Skip to content
dronacharya.ai
← JEE Main 2014 · 19 Apr · Shift 1
PhysicsSingle correct+4 / -1Question 17 of 90

JEE Main 2014 · 19 Apr · Shift 1, Physics question 17

The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from ϵ1\epsilon_1 at one plate to ϵ2\epsilon_2 at the other. The capacitance of capacitor is :

Choose one option
Answer and worked solution

Official answer: D

ϵ(x)=ϵ0[ϵ1+(ϵ2−ϵ1)xd]\epsilon(x)=\epsilon_0\left[\epsilon_1+(\epsilon_2-\epsilon_1)\frac xd\right]. Thin slabs in series:
1C=∫0ddxAϵ(x)=dϵ0A(ϵ2−ϵ1)ln⁡ϵ2ϵ1.\frac1C=\int_0^d\frac{dx}{A\epsilon(x)}=\frac{d}{\epsilon_0A(\epsilon_2-\epsilon_1)}\ln\frac{\epsilon_2}{\epsilon_1}.
C=ϵ0(ϵ2−ϵ1)Adln⁡(ϵ2/ϵ1).C=\frac{\epsilon_0(\epsilon_2-\epsilon_1)A}{d\ln(\epsilon_2/\epsilon_1)}.

Topics:Dielectrics
← Previous questionNext question →