Q 12-02-041JEE MainJEE Main 2026 (4 Apr, Shift 1)Medium
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 ______.
Answer: (A) $-2$
With the battery connected, $V$ is fixed: $U = \dfrac{1}{2}CV^2 = \dfrac{\epsilon_0AV^2}{2x}$.
$$\frac{dU}{dt} = -\frac{\epsilon_0AV^2}{2x^2}\frac{dx}{dt} = -\frac{\epsilon_0AV^2v}{2x^2} \propto x^{-2}$$
Solution by Sreeraj P, M.Sc Physics