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ECE 329
Homework 9
Due: Fri, July 15, 2011, 5PM
1. For each of the four plane TEM waves (in free space) described by
a)
E
1
=2cos(
ωt

βz
)ˆ
x
V/m
b)
E
2
=
E
o
cos(
ωt

βz
)ˆ
x

E
o
sin(
ωt

βz
)ˆ
y
V/m
c)
H
3
=cos(
ωt
+
βz
+
π
3
)ˆ
x
+sin(
ωt
+
βz

π
6
)ˆ
y
A/m
d)
H
4
=cos(
ωt

βx
)ˆ
z
+sin(
ωt

βx
)ˆ
y
A/m:
i. Determine the corresponding
E
and
H
±eld phasors.
ii. Determine the timeaveraged Poynting vector
S
,tha
ti
s
±
S
²≡±
E
×
H
²
,byu
t
i
l
i
z
ingth
e
phasor cross product
˜
E
×
˜
H
*
appropriately.
iii. Determine the timeaveraged power that crosses a 1 m
2
area in the
xy
plane from

z
to
+
z
by using the results of (ii).
2. We have on
x
=0
plane a pulse of sheet current
J
s
(
t
)=ˆ
y
2
t
rect
(
t
τ
)
A/m, where
τ
=2
μ
s. Regions
adjacent to the current sheet are vacuum.
a) Determine and plot
E
y
(
x,t
)
and
H
z
(
x,t
)
vs
t
for
x
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This note was uploaded on 11/06/2011 for the course ECE 329 taught by Professor Kim during the Summer '08 term at University of Illinois, Urbana Champaign.
 Summer '08
 Kim

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