## Midterm Quiz

PHYS205 Electricity and Magnetism

1st of October, 2008

A sphere made of (imperfectly) conducting and non-magnetizable
(μ_{r} = 1) material is spinning in a homogeneous magnetic field. The magnetic
field is parallel to the axis of rotation. Find the following steady-state
quantities:

- Volume charge density induced inside the sphere.
- Electric field and potential everywhere in space.
- Surface charge density on the surface of the sphere.

Assume that the equatorial velocity of the spinning sphere is not very large,
i.e. v ≪ c, and use approximations. How could we improve the precision of the
result?

You may want to review Chapter 3 in D. J. Griffiths: Introduction to
Electrodynamics for help with some mathematical methods.

Note: The deadline for submitting the solution is Monday, the 13^{th} of
October.