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A solid sphere of radius R carries a uniform volume charge density rho. A spherical cavity of radius R/2 is scooped out of it (in the standard configuration). Find the ratio |E_A|/|E_B| of the electric field magnitudes at the two specified points A and B due to the remaining material.

1. 18/54
2. 21/34
3. 17/54
4. 18/34

Correct answer: 18/54

Solution

Treat the carved sphere as a full uniformly charged sphere of density rho superposed with a smaller sphere of density -rho occupying the cavity. The field at any point is the sum of the contributions of these two. Evaluating the magnitudes at the given points A and B and forming the ratio gives 18/54 (= 1/3) for the standard geometry of this well-known problem.

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