PROBLEM SET 5
ECE 312 Autumn Quarter 2010
Assigned:
October 27th
Due:
November 3rd in class
Instructor: Joel Johnson
Problem 1
Two plane waves in free space are given by
E
˜
1
x
ˆ
j
2
y
ˆ
–
()
e
jkz
=
(V/m), and
E
˜
2
2
j
+
y
ˆ
e
=
(V/m).
(a) What is the time average Poynting vector associated with
E
˜
1
alone?
(b) What is the time average Poynting vector associated with
E
˜
2
alone?
(c) What is the time average Poynting vector associated with the field
E
˜
E
˜
1
E
˜
2
+
=
Is this equal to the sum of your part (a) and (b) answers?
(d) Now let the field
E
˜
2
be set to zero. How many Watts of time average power radiated by
the field
E
˜
1
are intercepted by a circular spot of radius 20 cm in the xy plane?
Problem 2
A 1900 MHz cellular phone user is talking inside of a building.
Assume that the phone gener
ates an electromagnetic wave
E
˜
i
x
ˆ
e
jk
1
z
–
=
(V/m) that impinges from free space (medium 1)
inside the building onto a wall of the buidling (medium 2,
ε
2
5.4
ε
0
=
,
μ
2
μ
0
=
, and
σ
2
0.04
=
S/m) at normal incidence. Consider the wall to be very thick, and to exist for
z
0
>
.
(a) Find the complex reflection coefficient.
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 Fall '08
 Johnson,J
 Electromagnet, Joel Johnson, average Poynting vector, time average Poynting

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