COMEDK · Physics · 17. Electrostatics

A small conducting sphere of radius \(r\) is lying concentrically inside a bigger hollow conducting sphere of radius \(R\). The bigger and smaller spheres are charged with \(Q\) and \(q(Q>q)\) and are insulated from each other. The potential difference between the spheres will be

A \(\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{q}{r}-\frac{q}{R}\right)\)
B \(\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{q}{R}-\frac{Q}{r}\right)\)
C \(\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{q}{r}-\frac{Q}{R}\right)\)
D \(\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{Q}{R}+\frac{q}{r}\right)\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{q}{r}-\frac{q}{R}\right)\)

Step-by-step Solution

Detailed explanation

According to given situation, potential at the surface of small conducting sphere of radius \(r\), \[ V_{r}=\frac{k q}{r}+\frac{k Q}{R} \] Potential at the surface of bigger conducting sphere of radius \(R\), \[ V_{R}=\frac{k q}{R}+\frac{k Q}{R} \] \(\therefore\) Potential…

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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