WBJEE · Physics · Electrostatics

Consider two concentric spherical metal shells of radii \(r_{1}\) and \(r_{2}\left(r_{2}>r_{1}\right)\). If the outer shell has a charge \(q\) and the inner one is grounded, the charge on the inner shell is

A \(\frac{-r_{2}}{5}, q\)
B zero
C \(\frac{-r_{1}}{r_{2}} q\)
D \(-q\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{-r_{1}}{r_{2}} q\)

Step-by-step Solution

Detailed explanation

Let, the charge on the inner shell be \(q^{\prime}\) The total charge will be zero So, \(\frac{k q^{\prime}}{r_{1}}+\frac{k q}{r_{2}}=0\) \(\left(\because r_{2}>r_{1}\right)\) \(\Rightarrow \quad q^{\prime}=-\frac{K q / r_{2}}{K / r_{1}}\)…

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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