Download PH2200 Practice Exam III Ssummer 2004

PH2200 Practice Exam III
Summer 2004
Instructions
1. Write your name and student identification number on the answer sheet.
2. This a ninety minute exam.
3. Please cover your answer sheet at all times.
4. This is a closed book exam. You may use the PH2200 formula sheet that is included with the exam.
5. Equations may not be stored in calculators, nor may calculators be exchanged.
6. Record your answers in the form A, B, C, etc, on the answer sheet.
7. This exam consists of 10 concept questions worth five points each and six problems having a total of 20 parts.
The problem parts are equally weighted: each is worth five points. The total number of points on the exam is 150.
8. If you have any questions during the exam, please raise your hand and wait for assistance.
PH2200 Practice Exam III
Summer 2004
Concept Questions: Each question has a single correct answer and is worth five points.
The following information pertains to the first three questions.
A chamber is filled with a uniform magnetic field B directed into the plane
of the paper. Two particles are produced simultaneously at point P in the
chamber. Parts of their tracks through the chamber are shown in the figure.
The tracks lie in the plane of the paper. Particle X has a smaller mass than
particle Y, m X  mY , but the magnitudes of the charges of the particles


X
Y
are identical, qX  qY . Neglect the electric and magnetic forces
the particles exert on each other - assume the only force acting on each
particle is due to the uniform magnetic field B .
1. Which of the following is a true statement about the speeds of the particles?

P


(A) vX  vY
(B) vX  vY
(C) vX  vY
2. Which particle is first to return to point P?
(A)
(B)
(C)
(D)
Particle X
Particle Y
The particles return to point P simultaneously.
The particles never return to point P.
3. The circling charged particles X and Y can be thought of as loops of current. These currents produce their own
magnetic fields. At the center of the circle described by the path of particle X, the direction of the magnetic
field due to the motion of particle X alone is
(A)
(B)
(C)
(D)
into the plane of the paper.
out of the plane of the paper.
to the right in the figure above.
to the left in the figure above.
a
4. The figure to the right shows several closed paths surrounding a
single current-carrying wire. Rank the magnitudes of  B  ds
for the closed paths in the figure, from greatest to least.
(A)
(B)
(C)
(D)
(E)
a, b, c, d (Path a has the greatest value and path d the least.)
a, c, d, b
a = c = d, b
a = b = c, d
a=b= c=d
2
b
c
d
PH2200 Practice Exam III
Summer 2004
The following information pertains to the next three questions.
Two identical, ideal solenoids are arranged as shown below in cross-sectional view. The current in each solenoid is the
same.


The two solenoids are now joined to make one solenoid, as shown in the figure below. The current in this solenoid is the
same as the current in each of the original solenoids.

5. The magnetic field in this solenoid, compared with the magnetic field in each of the original solenoids, is
(A)
(B)
(C)
(D)
(E)
one-fourth as big.
half as big.
twice as big.
four times as big.
the same.
6. If the current in this solenoid is reversed so that it flows in the opposite direction, the magnetic field in the solenoid
will
(A) reverse direction.
(B) stay the same.
7. The self inductance of this solenoid, in comparison with the self inductance of one of the two original solenoids, is
(A)
(B)
(C)
(D)
(E)
one-fourth as big.
half as big.
twice as big.
four times as big.
the same.
3
PH2200 Practice Exam III
Summer 2004
The following information pertains to the next two questions.
A uniform magnetic field permeates a region of space as shown
in the figure to the right. The magnetic field is directed into the
plane of the paper, and the magnetic field vanishes outside the
rectangular region. Identical wire loops are moving with an
identical speed v, but with velocity oriented in different directions,
as indicated in the figure.
8. For which of the wire loops is the magnitude of the induced
emf greatest at the instant shown in the figure?
(A)
(B)
(C)
(D)
A









