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JEE MAIN_2026
04-04-26_S2
Question
A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If $x$ is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^\alpha$, where $\alpha$ is $\_\_\_\_$ .
Select the correct option:
A
-2
B
1
C
-1
D
2
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
\begin{aligned} & \text { Capacitance }=\mathrm{C}=\frac{\varepsilon_0 \mathrm{~A}}{\mathrm{x}} \\ & \text { Energy stored }=\mathrm{U}=\frac{1}{2} \mathrm{CV}^2 \\ & \mathrm{U}=\frac{1}{2} \frac{\varepsilon_0 \mathrm{~A}}{\mathrm{x}} \mathrm{~V}^2 \\ & \frac{\mathrm{dU}}{\mathrm{dt}}=\frac{1}{2} \varepsilon_0 \mathrm{AV}^2\left(-\frac{1}{\mathrm{x}^2}\right) \frac{\mathrm{dx}}{\mathrm{dt}} \\ & \frac{\mathrm{dU}}{\mathrm{dt}} \propto \frac{1}{\mathrm{x}^2} \end{aligned}
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