Electrostatics Question 784

Question: 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

Options:

A) -4Q/3

B) -8Q/11

C) -5Q/3

D) -3Q/7

Show Answer

Answer:

Correct Answer: B

Solution:

[b] From given conditions, $ V _{A}=V _{B} $ and $ V _{B}=0 $

$ \Rightarrow V _{B}=\frac{k( Q-q _{1} )}{3\alpha }+\frac{kq _{2}}{2\alpha }+\frac{kq _{1}}{2\alpha }=0 $

$ \Rightarrow 2Q+q _{1}+3q _{2}=0 $ .(i) Using $ V _{A}=V _{C} $

$ \frac{k( Q-q _{1} )}{3\alpha }+\frac{kq _{2}}{2\alpha }+\frac{kq _{1}}{2\alpha }=\frac{kq _{1}}{2\alpha }+\frac{k( Q-q _{1} )}{3\alpha }+\frac{kq _{2}}{2\alpha } $

$ \Rightarrow q _{1}=-\frac{q _{2}}{4} $ ?(ii) Using it in (1), $ q _{2}=-\frac{8}{11}Q $



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