PHY2061
R. D. Field
Exam 2 Solutions
Page 1 of 9
November 13, 2003
PHY 2061 Exam 2 Solutions
Problem 1 (10 points):
Circle true or false for following (1 point 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 direction of a charged particle.
(c) (True or False)
The magnetic field produced by a 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 of a charged particle depends on its speed, but the ratio of its
electric charge to its mass is independent of the particles speed.
(f) (True or False)
There can be no electric or magnetic force on an electrically neutral wire.
(g) (True or False)
There are two ways to produce an electric field (charged particles or
magnetic fields that changes with time), but only one way to produce a magnetic field (moving
charges).
(h) (True or False) The vector function
y
y
x
x
y
x
B
ˆ
ˆ
)
,
(
+
=
r
represents a possible magnetic field in
a vacuum 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)
Light has no mass and no momentum but it has energy.
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PHY2061
R. D. Field
Exam 2 Solutions
Page 2 of 9
November 13, 2003
Problem 2 (relativity, 18 points):
y
x
z
Neutral Wire
O
V
+ + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + +
                              
                              
Neutral Wire
V
y'
x'
z'
O'
V
+ + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + +
                              
                              
V
In the lab frame (
Oframe
) there are two identical parallel
neutral
wires consisting of a line of
positive charges moving to the right with speed V = 0.8c and a line of negative charges at rest as
shown in the figure.
The
O'frame
is moving the right at speed V = 0.8c relative to the Oframe.
In the O'frame the positive charges are at rest and the negative charges are moving to the left at
speed V = 0.8c.
The rest density of the positive charges is
0.75
µ
C/m
.
Part A (3 points):
What is the current carried by one of the wires in the
lab frame
(
in A
)?
Answer:
300
Solution:
The current in the
lab frame
is given by
A
s
m
m
C
c
V
V
I
300
)
/
10
3
)(
/
10
75
.
0
)(
333
.
1
(
8
6
0
0
=
×
×
=
=
=
=
−
+
+
+
βγλ
γλ
λ
,
where I used
667
.
1
1
/
1
2
=
−
=
β
γ
and
333
.
1
=
βγ
. Note that the wires are neutral in the lab
frame which implies that
0
0
0
=
−
=
−
=
−
+
−
+
λ
γλ
λ
λ
λ
,
and hence
+
−
=
0
0
γλ
λ
,
where
λ
0
+
and
λ
0

are the rest densities of positives and negatives, respectively.
Part B (3 points):
Which of the following statements is true in the
lab frame
? (
circle all correct statements
)
(a)
There is an electric force attracting the two wires.
(b)
There is an electric force repelling the two wires.
(c)
There is a magnetic force attracting the two wires.
(d)
There is a magnetic force repelling the two wires.
(e)
There are no forces on the wires.
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 Physics, Light, Magnetic Field, Electric charge

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