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Q.

An uncharged thin conducting spherical shell A of radius ‘a’ is placed concentrically with a thick conducting spherical shell B of inner radius 2a and outer radius 3a as shown in the figure If the shell B is given a total charge +Q, then:

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a

Charge on outer surface of shell B will be $\frac{3 Q}{5}$

b

Charge on outer surface of shell B will be $\frac{Q}{5}$

c

Charge on shell A will be $- \frac{Q}{5}$

d

Charge on shell A will be $- \frac{2 Q}{5}$

answer is B, C.

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Detailed Solution

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$V_{A} = \frac{K (Q - q)}{3 a} + \frac{K q}{2 a} + \frac{K q^{'}}{a} = 0$
also $q^{'} = - q$
$\begin{array}{l} \Rightarrow \frac{Q - q}{3 a} + \frac{q}{2 a} - \frac{q}{a} = 0 \\ \Rightarrow q= \frac{2 Q}{5} \\ ∴ q^{'} = - \frac{2 Q}{5} \end{array}$

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