The GATE Grind

GATE 2018 EE – Question 20

Electromagnetic Fields · Coulomb's Law, Electric Field Intensity, Electric Flux Density, Gauss's Law, Divergence · 1 mark · Multiple choice

A positive charge of 1 nC is placed at $(0,0,0.2)$ where all dimensions are in metres. Consider the $x$-$y$ plane to be a conducting ground plane. Take $\epsilon_0=8.85\times10^{-12}$ F/m. The $z$ component of the E field at $(0,0,0.1)$ is closest to

  1. 899.18 V/m
  2. $-899.18$ V/m
  3. 999.09 V/m
  4. $-999.09$ V/m

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) $-999.09$ V/m

Explanation

Use an image charge $-1$ nC at $(0,0,-0.2)$. At $z=0.1$ the real charge (0.1 m above) gives $-\frac{Q}{4\pi\epsilon_0(0.1)^2}=-899.2$ V/m, and the image (0.3 m below) gives $-\frac{Q}{4\pi\epsilon_0(0.3)^2}=-99.9$ V/m, both pointing in $-z$. The total is $-999.1$ V/m.