question_answer

Figure shows a system of three concentric metal shells A, B and C with radii a, 2a and 3a respectively. Shell B is earthed and shell C is given a charge Q. Now if shell C is connected to shell, A then the final charge on the shell B, is equal to

A) -4Q/3

B) -8Q/11

C) -5Q/3

D) -3Q/7

Correct Answer: B

Solution :

[b] From given conditions, \[{{V}_{A}}={{V}_{B}}\]and \[{{V}_{B}}=0\] \[\Rightarrow {{V}_{B}}=\frac{k\left( Q-{{q}_{1}} \right)}{3\alpha }+\frac{k{{q}_{2}}}{2\alpha }+\frac{k{{q}_{1}}}{2\alpha }=0\] \[\Rightarrow 2Q+{{q}_{1}}+3{{q}_{2}}=0\]                            ?.(i) Using \[{{V}_{A}}={{V}_{C}}\] \[\frac{k\left( Q-{{q}_{1}} \right)}{3\alpha }+\frac{k{{q}_{2}}}{2\alpha }+\frac{k{{q}_{1}}}{2\alpha }=\frac{k{{q}_{1}}}{2\alpha }+\frac{k\left( Q-{{q}_{1}} \right)}{3\alpha }+\frac{k{{q}_{2}}}{2\alpha }\] \[\Rightarrow {{q}_{1}}=-\frac{{{q}_{2}}}{4}\]                                     ?(ii) Using it in (1), \[{{q}_{2}}=-\frac{8}{11}Q\]