A parallel plate capacitor having plate area ' A ' and separation ' d… | MHT CET 2025 (21 Apr, Shift 2)

Q10MHT CET 2025 · 21 APR · SHIFT 2Medium

Energy Stored & Force between Plates

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 ( $\varepsilon_0 =$ permittivity of free space)

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Answer: (d)

Battery disconnected: $Q$ constant, $U = \frac{Q^2}{2C}$ .
$d \to 4d \Rightarrow C \to \frac{C}{4}$ , so $U_f = 4U_i$ .
$W = U_f - U_i = 3U_i = 3 \times \frac{1}{2}\frac{\varepsilon_0 A}{d}V^2$
So the answer is (d) $\frac{3\varepsilon_0 AV^2}{2d}$ .

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