A uniform spherical charge distribution of radius R1 is centered at origin O. A spherical cavity of radius R2 is carved out, centered at P, with OP = a = R1 - R2. If E(r) is the electric field at a point inside the cavity, which statement is correct?

E is uniform; its magnitude is independent of R2 but its direction depends on r
E is uniform; its magnitude depends on R2 and its direction depends on r
E is uniform; its magnitude is independent of a but its direction depends on the vector a
E is uniform and both its magnitude and direction depend on the vector a

Correct answer: E is uniform and both its magnitude and direction depend on the vector a

Solution

Superposition gives E_cavity = (rho/3epsilon0)*a, a constant vector. It is uniform, and both its magnitude and direction are set by the displacement vector a between centers.

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