Munoz (gm7794) – HW09 – TSOI – (92515)
1
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001
(part 1 of 3) 10.0 points
A heliumneon laser intended for classroom
produces 4
.
1 mW of light power.
At
a
point
where
the
cross
section
of
the beam has an area of 2
.
1 mm
2
,
what
is the maximum value of the electric field
E
?
The
permeability
of
free
space
is
1
.
25664
×
10

6
N
/
A
2
and the speed of light is
2
.
99792
×
10
8
m
/
s.
Correct answer: 1212
.
87 N
/
C.
Explanation:
Let :
P
= 4
.
1 mW = 0
.
0041 W
,
A
= 2
.
1 mm
2
= 2
.
1
×
10

6
m
2
,
μ
0
= 1
.
25664
×
10

6
N
/
A
2
,
and
c
= 2
.
99792
×
10
8
m
/
s
.
The intensity
I
of the beam is given by
I
=
P
A
.
LASER
L
face B
face A
This is related to the electric and magnetic
field peak amplitudes by
I
=
E
max
B
max
2
μ
0
=
E
2
max
2
μ
0
c
,
so
E
2
max
= 2
c μ
0
I
= 2
μ
0
c
P
A
and
E
max
=
2
μ
0
c
P
A
=
2 (1
.
25664
×
10

6
N
/
A
2
)
×
2
.
99792
×
10
8
m
/
s
×
0
.
0041 W
2
.
1
×
10

6
m
2
=
1212
.
87 N
/
C
.
002
(part 2 of 3) 10.0 points
What is the electromagnetic energy in a beam
of length 1
.
9 m?
Correct answer: 2
.
59846
×
10

11
J.
Explanation:
The amount of energy that has passed
through
face A
of a column is
P t
, after a
time
t
. For
t <
L
c
, the energy passing through
face A
has not passed through
face B
. Hence,
in this time interval all the energy that has
passed through
face A
is within the column,
so the energy stored in the column is
U
=
P L
c
=
(0
.
0041 W) (1
.
9 m)
2
.
99792
×
10
8
m
/
s
=
2
.
59846
×
10

11
J
.
Alternate Solution:
The amount of energy
U
in a column of light with volume
V
is
U
=
u V
where
u
is the energy per unit volume.
For an electromagnetic wave
u
=
1
2
0
E
2
max
,
so the total energy is
U
=
u V
=
1
2
0
E
2
max
A L
=
1
2
(7
.
15207
×
10
22
C
2
/
N
·
m
2
)
×
(1212
.
87 N
/
C)
2
(2
.
1 mm
2
) (1
.
9 m)
=
2
.
59846
×
10

11
J
.
003
(part 3 of 3) 10.0 points
What is the corresponding momentum of the
beam?
Correct answer: 8
.
66754
×
10

20
J
·
s
/
m.
Explanation:
Let
U
be the energy. The momentum is
p
=
U
c
=
2
.
59846
×
10

11
J
2
.
99792
×
10
8
m
/
s
=
8
.
66754
×
10

20
J
·
s
/
m
.
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Munoz (gm7794) – HW09 – TSOI – (92515)
2
004
(part 1 of 2) 10.0 points
Lasers have been used to suspend spherical
glass beads in the Earth’s gravitational field.
A bead has a mass of 10
μ
g and a density
of 0
.
4 g
/
cm
3
.
The laser beam is larger than
the glass bead with a radius 1230
μ
m and
fully impinges on the bead. Assume complete
absorption.
The acceleration of gravity is 9
.
8 m
/
s
2
.
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 Summer '08
 morrison
 Physics, Light, Snell's Law, Correct Answer, Total internal reflection, Munoz

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