EE 151
Caltech
Electromagnetic Engineering
Spring ‘05
Homework 7
Due Thursday, May 26
th
in class
1. (
Retarded Vector Potential
) Problem from
Engineering Electromagnetics
by Hayt and Buck.
In a region where
µ
R
=
ε
R = 1
and
σ
= 0, the retarded potentials are given by V =
x
(
z-ct
) V and
A
=
x
(
z/c-t
)
a
z
Wb/m, where
c
= 1/sqrt(
µ
0
ε
0
).
(a). Show that
t
V
∂
∂
−
=
⋅
∇
µε
A
(b). Find
B
,
H
,
E
and
D
.
(c). Show that these results satisfy Maxwell’s equations if
J
and
ρ
v
are zero.
2. (
Dipole
Antenna
) Problem from
Engineering Electromagnetics
by Hayt and Buck.
A dipole antenna in free space has a linear current distribution. If the length d is 0.02
λ
, what value of I
0
is
required to:
(a). provide a radiation field amplitude of 100mV/m at a distance of 1mi, at
θ
= 90
0
;
(b). radiate a total power of 1 W?
3. (
Antenna
) A square loop antenna, in which a time-harmonic current Ie
j
ω
t
is circling, is located in the x-z
plane as shown in Figure below. Consider a point P (0,0,z) in the far field of the loop antenna.

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