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.