Q145 / 160 · AP EAMCET 2023 (15 May Shift 1) · Physics

Two thin conducting concentric shells of radii $\mathrm{R}$ and $2 \mathrm{R}$ are shown in the figure. The outer shell carries a charge $+Q$ and the inner shell is neutral. Then the correct statement/s is (a) When the switch is closed, the potential on the inner shell becomes zero (b) With the switch closed, the charge on the inner sphere is $\frac{Q}{2}$ Figure

  • A
    (a) and (b) are correct
  • Correct answer
    B
    (a) is correct, (b) is wrong
  • C
    (a) is wrong, (b) is correct
  • D
    (a) and (b) are wrong

Solution

Let charge on inner shell after switch is closed be $q$ then, $\mathrm{V}_{\text {inner }}=\mathrm{V}_{\text {outer }}$ $$ \frac{K q}{R}+\frac{K(Q-q)}{2 R}=\frac{K q}{2 R}+\frac{K(Q-q)}{2 R} $$ $$ \therefore \mathrm{q}=0 $$

Hence, the correct answer is option: 'B'.

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