lim (kl9356) – Homework 20 – Weathers – (22202)
1
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printout
should
have
16
questions.
Multiplechoice questions may continue on
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before answering.
001
10.0 points
The magnetic field amplitude of an electro
magnetic wave is 9
.
1
×
10

6
T.
The speed of light is 2
.
99792
×
10
8
m
/
s
.
Calculate the amplitude of the electric field
if the wave is traveling in free space.
Correct answer: 2728
.
11 N
/
C.
Explanation:
Let :
c
= 2
.
99792
×
10
8
m
/
s and
B
= 9
.
1
×
10

6
T
.
According to Maxwell’s equations for an elec
tromagnetic wave in vacuum the relation be
tween the amplitude of the magnetic field and
the amplitude of the electric field must be
E
=
c B
= (2
.
99792
×
10
8
m
/
s) (9
.
1
×
10

6
T)
=
2728
.
11 N
/
C
.
The same relation applies even when the ve
locity of light in the medium is not
c
, in
general,
E
=
v B ,
where
v
is the velocity of light in that medium.
002
10.0 points
Gammaray bursters are objects in the uni
verse that emit pulses of gamma rays with
high energies. The frequency of the most en
ergetic bursts has been measured at around
3
.
0
×
10
21
Hz.
The speed of light is 3
×
10
8
m
/
s.
What is the wavelength of these gamma
rays?
Correct answer: 1
×
10

13
m.
Explanation:
Let :
f
= 3
.
0
×
10
21
Hz
and
c
= 3
.
00
×
10
8
m
/
s
.
The speed is
c
=
fλ
λ
=
c
f
=
3
×
10
8
m
/
s
3
×
10
21
Hz
=
1
×
10

13
m
.
003
(part 1 of 4) 10.0 points
A cylindrical filament has radius 2
.
96 mm. Its
resistance is 3
.
39 Ω and its length is 0
.
45 m.
The filament carries a uniform, steady current
of 0
.
829 A.
The permeability of free space is 4
π
×
10

7
N
/
A
2
.
Find the electric field inside the filament.
Correct answer: 6
.
24513 N
/
C.
Explanation:
Let :
ℓ
= 0
.
45 m
,
R
= 3
.
39 Ω
,
and
I
= 0
.
829 A
.
The electric field inside the filament has to
point in the direction of the current; the field
causes the current to flow. To find the field,
first consider the voltage drop across the ends
of the wire,
V
=
I R
.
The electric field inside the filament is
E
=
V
ℓ
=
I R
ℓ
=
(3
.
39 Ω) (0
.
829 A)
0
.
45 m
=
6
.
24513 N
/
C
.
004
(part 2 of 4) 10.0 points
Find
B
at the surface of the filament.
Correct answer: 5
.
60135
×
10

5
T.
Explanation:
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lim (kl9356) – Homework 20 – Weathers – (22202)
2
Let :
r
= 2
.
96 mm = 0
.
00296 m
,
and
μ
0
= 4
π
×
10

7
N
/
A
2
.
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 Spring '00
 Littler
 Magnetism, Energy, Work, Light, lim, Correct Answer

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