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Notes 10 Fall 2004.doc
Example:
The electrical constitutive parameters of moist earth at a frequency of 1 MHz are
m
S
1
10
−
=
σ
,
1
r
and
,
4
r
=
µ
=
ε′
.
Assuming that the electric field magnitude of a uniform plane wave at the
interface (on the side of the earth) is
m
V
2
10
3
−
×
, find:
a. The distance through which the wave must travel before the magnitude of the electric field
reduces to
m
V
2
10
104
.
1
−
×
.
Answer:
α
−
=
α
−
=
−
×
−
×
α
−
−
×
=
−
×
α
−
=
368
.
0
ln
z
z
e
2
10
3
2
10
104
.
1
z
e
2
10
3
2
10
104
.
1
z
e
0
x
E
E
G
We see that we must find the attenuation constant,
.
α
Find the loss tangent:
1
6
.
449
10
85
.
8
4
10
2
10
12
6
1
>>
=
×
∗
∗
∗
π
=
ε′
ε ′
′
=
ε′
ω
σ
−
−
, therefore this is
considered a highly conductive medium and we can approximate
σµ
π
=
β
=
α
f
.
1
m
628
.
0
7
10
4
1
.
0
6
10
−
=
−
×
π
∗
∗
∗
π
=
α
m
59
.
1
628
.
0
368
.
0
ln
z
=
−
=
b. The wavelength inside the earth.
Answer:
m
10
628
.
0
2
2
=
π
=
β
π
=
λ
(vs. 300m in free space)
c. The phase velocity inside the earth.
Answer:
s
m
6
10
10
628
.
0
6
10
2
2
p
v
×
=
∗
π
∗
=
β
π
=
β
ω
=
f
1
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View Full DocumentNotes 10 Fall 2004.doc
d. The intrinsic impedance inside the earth.
Answer:
ε ′
′
−
ε′
µ
=
ε
µ
=
η
j
0
Can we neglect one of the terms in the denominator?
Recall the loss tangent:
6
.
449
=
ε′
ε ′
′
.
So we
can neglect
ε
and
′
Ω
°
∠
=
×
π
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 Fall '10
 Czarnecki
 Frequency

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