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.

TestHub · Accepted Answer

Since surface charge densities are equal, Q is divided in the ratio of surface areas (i.e., $r^{2} . R^{2}$ )

$Q_{r} = \frac{r^{2} Q}{r^{2} + R^{2}} Q_{R} = \frac{R^{2} Q}{r^{2} + R^{2}}$

$∴ V = \frac{1}{4 π ε_{0}} [\frac{Q_{2}}{r} + \frac{Q_{R}}{R}] = \frac{1}{4 π ε_{0}} . \frac{Q}{r^{2} + R^{2}} [r + R]$

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