Question

Two thin conducting shells of radii $R$ and $2R$ are shown in figure. The outer shell carries a charge $+Q$ and inner shell is neutral. Choose the correct option.

• A. With switch open potential of inner sphere is same as that of point at distance $\frac{3R}{2}$ from centre
• B. When switch S is closed, potential of inner sphere becomes zero
• C. With switch S closed charge on inner sphere is $(-\frac{Q}{2})$
• D. With switch S closed charge on inner sphere is $(-Q)$
• E. With switch S open charge on inner sphere is $-4Q$
  

Answer 1

The correct option is B When switch S is closed, potential of inner sphere becomes zero

Let $q^{\prime }$ be the charge on inner shell after switch is closed.

$V_{inner}=V_{outer}$

$\frac{K{q}^{\prime }}{r}+k\frac{q-q^{\prime }}{2r}=\frac{k{q}^{\prime }}{2r}+\frac{k(q-q^{\prime })}{2r}$

$q^{\prime }=0$