Electric Potential of Sphere with Cavity · CAP 2001 #13

Physics · electromagnetism

Problem

A quantity of charge, Q, is distributed uniformly through a sphere of radius R. A smaller sphere, of radius d and concentric with the larger sphere, is now removed from it, leaving a spherical cavity with no charge in it. The charge density of the remaining shell has not changed. The electrostatic potential at a distance r>Rr > R, outside the shell, is (a) 14πϵ0Qr3d3\frac{1}{4π\epsilon_0} \frac{Qr^3}{d^3} (b) 14πϵ0Q(R3−d3)rR3\frac{1}{4π\epsilon_0} \frac{Q(R^3-d^3)}{r R^3} (c) 14πϵ0QR3rd3\frac{1}{4π\epsilon_0} \frac{QR^3}{r d^3} (d) 14πϵ0Qd3rR3\frac{1}{4π\epsilon_0} \frac{Q d^3}{r R^3}

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