A parallel plate capacitor has plate area ' A ' and separation… | MHT CET 2023 (10 May, Shift 1)

Q18MHT CET 2023 · 10 MAY · SHIFT 1Medium

Energy Stored & Force between Plates

A parallel plate capacitor has plate area ' $A$ ' and separation between plates is ' $d$ '. It is charged to a potential difference of $V_0$ volt. The charging battery is then disconnected and plates are pulled apart three times the initial distance. The work done to increase the distance between the plates is $(\varepsilon_0 =$ permittivity of free space)

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Answer: (d)

Battery disconnected: $Q$ constant, $U = \frac{Q^2}{2C}$ .
$d \to 3d \Rightarrow C \to \frac{C}{3}$ , so $U_f = 3U_i$ .
$W = 2U_i = 2 \times \frac{1}{2}\frac{\varepsilon_0 A}{d}V_0^2 = \frac{\varepsilon_0 AV_0^2}{d}$
So the answer is (d) $\frac{\varepsilon_0 AV_0^2}{d}$ .

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