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    • 6.2: Parallel Plate Waveguide- Introduction
      https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_II_(Ellingson)/06%3A_Waveguides/6.02%3A_Parallel_Plate_Waveguide-_Introduction
      \[\begin{align} \frac{\partial^2}{\partial x^2}\widetilde{E}_x + \frac{\partial^2}{\partial y^2}\widetilde{E}_x + \frac{\partial^2}{\partial z^2}\widetilde{E}_x &= - \beta^2 \widetilde{E}_x \label{m01...\[\begin{align} \frac{\partial^2}{\partial x^2}\widetilde{E}_x + \frac{\partial^2}{\partial y^2}\widetilde{E}_x + \frac{\partial^2}{\partial z^2}\widetilde{E}_x &= - \beta^2 \widetilde{E}_x \label{m0173_eEfx} \\ \frac{\partial^2}{\partial x^2}\widetilde{E}_y + \frac{\partial^2}{\partial y^2}\widetilde{E}_y + \frac{\partial^2}{\partial z^2}\widetilde{E}_y &= - \beta^2 \widetilde{E}_y \label{m0173_eEfy} \\ \frac{\partial^2}{\partial x^2}\widetilde{E}_z + \frac{\partial^2}{\partial y^2}\widetilde{…

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