A charge Q is distributed over two concentric hollow spheres of radii r and R R r such that the surface densities are equal. Find the potential at the common center.

Question

A charge Q is distributed over two concentric hollow spheres of radii r and R R > r such that the surface densities are equal. Find the potential at the common center., 1 4 π ε 0 Q R + r R 2 + r 2, 1 4 π ε 0 Q R - r R 2 + r 2, 1 4 π ε 0 Q R + r 2 R 2 + r 2, 1 4 π ε 0 Q R + r 2 R 2 + 2r 2

MARKS App · Accepted Answer

Since surface charge densities are equal, Q is divided in the ratio of surface areas (i.e., r 2 . R 2 ) Q r = r 2 Q r 2 + R 2 Q R = R 2 Q r 2 + R 2 ∴ V = 1 4 π ε 0 Q 2 r + Q R R = 1 4 π ε 0 . Q r 2 + R 2 r + R

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