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 :

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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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