Phys 742 – Assignment 7 – Due 2 April 96

1.

Jackson’s problem 5.7

2.

Solve the boundary-value problem for a (type I) superconducting sphere of radius a ni an external magnetic field B_{0}. What is the magnetization M in the sphere? What is the induced dipole moment m (in magnitude and direction)?

The magnetization is equivalent to a surface current K, which in this case is a real persistent surface current. Find the components of K as a function of suitably chosen angles θ and ϕ.

Find a vector potential A that describes the total B outside the sphere.

3.

Jackson’s problem 5.10

4.

A long hollow cylinder of inner radius a, outer radius b, and of magnetic permeability μ is placed in a region of initial magnetic-flux density B_{0}, at right angles to the field. Determine the screening factor, defined as the ratio between the field inside the cavity and B_{0}.