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Question 5.6: (a) A phonograph record carries a uniform density of “static...

(a) A phonograph record carries a uniform density of “static electricity” σ. If it rotates at angular velocity ω, what is the surface current density K at a distance r from the center?

(b) A uniformly charged solid sphere, of radius R and total charge Q, is centered at the origin and spinning at a constant angular velocity ω about the z axis. Find the current density J at any point (r, \theta, \phi) within the sphere. 

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(a) v=\omega r, \text { so } K=\sigma \omega r . \quad \text { (b) } v =\omega r \sin \theta \hat{\phi} \Rightarrow J =\rho \omega r \sin \theta \hat{ \phi }, \text { where } \rho \equiv Q /(4 / 3) \pi R^{3} .

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