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) $-2$
Concept. Battery connected: $V$ fixed, $U=\tfrac12CV^2=\dfrac{\varepsilon_0AV^2}{2x}$.
Step 1. Rate. $\dfrac{dU}{dt}=-\dfrac{\varepsilon_0AV^2}{2x^2}\dfrac{dx}{dt}=-\dfrac{\varepsilon_0AV^2v}{2x^2}$.
Answer. $\propto x^{-2}$ (Option A).
Solution by Sreeraj P, M.Sc Physics
