MHT CET · Physics · Capacitance

A parallel plate capacitor having plate area 'A' and separation 'd' is charged to a potential difference ' \(V\) '. The charging battery is disconnected and the plates are pulled apart to four times the initial separation. The work required to increase the distance between the plates is ( \(\epsilon_0=\) permittivity of free space)

A \(\frac{\epsilon_0 \mathrm{AV}^2}{3 \mathrm{~d}}\)
B \(\frac{\epsilon_0 \mathrm{AV}^2}{4 \mathrm{~d}}\)
C \(\frac{2 \in_0 A V^2}{d}\)
D \(\frac{3 \epsilon_0 A V^2}{2 d}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{3 \epsilon_0 A V^2}{2 d}\)

Step-by-step Solution

Detailed explanation

\(U_i = \frac{1}{2} C_i V^2 = \frac{1}{2} \left(\frac{\epsilon_0 A}{d}\right) V^2 = \frac{\epsilon_0 A V^2}{2d}\) \(Q = C_i V = \frac{\epsilon_0 A V}{d}\)

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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