Download CH34 CALC EMwave

Electromagnetic Waves
An electromagnetic wave consists of oscillating electric and magnetic fields traveling at the
speed of light. The wave carries both energy and momentum. The intensity and direction of
propagation of the wave can be described by the Poynting vector,
1
S 
0
EB .
(1)
The magnitude of S gives the intensity of the wave,
S 
dU / dt
A
(W/m2),
(2)
and the direction of S is the direction of propagation of the wave. For a monochromatic plane
wave
E  E m sin( k x  t )
B  B m sin( k x  t )
(3)
E and B are perpendicular to each other and perpendicular to the direction of propagation. The
magnitudes are related by E = cB. From (1) and (3)

S
.
1

E m Bm sin
0
(4)
Since <sin2(kx-t)>ave = ½, the time average of S is
S ave 
1
2 0
Em Bm .
(5)
Using E = cB, we can also write
S ave
(6)
2
2
Em
cBm


2 0c
2 0
.
2
(k x
An electromagnetic wave carries momentum, given by
p = U/c,
(7)
where U is the energy of the wave.
If the wave strikes a surface and is completely absorbed, then it imparts a force to the surface
given by
F

dp
dt
,

dU / dt
c
(8)
where A is the area of the surface. It therefore exerts a pressure on the surface given by
pressure 
F
A

S
c
.
(9)
If the wave is completely reflected by the surface, then the force and pressure are doubled
(why?).
Problem:
The intensity of the sunlight incident on the earth’s upper atmosphere is 1340 W/m2.
1. What are the peak values of the electric and magnetic fields associated with the sunlight?
2. If the sunlight were completely absorbed by the earth, what would be the net radiation
force?
3. Calculate the gravitation pull of the sun on earth and compare with the radiation force.
4. What is the intensity of sunlight incident on the upper atmosphere of Mars?
Msun = 2 * 1030 kg
Mearth = 6 * 1024 kg
Rearth = 6 * 106 m
Dearth-sun = 1.5 * 1011 m
Rmars = 3 * 106 m
Dmars-sun = 2.3 * 1011 m
G = 6.7 * 10-11Nm2/kg2
c = 3 * 108 m/s
o = 4 * 10-7 Tm/A
