Transcript Slide 1

Today’s agenda:
Electromagnetic Waves.
Energy Carried by Electromagnetic Waves.
Momentum and Radiation Pressure of an
Electromagnetic Wave.
Momentum and Radiation Pressure
EM waves carry linear momentum as well as energy.
The momentum density carried by an electromagnetic wave is
dp
dV
=
S
c
2
This equation is not on your
equation sheet, but you have
permission to use it for tomorrow’s
homework (if needed) (10.28)
where dp is the momentum carried in the volume dV.
Today’s lecture is brought
to you by the letter P.
When the momentum carried by an electromagnetic wave is
absorbed at a surface, pressure is exerted on that surface.
If we assume that EM radiation is incident on an object for a
time t and that the radiation is entirely absorbed by the
object, then the object gains energy U in time t.
Maxwell showed that the momentum
change of the object is then:
p =
U
c
incident
(to ta l a bso rptio n )
The direction of the momentum change of the object is in the
direction of the incident radiation.
If instead of being totally absorbed the radiation is totally
reflected by the object, and the reflection is along the incident
path, then the magnitude of the momentum change of the
object is twice that for total absorption.
incident
reflected
p =
2U
c
(to tal reflectio n alo n g in ciden t p ath )
The direction of the momentum change of the object is again
in the direction of the incident radiation.
Radiation Pressure
The radiation pressure on the object is the force per unit area:
P=
From Newton’s
2nd
F
A
Law (F = dp/dt) we have: P =
For total absorption,  p =
F
A
=
1 dp
A dt
U
c
incident
So
1 dp
1 d U
P=
=

A dt
A dt  c
 dU

S
 1
d
t

=
=
 c A  c


(Equations on this slide involve magnitudes of vector quantities.)
This is the instantaneous radiation pressure in the case of total
absorption:
P(t) =
S (t)
c
For the average radiation pressure, replace S by <S>=Savg=I:
Prad =
S average
c
=
I
c
Electromagnetic waves also carry momentum through space
with a momentum density of Saverage/c2=I/c2. This is not on your
equation sheet but you have special permission to use it in
tomorrow’s homework, if necessary.
Today’s lecture is brought
to you by the letter P.
Prad =
I
c
(to ta l a bso rptio n )
incident
absorbed
Using the arguments above it can also be shown that:
Prad =
2I
c
(to ta l re fle ctio n )
incident
reflected
If an electromagnetic wave does not strike a surface, it still
carries momentum away from its emitter, and exerts Prad=I/c
on the emitter.
Example: a satellite orbiting the earth has solar energy
collection panels with a total area of 4.0 m2. If the sun’s
radiation is incident perpendicular to the panels and is
completely absorbed find the average solar power absorbed
and the average force associated with the radiation pressure.
The intensity (I or Saverage) of sunlight prior to passing through
the earth’s atmosphere is 1.4 kW/m2.

3
Pow er = IA = 1.4  10 W
m
2

 4.0 m
2
 = 5.6  10 W = 5.6 kW
3
Assuming total absorption of the radiation:
Prad =
S average
c

I
= =
3
1.4  10 W
c

F = Prad A = 4.7  10
-6
 3  10
N
m
2

8
m
m
s
2

 4.0 m
2
 = 4.7  10
-6
Pa
 = 1.9  10 N
-5
Caution! The letter P
(or p) has been used
in this lecture for
power, pressure, and
momentum!
That’s because today’s lecture is
brought to you by the letter P.
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New starting equations from this lecture:
S=
E m ax
B m ax
k=
2

=
E
B
1
0
2
S average =
EB
=c=
1
,  = 2 f , f =
p =
U
c
or
2U
c
k
2 0c
uB = uE =
0 0

1 E m ax
=c
u =
1
2
1
2
2
=
1 cB m ax
2
2
 0E =
0
1B
2 0
2
2
 0 E m ax =
Pra d =
I
c
or
2
1 B m ax
2 0
2I
c
There are even more on your starting equation sheet; they are derived from the above!