W9_parallel_resonance.eps

224 Week 6: Moving Charges and Magnetic Force

Problem 6.

Q,M

L

ω

A nonconducting rod of total massMand lengthLhas a chargeQuniformly distributed along
it. It is pivoted around one end and is rotating in thex−yplane around thez-axis at angular
frequencyω.

a) Consider a small bit of chargedqa distancerfrom the pivot and compute its average magnetic

moment in thez-direction,dmz.

b) Integrate this result and find the total magnetic (dipole) moment of the rotating rodmz

c) Show that the result can be expressed asmz= 2 QMLzwhereLzis the angular momentum of

the rod about the pivot (that is to say, in thez-direction).