Page 466 - Engineering Electromagnetics, 8th Edition

448 ENGINEERING ELECTROMAGNETICS

CHAPTER 12 PROBLEMS
10
12.1 A uniform plane wave in air, E + = E x10 cos(10 t − βz) V/m, is normally
+
x1
incident on a copper surface at z = 0. What percentage of the incident
power density is transmitted into the copper?
12.2 The plane z = 0 defines the boundary between two dielectrics. For z < 0,
r1 = 9, r1 = 0, and µ 1 = µ 0 .For z > 0, r2 = 3, r2 = 0, and µ 2 = µ 0 .

Let E + = 10 cos(ωt − 15z) V/m and find (a) ω;(b) S ;(c) S ;
+
−
x1
1
1
(d) S .
+
2
12.3 A uniform plane wave in region 1 is normally incident on the planar
3

boundary separating regions 1 and 2. If = = 0, while r1 = µ and

2
1
r1
3

r2 = µ , find the ratio / if 20% of the energy in the incident wave is
r2
r2
r1
reflected at the boundary. There are two possible answers.
12.4 A10 MHz uniform plane wave having an initial average power density of
2
5 W/m is normally incident from free space onto the surface of a lossy

material in which / = 0.05, r2 = 5, and µ 2 = µ 0 . Calculate the

2
2
distance into the lossy medium at which the transmitted wave power density
2
is down by 10 dB from the initial 5 W/m .
12.5 The region z < 0is characterized by = µ r = 1 and = 0. The total E

r
r
field here is given as the sum of two uniform plane waves, E s =
150 e − j10z a x + (50
20 ) e j10z a x V/m. (a) What is the operating frequency?
◦
(b) Specify the intrinsic impedance of the region z > 0 that would provide
the appropriate reflected wave. (c)At what value of z, −10 cm < z < 0, is
the total electric field intensity a maximum amplitude?
12.6 In the beam-steering prism of Example 12.8, suppose the antireflective
coatings are removed, leaving bare glass-to-air interfaces. Calcluate the
ratio of the prism output power to the input power, assuming a single transit.
12.7 The semi-infinite regions z < 0 and z > 1m are free space. For
0 < z < 1m, = 4, µ r = 1, and = 0. A uniform plane wave with

r
r
8
ω = 4 × 10 rad/s is traveling in the a z direction toward the interface at
z = 0. (a) Find the standing wave ratio in each of the three regions. (b) Find
the location of the maximum |E| for z < 0 that is nearest to z = 0.
12.8 Awave starts at point a, propagates1m through a lossy dielectric rated at
0.1 dB/cm, reflects at normal incidence at a boundary at which
= 0.3 + j0.4, and then returns to point a. Calculate the ratio of the final
power to the incident power after this round trip, and specify the overall loss
in decibels.
12.9 Region 1, z < 0, and region 2, z > 0, are both perfect dielectrics (µ = µ 0 ,
= 0). A uniform plane wave traveling in the a z direction has a radian

frequency of 3 × 10 10 rad/s. Its wavelengths in the two regions are λ 1 =
5cmand λ 2 = 3 cm. What percentage of the energy incident on the