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

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

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

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

answer is B.

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Detailed Solution

$q_{A} = σ (4 π a^{2})$

$q_{B} = σ (4 π b^{2})$

$q_{C} = σ (4 π c^{2})$

$V_{B} = \frac{K q_{A}}{b} + \frac{K (- q_{B})}{b} + \frac{K q_{C}}{c}$

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