Two thin conducting shells of radii R and 3R are shown in figure. outer shell carries a charge + Q a

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2. Electric Potential and Capacitance

hard

Two thin conducting shells of radii $R$ and $3R$ are shown in the figure. The outer shell carries a charge $+ Q$ and the inner shell is neutral. The inner shell is earthed with the help of a switch $S$.

A

With the switch $S$ open, the potential of the inner sphere is equal to that of the outer.

B

When the switch $S $ is closed, the potential of the inner sphere becomes zero.

C

With the switch $S$ closed, the charge attained by the inner sphere is $- q/3$.

D

all of the above

Solution

Let $q$ be the charge attained by the inner shell.

As the inner shell is earthed so potential at any point on the surface of the shell is zero

i.e. $V=0=V_{\text {in}}+V_{\text {out}}=\frac{k q}{R}+\frac{k Q}{3 R}$

$\therefore q=-\frac{Q}{3}$

Standard 12

Physics

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