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πωȺI
()
(
)
2
b
=−
−−
0
e
H
kρ
n
ν
0
2
παβ
)
()
()
()
Jka
πωȺI
()
(
2
v
c
=
0
e
H
kρ
n
ν
0
2
παβ
−−
2
H a
YkaJ kρ
ν
(11.102)
(
)
(
)
(
)
(
)
πωȺI
dj
παβ
−
JkaY ρ
ν
v
0
v
ν
0
=
0
e
n
()
()
2
−−
2
H a
ν
1
()
()
()
2
a
=
b J
ka
+
c H
ka
=
0
(
)
n
n
v
n
ν
Jka
v
1
Note that the expressions of
b
n
and
c
n
will yield zero tangential electric field
at
ρ
=
a
when substituted in Eq.(11.69).
Case IV:
(no cap); The expressions of the coefficients in this case
may be obtained by setting
a
→
0
k
1
=
k
, or by taking the limit as
a
approaches
zero. Thus,
()() ()()
()
()()
()
()()
′
′
kJ
ka J
ka
−
kJ
ka J
ka
πωȺI
()
(
)
2
v
v
v
v
c
=
0
e
H
kρ
=
0
n
ν
0
2
παβ
−−
2
′
2
kH
ka J
ka
−
kH
ka J
′
ka
ν
v
ν
v
πωȺI
()
(
)
2
b
=−
−−
0
e
H
kρ
n
ν
0
2
1
παβ
()
()
()
()
(
2
a
=
b J
ka
+
c H
ka
=
b
n
n
v
n
ν
n
Jka
v
(11.103)
)
(
)
()
(
)
()
()()
′
′
2
2
kJ
k a
J
ka H
kρ
−
H aJ ρ
+
K
v
1
v
ν
0
ν
v
0
(
)
()
()() ()
()
(
)
′
2
2
kJ
ka
H
ka J
kρ
−
JkaH
kρ
πωȺI
1
v
1
ν
v
0
v
ν
0
d
=
0
e
n
2
παβ
−−
()
()()
()
()()
′
2
2
′
kH
ka J
k a
−
k H
ka J
k a
ν
v
1
1
ν
v
1
πωȺI
J ρ
παβ
(
)
=−
−−
a
0
e
v
0
2
Case V:
and (semi-infinite PEC plane); In this case, the
coefficients in Eq. (11.103) become valid with the exception that the values of
reduce to . Once, the electric field component in the different
regions is computed, the corresponding magnetic field component
0→α
==
β
0
v
n
⁄
2
E
z
H
ϕ
H
ρ
can be
computed using Eq. (11.71) and the magnetic field component
may be
computed as
11
z
∂
E
H
=−
(11.104)
ρ
j
ωµρ φ
∂
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