The electric field in a rectangular waveguide of inner dimensions $a\times b$ is given by $$ \mathbf{E}=\left(\frac{\omega\mu}{h^2}\right)\left(\frac{\pi}{a}\right)H_0\sin\left(\frac{2\pi x}{a}\right)\sin(\omega t-\beta z)\,\hat{y} $$ where $H_0$ is a constant, and $a$ and $b$ are

Question

The electric field in a rectangular waveguide of inner dimensions $a\times b$ is given by $$ \mathbf{E}=\left(\frac{\omega\mu}{h^2}\right)\left(\frac{\pi}{a}\right)H_0\sin\left(\frac{2\pi x}{a}\right)\sin(\omega t-\beta z)\,\hat{y} $$ 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

Accepted Answer

TE20. In rectangular waveguides, TM modes have a longitudinal electric field, while TE modes have no longitudinal electric field. The dependence $\sin(2\pi x/a)$ corresponds to $m=2$ and there is no variation in $y$, so $n=0$. Therefore the mode is TE$_{20}$.

Solution

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