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The purpose of this wiki is to provide physics graduate students and other scientists with peer-reviewed solutions to the types of problems that can be found on PhD qualifying exams. The articles consist of graduate-level problems from public problem banks. Public problem banks are often compiled by various university physics departments and include questions that they have given on previous PhD qualifying/prelim exams. The community can submit problems, search for problems, and post or correct solutions to these problems.

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Featured Problem

Meissner effect in super conducting sphere

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.