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Physics 10
Spring 2008
Class Notes
Week 9
Walter Gekelman
There is an mathematical equation for the electric and magnetic field of light which is
called the wave equation. It was derived by the famous Scottish physicist James Clerk
Maxwell.
We wont write down the equations because they are differential equations
(calculus) but we can write down the solutions and develop a picture for the wave.
The
solution for the electric field for a wve travelling in the x direction is.
(1)
E
=
E
0
sin
kx
!
"
t
( )
=
2
#
f
(angular frequency)
k=
2
$
(wavenumber)
It turns out that the solution for the magnetic field is exactly the same and as Maxwell
proved that
(2)
E
B
=
c
Another point about Fourier series is since they are sines and cosines all the functions,
which they describe, must be periodic.
Suppose you wished to describe a pulse over
some spatial interval by a Fourier series.
The infinite series gives you a series of pulses
separated by some distance, which is the periodicity of the series.
So you must realize
that your answer is good in a certain interval and then repeats as in the figure 1 below.
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The argument of the cosine must be an angle in radians so that kx must be in radians.
If
we define
k
=
2
!
"
then kx=2
x
.
Also
t
=
2
ft
=
2
T
t
T is the period of the wave
.
Now the distance is expressed in wavelengths. T , the period of the wave or the time it
takes the wave, which moves at velocity v to travel one wavelength. The solution is now
(2)
E
=
E
0
sin 2
x
#
t
T
$
%
’
(
)
*
+
,

.
/
.
The field of the wave is naturally expressed in wavelengths and its period.
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This note was uploaded on 06/29/2008 for the course PHYS 10 taught by Professor Gruner during the Spring '08 term at UCLA.
 Spring '08
 GRUNER
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