Capacitors

JEE Main level, single correct, medium

4 of 180

Question 4 of 180

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed vv. If xx is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to xαx^\alpha, where α\alpha is _____.

Show answer and solution

Answer: (A) −2-2

The electrostatic energy of a parallel plate capacitor is given by U=12CV2U = \dfrac{1}{2} C V^2.

For a parallel plate capacitor, the capacitance is C=ε0AxC = \dfrac{\varepsilon_0 A}{x}, where xx is the separation between the plates.

Since the capacitor remains connected to the battery, the potential difference VV across the plates is constant.

Substituting CC into the energy equation gives:

U=ε0AV22xU = \dfrac{\varepsilon_0 A V^2}{2x}

Differentiating UU with respect to time tt to find the time rate of change of electrostatic energy:

dUdt=ddt(ε0AV22x)=−ε0AV22x2dxdt\dfrac{dU}{dt} = \dfrac{d}{dt} \left( \dfrac{\varepsilon_0 A V^2}{2x} \right) = -\dfrac{\varepsilon_0 A V^2}{2x^2} \dfrac{dx}{dt}

Given that the plates are pulled apart at a uniform speed vv, we have dxdt=v\dfrac{dx}{dt} = v.

dUdt=−ε0AV2v2x2\dfrac{dU}{dt} = -\dfrac{\varepsilon_0 A V^2 v}{2x^2}

From the above expression, it is clear that dUdt∝x−2\dfrac{dU}{dt} \propto x^{-2}.

Comparing this with xαx^\alpha, we get α=−2\alpha = -2.

Answer: −2-2

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Capacitors, dielectrics and RC circuits simulationDrag the sliders and watch the numbers in this question change.

More Physics practice

JEE Main Physics practice question on Capacitors (Capacitance), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.