D



C




v


v


v


A
B
C
D


B
9. Which of the wire loops experiences a magnetic force towards the top of the page?
(A)
(B)
(C)
(D)
A
B
C
D
10. A switch is present in a circuit that has a large inductance. A spark is more likely to be produced at the switch
when the switch is being
(A) closed.
(B) opened.
(C) closed or opened, it doesn't matter which.
4
v
PH2200 Practice Exam III
Summer 2004
Problems: Each part of each problem is worth five points.
1. The magnetic field at the surface of a neutron star has a magnitude of 3.00  107 T . An electron moves with speed
2.50 106 m/s through this magnetic field with its velocity always perpendicular to the magnetic field. Assume
the magnetic field is uniform in the region of space in which the electron moves, and also assume the only force
acting on the electron is the magnetic force.
(1-1) What is the magnitude of the magnetic force acting on the electron?
(A)
(B)
(C)
(D)
(E)
1.05 105 N
1.20 105 N
1.35 105 N
1.50 105 N
1.65 105 N
(1-2) What is the radius of the circular orbit of the electron?
(A)
(B)
(C)
(D)
(E)
1.19 1013 m
2.38  1013 m
3.611013 m
4.74  1013 m
5.90  1013 m
(1-3) If the speed of the electron were doubled, the angular speed (or cyclotron frequency) of the electron would be
(A)
(B)
(C)
(D)
(E)
quartered.
halved.
the same.
doubled.
quadrupled.
(1-4) What is the magnetic energy density near the surface of the neutron star?
(A)
(B)
(C)
(D)
(E)
5.52 104 J/m3
9.73 108 J/m3
4.49 1012 J/m3
1.67 1016 J/m3
3.58 1020 J/m3
(1-5) At the surface of the neutron star, what is the flux of the magnetic field,
the shape of a cube having sides of length 1.00 m?
(A)
(B)
(C)
(D)
(E)
0
3.00 107 T  m2
6.00 107 T  m2
9.00 107 T  m2
12.00 107 T  m2
5
 B  dA , through a closed surface in
PH2200 Practice Exam III
Summer 2004
2. Shown in the figure to the right is a cross-sectional view of three
long straight wires. The two lower wires are 0.0400 m apart and
are attached to a table. The upper wire "floats" when positioned
so as to form an isosceles right triangle with the lower wires.
The three wires carry equal currents of 16.0 A; the current carried
by the lower wires is out of the page, and the direction of the current
carried by the upper wire is to be determined. Gravity acts downward
(toward the bottom of the page) in the figure, and assume g  9.80 m/s2 .
90
0.0283 m
0.0283 m
0.0400 m
(2-1) What is the magnitude of the magnetic force per unit length that the lower wire on the left exerts on the lower
wire on the right?
(A)
(B)
(C)
(D)
(E)
1.28 103 N/m
1.79 103 N/m
2.13 103 N/m
2.49 103 N/m
2.97 103 N/m
(2-2) What is the direction of the current in the upper wire so that it "floats"?
(A) into the page
(B) out of the page
(2-3) What is the mass per unit length of the upper wire?
(A) 1.05 104 kg/m
(B) 1.90 104 kg/m
(C) 2.61104 kg/m
(D) 3.35 104 kg/m
(E) 4.52 104 kg/m
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PH2200 Practice Exam III
Summer 2004
3. Current I passes through a long, straight, hollow pipe having inner radius a and outer radius b. Assume the current is
uniformly distributed over the cross-section of the pipe. Let r denote the distance from the symmetry axis of the
pipe. Express all answers in terms of I, a, b, r, and any necessary physical constants.
a
b
cross-sectional view:
current I is uniformly distributed
over the gray region
(3-1) What is the magnitude of the magnetic field for r  b , that is, at a point outside the pipe?
(A)
(B)
(C)
(D)
(E)
0
o I / 2 r
 o I / 2 b
 o I / 2 a
o I / 2 (r  b)
(3-2) What is the magnitude of the magnetic field for r  a , that is, at a point inside the hollow portion of the pipe?
(A)
(B)
(C)
(D)
(E)
0
o I / 2 r
 o I / 2 b
 o I / 2 a
o I / 2 (r  b)
(3-3) What is the magnitude of the magnetic field for a  r  b , that is, at a point between the inner and outer walls
through which current flows?
(A)
(B)
(C)
(D)
0
o I / 2 r
o I / 2 (r  a)
o I / 2 (b  r )
(E)
o  r 2  a 2 

