Below a critical magnetic field H_c, 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 \vec B 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, \vec B = -\vec \nabla \phi. State the boundary value problem (differential equation and boundary conditions) satisfied by \phi.

(c)Consider a superconducting sphere of radius a placed in an otherwise uniform magnetic induction \vec B_0. Find the magnetic induction outside the sphere.