EAD 234B: E&M
Homework #5
Due Thursday, May 13, 2010
(1)
Consider the long wire shown below.
(a)
Find the potentials and the fields produced by a current I(t) = I
0
Θ
(t) that turns on abruptly at t
= 0 in a neutral, filamentary wire coincident with the entire zaxis.
(b)
Show that the electric and magnetic fields approach their expected values as t
→
∞
.
(2)
Consider a dipole
d
G
, rotating in a plane (say, the xy plane) with a constant angular velocity
ω
.
(a) Find the angular distribution of the radiation.
(b) Find the timeaveraged total radiation.
(c) Determine the polarization of the radiation wave.
(3)
Consider the current density located at the origin
()
(
)
()()
ˆˆ
jt
Jx
j
y
x
y
y
e
ω
αβ
δ
δ
δ
where
α
and
β
are real constants and
1
j
=
−
.
a) Find the farfield Poynting vector.
b) Find the value of
β
and
α
that makes the radiation pattern as nearly isotropic as possible.
(4) Consider the case of a symmetrical, thin, centerfed antenna of length L as shown in the
figure below.
(a) Derive expressions valid in the farfield for
E and H
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 Spring '10
 NCL
 electric dipole moment, Axial multipole moments, quadrupole, Monopole, Multipole expansion

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