PH2200 Practice Final Exam
Spring 2004
Instructions
1. Write your name and student identification number on the answer sheet.
2. This a two-hour 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 20 concept questions worth six points each and nine problems having a total of 30 parts.
The problem parts are equally weighted: each is worth six points. The total number of points on the exam is 300.
8. If you have any questions during the exam, please raise your hand and wait for assistance.
* The formula sheet is omitted from this practice exam.
PH2200 Practice Final Exam
Spring 2004
Concept Questions: Each question has a single correct answer and is worth six points.
1. The figure below shows five pairs of plates: plates A, B and D are charged insulating plates and C is an electrically
neutral conducting plate. The electrostatic forces between the plates are shown for three of the pairs. For the
remaining two pairs, do the plates repel or attract each other?
(A)
(B)
(C)
(D)
A
A
A
B
C
B
C
D
D
D
B and D repel; C and D repel
B and D repel; C and D attract
B and D attract: C and D repel
B and D attract: C and D attract
2. The figure below shows four situations in which charged particles are fixed in place on an x-axis. In which
situation is there a point on the x-axis to the left of the particles where an electron will be in equilibrium? Exclude
the point at infinity.
+q
-q
(A)
+q
-2q
+2q
(B)
-q
+2q
(C)
The following two questions refer to the figure to the right.
A spherical shell with a uniform positive surface charge
density is near a positive point charge.
+2q
(D)





3. What type of material is the spherical shell?

(A) Metal
(B) Insulator
(C) Need more information

Einside  ?



4. Is the electric field inside the sphere zero?
(A) Yes
(B) No
(C) Need more information
2



PH2200 Practice Final Exam
Spring 2004
5. One proton is accelerated from rest by a uniform electric field while a second proton is accelerated from rest by
a non-uniform electric field. The two protons move through the same electric potential difference. Is the final
speed of the proton in the uniform electric field greater than, equal to, or less than the final speed of the proton
in the non-uniform electric field?
(A)
(B)
(C)
(D)
Greater than
Equal to
Less than
Not enough information is given
The figure to the right applies to the next two questions. A capacitor C is
made of two parallel plates separated by a distance d. The dimensions of
the plates are very large when compared with d. This capacitor is
connected to a battery with emf E and a switch as shown. The switch is
initially closed.
E
+
-
A
C
B
6. With the switch closed, the electric potential of plate A is higher than the
electric potential of plate B.
(A) True
(B) False
7. Let E be the magnitude of the electric field between the plates when the switch is closed. At t  0 , the switch is
opened, and then the plates of the capacitor are pushed closer to a distance d '  12 d . The magnitude of the electric
field, E ' , between the plates after making these changes is
(A) E '  12 E
(B) E '  E
(C) E '  2 E
8. Two types of resistors are made of the same material. A type 1 resistor
has twice the diameter of a type 2 resistor but is half as long as the
type 2 resistor. Which of the configurations shown has the higher net
resistance?
(A) A
(B) B
(C) A and B have the same resistance.
A – Type 1
3
B – Type 2
PH2200 Practice Final Exam
Spring 2004
9. An ordinary resistive light bulb and a resistor R are in series with a
battery that provides an emf E . The circuit is first at room
temperature, and then the resistor R is immersed in liquid nitrogen so
that its temperature is significantly decreased. As a result of this
change,
(A)
(B)
(C)
(D)
(E)
the bulb glows more brightly because R increases.
the bulb glows more brightly because R decreases.
the bulb glows less brightly because R increases.
the bulb glows less brightly because R decreases.
there is no change in the brightness of the bulb.
E
R
The figure to the right applies to the next two questions. Three
particles having the same charge and the same speed, but differing
in mass, enter a region of uniform magnetic field directed into
the plane of the page.
10. Which particle has the largest mass?
(A)
(B)
(C)
(D)
particle A
particle B
particle C
Not enough information is given
A
B
12
Q
A, B, C
11. A uniform electric field is now applied in the region of the
magnetic field so that particles continue to move up toward the top
of the page without being deflected. What should be the direction
of this electric field?
(A)
(B)
(C)
(D)
(E)
right
left
up
down
into the page
12. A point charge +Q is placed at the end of the second-hand of a watch, as
shown in the figure. What is the direction of the magnetic field at the center
of the watch due to this moving charge?
(A) into the page
(B) out of the page
(C) depends on the position of the charge
9
3
6
4
C
PH2200 Practice Final Exam
Spring 2004
13. Recall that the magnetic field of a long, straight wire consists of circular field lines.
Does Ampere's Law hold for a square loop surrounding this wire?
(A) Yes
(B) No
(C) Not enough information is given
loop
14. There is a wire carrying current out of the paper as shown by a thick circle with a dot in the middle. Concentric
circles with arrows outside the wire represent the magnetic field lines. Which one of these diagrams best represents
the magnetic field lines?



