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GATE 2014 EE (EE2) – Question 18

Electromagnetic Fields · Effect of dielectric medium, Capacitance of simple configurations · 1 mark · Multiple choice

A parallel-plate capacitor contains two dielectrics as shown. The central slab is symmetric about the plates. Applied voltage is 10 V, and one plate to the nearest dielectric interface has potential difference 2 V. Find ε₁:ε₂.

Diagram for GATE 2014 EE (EE2) question 18
  1. 1:4
  2. 2:3
  3. 3:2
  4. 4:1

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Show answer and explanation

Correct answer: (C) 3:2

Explanation

Symmetry gives2V across each outer layer of thickness d/4,leaving6V across the central layer d/2. Thus E1=8/d and E2=12/d. Normal displacement is continuous at interfaces without free charge:ε1E1=ε2E2. Therefore **ε1:ε2=3:2,C**.