PHY2061
R. D. Field
Exam 2 Solutions
Page 1 of 7
March 27, 2003
PHY 2061 Exam 2 Solutions
Problem 1 (20 points):
Circle true or false for following (2 points each).
(a) (True or False)
The speed of light in a vacuum is independent of the velocity of the source of
the light, but depends on the velocity of the observer.
(b) (True or False)
The magnetic force cannot change the speed of a charged particle.
(c) (True or False)
The magnetic field produced by a moving charged particle is perpendicular to
the velocity of the particle.
(d) (True or False)
The magnetic force on a charged particle is perpendicular to the velocity of
the particle.
(e) (True or False)
The mass and charge of a particle depends on its speed.
(f) (True or False)
There can be no electric or magnetic force on an electrically neutral wire.
(g) (True or False)
Magnetic field lines are always perpendicular to electric field lines.
(h) (True or False)
The vector function
y
y
x
x
y
x
B
ˆ
ˆ
)
,
(
+
=
r
represents a possible magnetic field
with magnitude given by
2
2
)
,
(
y
x
y
x
B
+
=
.
(i) (True or False)
The total
net
magnetic flux through any closed surface is always zero.
(j) (True or False)
Electric and magnetic fields are massless, but contain energy.
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PHY2061
R. D. Field
Exam 2 Solutions
Page 2 of 7
March 27, 2003
Problem 2 (relativity, 20 points):
Protons leave a particle accelerator with a speed of
v = 0.75c
to enter and travel through an
evacuated tube that is at rest in the laboratory and is
9 m
long, as measured by an observer in the
laboratory, and then finally reach a detector.
(Note: c = 3.0x10
8
m/s)
Part A (5 points):
How long does it take for a proton to travel from one end of the tube to the other (
in
nanoseconds
) according to an observer in the laboratory frame?
Answer:
40
Solution:
In any frame, distance equals speed times time and hence
ns
s
s
m
m
v
d
t
40
10
4
)
/
10
3
(
75
.
0
9
8
8
=
×
=
×
=
=
−
.
Part B (6 points):
How long does it take for a proton to travel from one end of the tube to the other (
in
nanoseconds
) according to an observer traveling with a proton?
Answer:
26.5
Solution:
The proton frame is the proper time and hence
ns
ns
t
t
5
.
26
512
.
1
40
=
=
=
=
′
γ
τ
,
where I used
512
.
1
1
/
1
2
=
−
=
β
γ
.
Part C (5 points):
What is the tube’s length (
in m
) as measured by an observer traveling with a proton?
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 Physics, Light, Magnetic Field, R. D. Field

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