A solid sphere of radius carries a total charge spread uniformly through its volume…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetostatics · Magnetostatics

The Boundary-Value Problem, Ch The magnetic multipole expansion and the magnetic scalar potential

Problem

A solid sphere of radius a=0.050 ma = 0.050\,\mathrm{m} carries a total charge Q=2.0×10−6 CQ = 2.0\times10^{-6}\,\mathrm{C} spread uniformly through its volume and spins steadily about a diameter with angular speed ω=100 rad s−1\omega = 100\,\mathrm{rad\,s^{-1}}. ((a)) Treat the sphere as a nest of thin spherical shells, each spinning at ω\omega, and use the moment of a spinning charged shell to show that m=15Qa2ω\mathbf m = \tfrac15 Qa^2\boldsymbol\omega. ((b)) Evaluate mm for the numbers given, and say why it is smaller than the moment of a thin shell with the same QQ, aa and ω\omega.

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