UVa EM:Meissner effect in super conducting sphere
From Physics: Problems and Solutions
[edit] Problem
Below a critical magnetic field 
, type I superconductors exhibit the Meissner effect, in which the magnetic induction is excluded from the volume of the superconductor. Assume that in this case the superconductor in question has no holes – i.e., it is topologically like a sphere and not like a ring.
(a)Explain why the component of 
normal to the surface vanishes just outside the superconductor.
(b)Explain why the magnetic induction outside the superconductor can be derived from a scalar potential, 
. State the boundary value problem (differential equation and boundary conditions) satisfied by 
.
(c)Consider a superconducting sphere of radius 
placed in an otherwise uniform magnetic induction 
. Find the magnetic induction outside the sphere.
