Phys 3327 Fall 2010
HW 8
Due Wednesday 11/3/10 in lecture
Homework 8
Wave Guides
Ex 8.1: Electromagnetic wave incident on conductor
An electromagnetic wave of frequency
ω
, moving in a medium with dielectric constant
±
and
magnetic permeability
μ
= 1, is incident normally on the surface of a metal. The metal has
±nite but large conductivity
σ
m
and dielectric constant
±
m
.
We choose coordinate axes such that the surface of the metal is the
xy
plane and the metal
±lls the halfspace
z>
0, see ±gure. The electric ±eld of the incident wave is
E
0
(
r
,t
)=
Re
E
0
0
e
i
(
kz

ωt
)
e
x
, with
z<
0. The frequency
ω
satis±es the inequality
ω
±
σ
m
, and you may
give all your answers below to leading order in the small ratio
ω/σ
m
. In the questions below,
indicate directions using a righthanded coordinate system with unit vectors
e
x
,
e
y
and
e
x
.
a) What are the electric and magnetic ±elds
E
1
(
r
) and
B
1
(
r
) of the re²ected wave?
Write your answer in terms of the amplitude
E
0
, wavenumber
k
, and frequency
ω
of
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 '10
 Cohen
 Magnetism, Energy, Work, Frequency, Wavelength, Heald

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