Three concentric spherical shells have radii a, b, and c ( a

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Three concentric spherical shells have radii a, b, and c ( a < b < c ) and have surface charge densities σ , − σ and σ respectively. If V A ​ , V B ​ and V C ​ denote the potentials of the three shells, then, for c = a + b , we have :NEET 2009 (Mains)

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q A ​ q B ​ q C ​ V A ​ V B ​ ​ = 4 π a 2 σ , = − 4 π b 2 σ , = 4 π c 2 σ , c = a + b = 4 π ∈ 0 ​ 1 ​ ( a q A ​ ​ + b q B ​ ​ + c q C ​ ​ ) = ϵ 0 ​ 2 σ a ​ = 4 π ϵ 0 ​ 1 ​ ( a q A ​ ​ + b q B ​ ​ + c q C ​ ​ ) ​ V C ​ ​ = ϵ 0 ​ σ ​ ( b a 2 ​ − b + c ) = ϵ 0 ​ σ ​ ( a + b a 2 ​ ) = 4 π ∈ 0 ​ 1 ​ ( a q A ​ ​ + b q B ​ ​ + c q C ​ ​ ) = ϵ 0 ​ σ ​ ( c a 2 − b ​ + c ) = ϵ 0 ​ 2 σ a ​ ​ So, V C ​ = V A ​  = V B ​

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