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Three concentric spherical metal shells A,B,C of radii a,b,c $(c > b > a)$ have surface charge density $+ σ, - σ$ and $+ σ$ respectively. The potential of the middle shell is $\frac{σ}{ε_{0}}$ times

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$(a - b + c)$

$\frac{a^{2} - b^{2} + c^{2}}{c}$

$(a - b + \frac{c^{2}}{b})$

$(\frac{a^{2}}{b} - b + c)$

answer is C.

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Detailed Solution

$q_{A} = σ 4 π a^{2}, q_{B} = - σ 4 π b^{2}, q_{C} = σ 4 π c^{2}$

$V_{B} = \frac{1}{4 π ε_{0}} (\frac{q_{A}}{b} + \frac{q_{b}}{b} + \frac{q_{c}}{c}) = \frac{σ}{ε_{0}} (\frac{a^{2} - b^{2}}{b} + c)$

$∴ V_{B} = \frac{σ}{ε_{0}} (\frac{a^{2}}{b} - b + c)$

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