Consider a parallel plate waveguide with plate separation d as shown in figure. The electric and magnetic fields for the TEM mode are given by
E_{x}=E_{0} e^{-j k z+j \omega t}, H_{y}=\frac{E_{0}}{\eta} e^{-j k z+j \omega t}Where k = T < one.
(a) Determine the surface charge densities \rho_{s} on the plates at x = 0 and x = d.
(b) Determine the surface current densities \vec{J}_{s} on the same plates.
(c) Prove that \rho_{s} \text { and } \vec{J}_{s} satisfy the current continuity condition.