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 $
