A monochromatic plane wave in vacuum (x > 0) with E_z > 0 and Ex < 0 strikes a perfect conductor (x < 0) at an angle of incidence θ.
(a) Show that, in steady state, a non-uniform TM wave occupies the vacuum space above the conductor.
(b) Calculate the time-averaged Poynting vector everywhere.

(c) Calculate the charge density and current density induced on the surface of the conductor. Do they satisfy a continuity equation?