faraday's law (13.23) shows that, inside a perfect conductor, B
G
cannot change with time
constor0 ==×−∇=∂ ∂ BE
t B GGG (45.2)
Inside an electrical conductor which is cooled below in an external magnetic field cT 0B G
and then becomes a perfect conductor, one would expect the magnetic flux through the sample to be maintained even after switching off the external field, due to induced persistent currents. However, it was found experimentally that, if a superconductor is cooled below in an applied magnetic field, the magnetic flux is expelled rather than frozen, as in Figure 45.2. In other words, in the superconducting state it is always required that
cT
0=BG (45.3) This result, which is not predicted by Eq.(45.2), is called the Meissner effect, and can be described in terms of the perfect diamagnetism defined by Eq.(44.7).
