JEE Main 2021 · PhysicsMultiple choiceSingle correctHardMulti-step

JEE Main 25 July 2021, Shift 1, Physics Q2

Question 2 of 90 in this shift, Physics question 2 of 30, Section A.

A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as :

\varepsilon(x)=\varepsilon_0+kx

, for

\left(0<x\le\frac{d}{2}\right)

\varepsilon(x)=\varepsilon_0+k(d-x)

, for

\left(\frac{d}{2}\le x\le d\right)

(1) $\frac{kA}{2\ln\left(\frac{2\varepsilon_0+kd}{2\varepsilon_0}\right)}$ Official answer
(2) $\frac{kA}{2}\ln\left(\frac{2\varepsilon_0}{2\varepsilon_0-kd}\right)$
(3) $\left(\varepsilon_0+\frac{kd}{2}\right)^{2/kA}$
(4) $0$

Official answer

Option 1

NTA final key.

Chapter: Electrostatic Potential and Capacitance
Topic: Parallel Plate Capacitors
Idea tested: Variable Dielectric (Distance Dependent)

Same topic in other shifts

All Parallel Plate Capacitors questions

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.