ECE 329
Homework 8
Due: Tue, Mar 11, 2008, 5PM
1. Two perfect dielectric materials are separated by a boundary coinciding with
x
=0
plane. The
dielectric located at
x<
0
(denoted by subscript 1) is characterized by a permittivity of
3
±
o
, while
that located at
x>
0
(denoted by subscript 2) is characterized by a permittivity of
5
±
o
. The bondary
contains no surface charge. If the electric Feld on the
+
x
side of the boundary is given by
E
1
=
E
o
(ˆ
x
+ 3ˆ
y
)
V/m and
E
2
denotes the Feld on

x
side, Fnd the following: (a)
E
2
x
/E
1
x
, (b)
E
2
y
/E
1
y
,
(c)
E
2
z
, (d)

E
2

/

E
1

, and (e)

D
2

/

D
1

.
2. Assume that region
z<
0
is occupied by an ideal dielectric with
±
=
±
1
and
μ
=
μ
1
while we have
another ideal dielectric in the region
z>
0
having the parameters
±
=
±
2
and
μ
=
μ
2
. Show that
plane wave Felds with phasors
˜
E
1
=ˆ
xE
o
e

jβ
1
z
in
z<
0
and
˜
E
2
=ˆ
xE
o
e

jβ
2
z
in
z>
0
, and the
corresponding magnetic Feld phasors
˜
H
1
and
˜
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This note was uploaded on 04/14/2009 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 FRANKE

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