8.1) Aplane wave in air with an electric field amplitude of 10v/m is incident normlly upon the surface of a lossless, nonmagnetic medium with e_r=25.  Find
a. The reflection and transmission coefficient
b. the standing-wave ratio in the air medium
the average power densities of the incident, reflected and transmited waves.
answer:  |E1|_max = 51.3 V/m ; L _max = 1.5 m

8.9) The 3 regions shown contain perfect dielectrics.  For a wave in medium 1, incident normally upon the boundary at z=-d , what combination of e_r2, and d produces no reflection?  Express your answers in terms of e_r1, e_r3 and the oscillation frequency of the wave, f .

answer:   d= c/[4f (e_r1 e_r3)¼]
(e_r2)²=e_r1 e_r3
 
 

8.13) A plane wave of unknown frequency is normally incident in air upon the surface of a perfect conductor.
Using an electric-filed meter, it was determined that the total electric field in the air meduim is
always zero when measured at a distance of 2.5 m from the conductor surface.  Moreover, no such nulls
were observed at distances closer to the conductor.  What is the frequency of the incident wave?
answer:    f= 60 MHz
 

8.15)  A 5-MHz plane wave with electric field amplitude of 20 V/m is normally incident in air onto the plane surface of a semi-infinicte  conducting material with e_r=4, µ=1 and s=100 S/m. Determine the average power dissipated (lost ) per unit cross-section ara in a 2-mm penetration of the conducting medium.
answer:    P'= 4.04 x 10^-4 W/m²

8.27) A plane wave in air with

Hⁱ= y .02 e ^-j(8x+6z)  V/m

is incident upon the planar surface of a dielectric material with e_r=9,occupying the half-space z>0.  Determine
a. the polarization of the incident wave
b. the angle of incidence
c. the time-domain expresssions for the reflected electric and magnetic fiels.
answer: a) parallel incidence, b)53 degrees
 
 

8.29) A parallel-polarized plane wave is incident from air onto a dielectric medium with e_r=9 at the Brewster angle.  What is the refraction angle?
answer: q_t= 18.44^o