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Electromagnetic Induction. Maxwells Equations

Problem 3.361

A long solid aluminum cylinder of radius \(a=5.0 \mathrm{~cm}\) rotates about its axis in a uniform magnetic field with induction \(B=10 \mathrm{~m} \mathrm{~T}\). The angular velocity of rotation equals \(\omega=45 \mathrm{rad} / \mathrm{s}\) with \(\omega \uparrow \uparrow\). Neglecting the magnetic field of appearing charges, find their space and surface densities.

Reveal Answer
ρ=−2εωB=−0.08nC/m3,σ=ε0aωB=2pC/m2\rho=-2 \varepsilon \omega \mathbf{B}=-0.08 \mathrm{nC} / \mathrm{m}^{3}, \quad \sigma=\varepsilon_{0} a \omega \mathrm{B}=2 \mathrm{pC} / \mathrm{m}^{2}
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