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GATE 2015 EC – Question 63

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

The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression

$$H_z(x, y, z, t) = 0.1\cos(25\pi x)\cos(30.3\pi y)\cos(12\pi \times 10^9 t - \beta z) \text{ (A/m)}$$

The cross-sectional dimensions of the waveguide are given as $a = 0.08$ m and $b = 0.033$ m. The mode of propagation inside the waveguide is

  1. $TM_{12}$
  2. $TM_{21}$
  3. $TE_{21}$
  4. $TE_{12}$

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Correct answer: (C) $TE_{21}$

Explanation

A longitudinal magnetic field $H_z$ exists only in TE modes. In a rectangular guide $H_z \propto \cos\frac{m\pi x}{a}\cos\frac{n\pi y}{b}$. Here $\frac{m\pi}{a} = 25\pi$ gives $m = 25 \times 0.08 = 2$, and $\frac{n\pi}{b} = 30.3\pi$ gives $n = 30.3 \times 0.033 = 1$. So the mode is $TE_{21}$.