[UPSC CSE 2022] Electromagnetic Theory (Q314, 20M)

In a partially conducting medium, \varepsilon_r = 18.5, \mu_r = 800 and \sigma = 1\ \mathrm{S\,m^{-1}}. Find \alpha, \beta, \eta and the velocity u, for a frequency of 10^9\ \mathrm{Hz}. Determine \vec{H}(z,t). Given, \vec{E}(z,t) = 50e^{-\alpha z}\cos(\omega t - \beta a_z)a_y\ \mathrm{V\,m^{-1}}.