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GATE 2022 EC – Question 52

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

A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of $10^{-4}$ cm, with air as the dielectric. Assume the speed of light in air to be $3\times10^8$ m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/are ________.

  1. $6\times10^{15}$ Hz
  2. $0.5\times10^{12}$ Hz
  3. $8\times10^{14}$ Hz
  4. $1\times10^{13}$ Hz

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Correct answer: (A) $6\times10^{15}$ Hz; (B) $0.5\times10^{12}$ Hz; (C) $8\times10^{14}$ Hz; (D) $1\times10^{13}$ Hz

Explanation

For parallel plates of separation $d=10^{-6}$ m, the TM$_m$ mode has cutoff $f_c=\frac{mc}{2d}=m\times1.5\times10^{14}$ Hz. The TM$_0$ mode has $m=0$, so it has no cutoff and propagates at every frequency. All four frequencies can therefore propagate.