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Three concentric metal shells A,B and C of respective radii a,b and c $(a < b < c)$ have surface charge densities $+ σ, - σ$ and $+ σ$ respectively. The potential of shell B is

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$\frac{σ}{\in_{0}} [\frac{b^{2} - c^{2}}{c} + a]$

$\frac{σ}{\in_{0}} [\frac{a^{2} - b^{2}}{b} + c]$

$\frac{σ}{\in_{0}} [\frac{b^{2} - c^{2}}{b} + a]$

answer is B.

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Detailed Solution

$V_{B} = \frac{1}{4 π \in_{0}} [\frac{σ 4 π a^{2}}{b} - \frac{σ 4 π b^{2}}{b} + \frac{σ 4 π c^{2}}{c}]$

$V_{B} = \frac{σ}{\in_{0}} [\frac{a^{2} - b^{2}}{b} + c]$

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