A plane wave with $\overrightarrow{\mathrm{E}}=10 e^{j((\omega t-\beta z)} \overrightarrow{a_{y}}$ is incident normally on a thick plane conductor lying in the $x-y$ plane. Its conductivity is $6 \times 10^{6} \mathrm{~S} / \mathrm{m}$ and surface impedance is $5 \times 10^{-4} \angle 45^{\circ} \; \Omega$. Determine the propagation constant and the skin depth in the conductor.
