**Question **# 3) An electromagnetic wave propagating in the z-direction can be described as a time-harmonic combination of E and H fields. In a low-loss dielectric, the characteristic impedance can be written as iou/y, where w is the angular frequency of the electromagnetic wave, u is the magnetic permeability of the medium and y is the propagation constant. a) Show that this results in the electric and magnetic fieldsbeing out of phase, and determine an expression for thephase angle between the fields in terms of the attenuationand phase constants, a and B. b) Explain briefly the resulting spatial variation in the electricfield component of this electromagnetic wave as a function of distance in the direction of propagation, with explicit reference to any dependence upon the angular frequency of the wave c) A wave propagating through one dielectric medium isincident upon a second dielectric medium with a differentrelative permittivity. Briefly describe the processes thatcan take place depending upon the angle of incidence andthe difference in permittivities. Your answer should alsoinclude relevant information about directions of the electricand magnetic components of the electromagnetic wavebefore and after it arrives at the interface between the twomedia. [9 marks]d) An electromagnetic wave with angular frequency1.6 x 106 radians/s is incident upon a piece of sheet of copper foil used to shield critical medical equipment from electromagnetic interference. By quantitative consideration of the skin effect, determine whether or not a copper foil of thickness 0.25 mm is sufficient to exclude at least 99.9% of such electromagnetic interference.