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GATE 2014 EC (EC1) – Question 35

Electromagnetics · Maxwell's Equations · 1 mark · Multiple choice

A point charge +q is distance d from an infinite grounded metal plate in a medium of permittivity $\epsilon$. Find its force.

  1. 0
  2. $q^2/(16\pi\epsilon d^2)$, away from the plate
  3. $q^2/(16\pi\epsilon d^2)$, toward the plate
  4. $q^2/(4\pi\epsilon d^2)$, toward the plate

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Correct answer: (C) $q^2/(16\pi\epsilon d^2)$, toward the plate

Explanation

Replace the infinite grounded conducting plane by an image charge−q at the mirror point. The real charge and image are separated by2d. Coulomb’s law gives force magnitude q²/[4πε(2d)²]=q²/(16πεd²), directed toward the oppositely charged image and hence **towards the plate,C**.