COMEDK · Physics · 17. Electrostatics

If 216 drops of the same size are charged at \(200 \mathrm{~V}\) each and they combine to form a bigger drop, the potential of the bigger drop will be

A 8200 V
B 7200 V
C 1200 V
D 2400 V

Verified Solution

Answer & Solution

Correct Answer

(B) 7200 V

Step-by-step Solution

Detailed explanation

Let \(r\) be the radius of each small drop and \(q\) be the charge on each small drop. The potential of a small drop is given by \(V = \dfrac{kq}{r} = 200 \text{ V}\). When \(n = 216\) drops combine to form a bigger drop of radius \(R\) and charge \(Q\), the volume remains…

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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