JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Capacitance

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^{α}

, where

α

is _____ .

(A)-2✓ Correct
(B)1
(C)-1
(D)2

Answer: (A)

Solution

With the battery connected the voltage

V

is constant while

C = \frac{ε _{0} A}{x}

. The stored energy is

U = \frac{1}{2} C V^{2} = \frac{ε _{0} A V ^{2}}{2 x}

, so

\frac{d U}{d t} = - \frac{ε _{0} A V ^{2}}{2 x ^{2}} \frac{d x}{d t}

. Since

\frac{d x}{d t} = v

is constant,

\frac{d U}{d t} \propto x^{- 2}

, giving

α = - 2

JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Single correct option

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