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Q.

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

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

b

(a – b + c)

c

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

d

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

answer is A.

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Detailed Solution

$\begin{array}{l} V_{B} = \frac{1}{4 {πϵ}_{0}} \frac{q_{A}}{b} + \frac{1}{4 {πϵ}_{0}} (\frac{- q_{B}}{b}) + \frac{1}{4 π \in_{0}} \frac{q_{C}}{C} \\ V_{B} = \frac{1}{4 {πϵ}_{0}} [\frac{σ (4 {πa}^{2})}{b} - \frac{σ (4 {πb}^{2})}{b} + \frac{σ (4 {πc}^{2})}{c}] \\ V_{B} = \frac{σ}{\in_{0}} [\frac{a^{2}}{b} - b + c] \end{array}$

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