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GATE 2023 EC – Question 20

Electromagnetics · Plane Waves and Properties · 1 mark · Multiple choice

Consider a narrow band signal, propagating in a lossless dielectric medium ($\epsilon_r=4,\ \mu_r=1$), with phase velocity $v_p$ and group velocity $v_g$. Which of the following statement is true? ($c$ is the velocity of light in vacuum.)

  1. $v_p>c,\ v_g>c$
  2. $v_p<c,\ v_g>c$
  3. $v_p>c,\ v_g<c$
  4. $v_p<c,\ v_g<c$

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Correct answer: (D) $v_p<c,\ v_g<c$

Explanation

In a lossless non-dispersive medium $v_p=v_g=\dfrac{c}{\sqrt{\epsilon_r\mu_r}}=\dfrac c2<c$. So both velocities are less than $c$.