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GATE 2019 EC – Question 47

Electromagnetics · Waveguides and Optical Fibers · 2 marks · Multiple choice

The dispersion equation of a waveguide, which relates the wavenumber $k$ to the frequency $\omega$, is

$$k(\omega)=(1/c)\sqrt{\omega^2-\omega_0^2}$$

where the speed of light $c=3\times10^8$ m/s, and $\omega_0$ is a constant. If the group velocity is $2\times10^8$ m/s, then the phase velocity is

  1. $1.5\times10^8$ m/s
  2. $2\times10^8$ m/s
  3. $3\times10^8$ m/s
  4. $4.5\times10^8$ m/s

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Correct answer: (D) $4.5\times10^8$ m/s

Explanation

From the dispersion relation, $v_gv_p=c^2$. So $v_p=\frac{(3\times10^8)^2}{2\times10^8}=4.5\times10^8$ m/s.