Δ
x
=
c
Δ
t
y
x
z
x
E
B
B
B
A
FIGURE 22–11
Electromagnetic
wave carrying energy through area
A.
E
and
B
from the Sun.
Radiation from the Sun reaches
the Earth (above the atmosphere) with an intensity of about
Assume that this is a single EM wave, and calculate the maximum
values of
E
and
B
.
APPROACH
We solve Eq. 22
–
8
for
in terms of
and use
SOLUTION
From Eq. 22
–
2,
so
NOTE
Although
B
has a small numerical value compared to
E
(because of the
way the different units for
E
and
B
are defined),
B
contributes the same energy
to the wave as
E
does,
as we saw earlier.
B
0
=
E
0
c
=
1.01
*
10
3
V m
3.00
*
10
8
m s
=
3.37
*
10
–
6
T.
B
=
E c
,
=
1.01
*
10
3
V m.
E
0
=
C
2
I
0
c
=
C
2
A
1350
J s m
2
B
A
8.85
*
10
–
12
C
2
N m
2
BA
3.00
*
10
8
m s
B
I
=
1350
J s m
2
.
I
E
0
A
I
=
1
2
0
cE
0
2
B
1350
J s m
2
.
1350
W m
2
=
EXAMPLE 22
;
4
C A U T I O N
E and B ha
v
e
v
ery different
v
alues (due to ho
w
units are defined),
but E and B contribute
equal
energy

SECTION 22
–
6
635
22–6
Momentum Transfer and
Radiation Pressure
If electromagnetic waves carry energy, then we would expect them to also carry
linear momentum. When an electromagnetic wave encounters the surface of an
object, a force will be exerted on the surface as a result of the momentum trans-
fer
just as when a moving object strikes a surface. The force per
unit area exerted by the waves is called
radiation pressure
, and its existence was
predicted by Maxwell. He showed that if a beam of EM radiation (light, for
example) is completely absorbed by an object, then the momentum transferred is
c
d
(22
;
9a)
where
is the energy absorbed by the object in a time
and
c
is the speed of
light. If, instead, the radiation is fully reflected (suppose the object is a mirror), then
the momentum transferred is twice as great, just as when a ball bounces elastically
off a surface:
c
d
(22
;
9b)
If a surface absorbs some of the energy, and reflects some of it, then
where
a
has a value between 1 and 2.
Using Newton’s second law we can calculate the force and the pressure
exerted by EM radiation on an object. The force
F
is given by
The radiation pressure
P
(assuming full absorption) is given by (see Eq. 22
–
9a)
We discussed in Section 22
–
5 that the average intensity
is defined as energy per
unit time per unit area:
Hence the radiation pressure is
(22
;
10a)
If the light is fully reflected, the radiation pressure is twice as great (Eq. 22
–
9b):
(22
;
10b)
c
fully
reflected
d
P
=
2
I
c
.
c
fully
absorbed
d
P
=
I
c
.
I
=
¢
U
A
¢
t
.
I
P
=
F
A
=
1
A
¢
p
¢
t
=
1
Ac
¢
U
¢
t
.
F
=
¢
p
¢
t
.
¢
p
=
a
¢
U
c
,
radiation
fully
reflected
¢
p
=
2
¢
U
c
.
¢
t
¢
U
radiation
fully
absorbed
¢
p
=
¢
U
c
,
(F
= ¢
p
¢
t
)
Solar pressure.
Radiation from the Sun that
reaches the Earth’s surface (after passing through the atmosphere) transports
energy at a rate of about
Estimate the pressure and force exerted
by the Sun on your outstretched hand.

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- Spring '14
- Dr.Zhang