AP EAMCET · PHYSICS · Electrostatics

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 \(\frac{Q}{2}\)

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

Verified Solution

Answer & Solution

Correct Answer

(B) (a) is correct, (b) is wrong

Step-by-step Solution

Detailed explanation

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

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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