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GATE ECE 2007 | Question-66

The $\vec{E}$ field in a rectangular waveguide of inner dimensions $a \times b$ is given by
\[ \vec{E}=\frac{\omega \mu}{h^{2}}\left(\frac{\pi}{a}\right) H_{0} \sin \left(\frac{2 \pi x}{a}\right) \sin (\omega t-\beta z) \hat{y}\]
where $H_{0}$ is a constant, and $a$ and $b$ are the dimensions along the $x$-axis and the $y$-axis respectively. The mode of propagation in the waveguide is

  1. $\mathrm{TE}_{20}$
  2. $\mathrm{TM}_{11}$
  3. $\mathrm{TM}_{20}$
  4. $\text{TE}_{10}$
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