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    • https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_II_(Ellingson)/06%3A_Waveguides/6.05%3A_Parallel_Plate_Waveguide-_TM_Case%2C_Electric_Field
      \[\begin{align} \widetilde{E}_x &= \frac{k_z}{\omega\epsilon}~e^{-jk_z z} \left[ A e^{-jk_x x} + B e^{+jk_x x} \right] \nonumber \\ &= \frac{B k_z}{\omega\epsilon}~e^{-jk_z z} \left[ e^{-jk_x x} + e^{...\[\begin{align} \widetilde{E}_x &= \frac{k_z}{\omega\epsilon}~e^{-jk_z z} \left[ A e^{-jk_x x} + B e^{+jk_x x} \right] \nonumber \\ &= \frac{B k_z}{\omega\epsilon}~e^{-jk_z z} \left[ e^{-jk_x x} + e^{+jk_x x} \right] \nonumber \\ &= \frac{2B k_z}{\omega\epsilon}~e^{-jk_z z} \cos k_x x\end{align} \nonumber \]

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