The electric field vector of a wave is given as $$$\vec E = {E_0}{\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y} \right)}}{\mkern 1mu} {{8{{\vec a}_x} + 6{{\vec a}_y} + 5{{\vec a}_z}} \over {\sqrt {125} }}\,\,V/m$$$

Its frequency is 10 GHz.

(i) Investigate if this wave is a plane wave.
(ii) Determine its propagation constant, and
(iii) Calculate the phase velocity in $$y$$-direction.

A uniform plane wave is normally incident from air on an infinitely thick magnetic material with relative permeability 100 and relative permittivity 4 (sec in Fig.). The wave has an electric field of 1 V/meter (rms). Find the average Poynting vector inside the material.

A uniform plane wave having parallel polarization is obliquely incident on an air - dielectric interface as shown in Fig. If the wave has an electric field $$E = 10\,\,V/m$$, find
(i) The angle of incidence $${\theta _i}$$ for which there is no reflection of the wave.
(ii) The surface charge density at the interface.

A wave traveling in the $$+Z$$-direction, is the resultant of two linearly polarized components, $${E_x}\,\,\, = \,\,\,\,\,\,3$$ $$\,\,\,\,\cos \omega t$$ and $$\,{E_y}\,\,\,\, = \,\,\,2\,\cos \,\left( {\omega t + {{45}^ \circ }} \right)$$

Determine
(1) The axial ratio
(2) The angle between the major axis of the polarization ellipse and the $$+x$$-axis.