A charge Q is distributed over two concentric conducting thin spherical shells radii r and R R r . If the surface charge densities on the two shells are equal, the electric potential at the common centre is :

Question

A charge Q is distributed over two concentric conducting thin spherical shells radii r and R R > r . If the surface charge densities on the two shells are equal, the electric potential at the common centre is :, 1 4 πϵ 0 R + r 2 R 2 + r 2 Q, 1 4 πϵ 0 2 R + r R 2 + r 2 Q, 1 4 πϵ 0 R + 2 r Q 2 R 2 + r 2, 1 4 πϵ 0 ( R + r ) R 2 + r 2 Q

MARKS App · Accepted Answer

Q 1 = σ 4 πr 2 Q 2 = σ 4 πr 2 ∴ Q = σ 4 π r 2 + R 2 ∴ σ = Q 4 π r 2 + R 2 V C = KQ 1 r + KQ 2 R = K 0 4 πr 2 r + K 0 4 πR 2 R = KQ 4 π ( r + R ) 4 π r 2 + R 2 = KQ ( r + R ) r 2 + R 2

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