W9_parallel_resonance.eps

0.1. POTENTIAL ENERGY OF A MAGNETIC DIPOLE 223

Problem 4.

B

m

R

N turns, carrying I

θ

A circular loop of wire with radiusR,N turns, and total massM carries a currentI. It is
pivoted about a line that passes through the loop as shown, then placed in a uniform magnetic field
B~=B 0 zˆso that its magnetic moment makes an initial angle ofθ≪πwith thez-axis at timet= 0,
and is then released.

Describe its small-angle motion quantitatively. Note well that this arrangement hasnoangular
momentum to speak of and will not precess.

Problem 5.

A disk of uniformly distributed massM, chargeQ, and radiusRis spinning at angular frequencyω
about its axis. Its axis, in turn, makes an angleθwith a powerful uniform magnetic fieldB~=B 0 zˆ.
Find the frequencyωpwith which the magnetic momentprecessesaround the magnetic field.