Problem Set 4

Due Monday, October 27, in lecture

Problem 1 [20 points]
a) Consider a spherical shell of radius R, with uniform surface charge density σ_o, centered on the origin. The shell is spining counterclockwise about the z axis with angular velocity ω. Find the magnetic vector potential A(r), far from the sphere, using the magnetic dipole approximation. Find the magnetic field B within this approximation.
b) Using the method of separation of variables, as applied to the scalar magnetic potential φ_M, find an expression for the exact magnetic field B both inside and outside the spining charged shell of part (a). How does your answer for the field outside compare with that obtained by the magnetic dipole approximation in part (a)?