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Question 4.5.6: In an air-filled rectangular waveguide, the vector electric ...

In an air-filled rectangular waveguide, the vector electric field is given by

\vec{E}=\cos (2 \pi y) \exp \left[-j\left(\frac{40 \pi}{3}\right) z+j \omega t\right] \hat{i}_{x} V / m

Find vector magnetic field and the phase velocity of the wave inside the waveguide.

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\begin{aligned}\vec{E} &=\cos (2 x y) \exp \left[-j\left(\frac{40 \pi}{3}\right) 2+j \omega t\right]_{ V / m }^{\hat{i}_{x}} \\\vec{\beta} &=\frac{40 \pi}{3} \\\bar{\eta} &=\frac{\omega \mu}{\bar{\beta}}=\frac{\omega \times 4 \pi \times 10^{-7}}{40 \pi / 3}=3 \omega \times 10^{-8} \\H_{y} &=\frac{E_{x}}{\eta}=\frac{1}{3 \omega \times 10^{-8}}\left\{\cos (2 x y) e\left\{-J\left(\frac{40 \pi}{3}\right) z+j \omega t\right\}\right.\\\vec{H} &=H_{x} j_{y}\end{aligned}

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