An electron of charge and mass moves on a circle of radius in a plane perpendicular…
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetic materials · Electromagnetic induction and alternating-current circuits
The Boundary-Value Problem, Ch Diamagnetism, paramagnetism and magnetic susceptibility
Problem
An electron of charge −e and mass me moves on a circle of radius r in a plane perpendicular to a uniform field B, which is switched on smoothly from zero to a final value B.
((a)) Using Faraday's law applied around the orbit, derive the change in orbital speed Δv produced by the switching-on, and show that the resulting change in orbital magnetic moment opposes B whichever way the electron was originally circulating.
((b)) A collection of Nv independent, permanent atomic moments of magnitude m per unit volume sits in a field B at temperature T. Starting from the Langevin orientational average ⟨mz⟩=mL(mB/kBT), with L(x)=cothx−1/x, derive the Curie law χm=μ0Nvm2/3kBT in the limit mB≪kBT.