PHY2061
R. D. Field
Department of Physics
chp38_12.doc
University of Florida
Electromagnetic Plane Waves (1)
We have the following two
differential
equations
for
E
y
(x,t)
and
B
z
(x,t)
:
∂
B
t
E
x
z
y
=−
(1)
and
∂µ
ε
E
t
B
x
y
z
1
00
(2)
Taking the time derivative of
(2)
and using
(1)
gives
2
2
2
2
11
1
E
tt
B
xx
B
t
E
x
y
zz
y
=−
=
which implies
µε
2
2
2
2
0
E
x
E
t
yy
−=
.
Thus
E
y
(x,t)
satisfies the wave equation with speed
v
=
1
/
εµ
and has a
solution in the form of traveling waves as follows:
E
y
(x,t) = E
0
sin(kx
ω
t)
,
where
E
0
is the
amplitude of the electric field oscillations
and where the
wave has a
unique speed
vc
k
fm
s
== = =
=
×
ω
λ
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.
 Spring '08
 FRY
 Physics

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