I
2 r  b2  a 2 
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PH2200 Practice Exam III
Summer 2004
4. A rectangular loop of area 0.160 m2 is placed in a region where the
magnetic field is perpendicular to the plane of the loop. In the figure
to the right, the magnetic field is directed out of the plane. For times
t  0 , the magnetic field has the constant value of 0.350 T and for times
t  0 , the magnetic field varies in time according to the expression
B(t )  0.350e0.5t where t is expressed in seconds and B(t ) is expressed
in tesla.
(4-1) What is the magnitude of the induced emf in the loop at time t  2.00 s ?
(A)
(B)
(C)
(D)
(E)
1.03 102 V
1.33 102 V
1.81102 V
2.19 102 V
2.43 102 V
(4-2) What is the direction of the induced current in the loop for times t  0 ?
(A) clockwise
(B) counter-clockwise
(4-3) What is the maximum magnitude of the induced emf in the loop?
(A)
(B)
(C)
(D)
(E)
2.60 102 V
2.80 102 V
3.00 102 V
3.20 102 V
3.40 102 V
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PH2200 Practice Exam III
Summer 2004
5. The figure below shows the top view of a bar of length 0.250 m that can slide without friction on two horizontal rails
that are connected with a strip of metal at the left-hand end. The rails and connecting strip have negligible resistance,
and the resistance of the bar is 18.0  . A constant magnetic field of magnitude 0.350 T points out of the page. The
bar moves with a constant velocity in the direction shown, and the current in the bar is 2.67 103 A .
v
(5-1) What is the magnitude of the applied force required to move the bar to the left with a constant velocity when
the current in the bar is 2.67 103 A ?
(A)
(B)
(C)
(D)
(E)
1.15 104 N
1.61104 N
2.02 104 N
2.34 104 N
2.98 104 N
(5-2) What is the direction of the current in the bar?
(A) up - towards the top of the page
(B) down - towards the bottom of the page
(5-3) What is the speed of the bar?
(A)
(B)
(C)
(D)
(E)
0.336 m/s
0.387 m/s
0.444 m/s
0.505 m/s
0.549 m/s
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PH2200 Practice Exam III
Summer 2004
6. Consider the RL circuit shown to the right. Assume the switch is
closed at time t  0.
8.00 Ω
(6-1) Calculate the ratio of the potential difference across the resistor
to that across the inductor when the current in the circuit is 2.00 A.
4.00 H
36.0 V
(A)
(B)
(C)
(D)
(E)
0.400
0.600
0.800
1.20
1.50
(6-2) How long after the switch is closed does it take the current in the circuit to reach the value of 2.00 A?
(A)
(B)
(C)
(D)
(E)
0.185 s
0.294 s
0.347 s
0.429 s
0.500 s
(6-3) What is the rate of increase of the current when the current is 4.00 A?
(A)
(B)
(C)
(D)
(E)
1.00 A/s
1.25 A/s
1.50 A/s
1.75 A/s
2.00 A/s
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PH2200 Practice Exam III
KEY
Name: ____________________________________
Summer 2004
ID#
___________________________________________
Concept Questions
Problems
C
1. _______
B
1-1 _______
E
3-3 _______
A
2. _______
D
1-2 _______
A
4-1 _______
B
3. _______
C
1-3 _______
B
4-2 _______
C
4. _______
E
1-4 _______
B
4-3 _______
E
5. _______
A
1-5 _______
D
5-1 _______
A
6. _______
A
2-1 _______
A
5-2 _______
C
7. _______
A
2-2 _______
E
5-3 _______
D
8. _______
C
2-3 _______
C
6-1 _______
A
9. _______
B
3-1 _______
B
6-2 _______
B
10. _______
A
3-2 _______
A
6-3 _______
10
Subtotal 1 _______
10
Subtotal 2 _______
10
Subtotal 3 _______
30
Exam Score _______
11