(A)
(B)
(C)


(D)
(E)
15. A uniform magnetic field is perpendicular to the paper within the
enclosed region indicated by the dots. The four rectangular loops
of conducting wire are lying flat on the paper and are moving to
the right with the same, constant velocity. The resistance is the
same for each loop. At the instant shown in the figure, in which
loop is the induced current the largest?
(A)
(B)
(C)
(D)
(E)
A
B
C
D
The induced current is the same in all loops.
..............................
B
. . . . . . . . . . . . . . . . . . . . . . . .C
......
..............................
. . . . . . . . . . . . . . . . . . . . . . . . . . . .A. .
..............................
..............................
D
16. The energy stored in an inductor depends on the direction of the current passing through it.
(A) True
(B) False
(C) Not enough information is given
5
PH2200 Practice Final Exam
Spring 2004
17. Two ac generators produce sinusoidal voltages with the same amplitude but different frequencies. How do their
rms voltages compare?
(A)
(B)
(C)
(D)
The rms voltage of the higher frequency source is greater.
The rms voltage of the higher frequency source is less.
The rms voltages are equal.
Not enough information is given
18. A plane electromagnetic wave (for example, a radio wave) propagates in a vacuum. The electric field of this wave
is entirely in the plus and minus z directions in space as described in an xyz coordinate system. Select the incorrect
statement about this wave.
(A) The magnetic field of this wave must be entirely in the x-y plane.
(B) If the magnetic field of this wave is entirely in the plus and minus x directions, the electromagnetic wave
is propagating in either the plus or minus y direction.
(C) Assuming that the maximum electric field is unchanged, the energy density associated with the wave
increases when the frequency of the wave is increased.
(D) The magnitude of the magnetic field of the wave is a maximum when the magnitude of the electric field is
a maximum.
(E) The ratio of the maximum value of the electric field of this wave to the maximum value of the magnetic
field of the wave is a constant, and this constant has the same value for all plane electromagnetic waves in
a vacuum.
19. A beam consisting of red and blue light is incident from air onto a
slab of glass. The index of refraction of blue light is greater than
that for red. When the light emerges at the bottom,
(A) the red and the blue light emerge at the same point.
(B) the red light emerges at a larger value of x along the axis
than does the blue light.
(C) the blue light emerges at a larger value of x along the axis
than does the red light.
glass
x
20. The person in the figure to the right is 2 m tall. A mirror is located 20 m
away and is 0.5 m tall. The top of the mirror is at the same height
as the top of the person’s head. Assume for simplicity that the
person’s eyes are at the height of the top of his head. What part
of his body does the person see in the mirror?
(A)
(B)
(C)
(D)
(E)
20 m
.5 m
2m
top 0.25 m
top 0.5 m
top 1 m
top 1.5 m
entire 2 m
6
PH2200 Practice Final Exam
Spring 2004
Problems: Each part of each problem is worth six points.
1. Positronium consists of an electron with charge -e bound by the attractive Coulomb force to its antiparticle, the
positron with charge +e. As shown in the figure below, assume the distance between the electron and positron is d.
Report all answers in terms of e, d, a, and any necessary physical constants.
+e
-e
d
A
a
(a) What is the magnitude of the electric force exerted on the electron by the positron?
(A) ke e / d
(B) kee / d 2
(C) ke e2 / d 2
(D) ke e / 4 o d
(E) ke e2 / 4 o d 2
Point A in the figure above is a distance a from the electron on the line connecting the electron and positron.
(b) What is the magnitude of the electric field at point A?
(A) keed (d  2a) / a2 (d  a)2
(B) kee(d 2  2ad  2a2 ) / a2 (d  a)2
(C) keea(a  2d ) / a2 (d  a)2
(D) kee(a2  2ad  2d 2 ) / a2 (d  a)2
(E) kee(d 2  a2 ) / a2 d 2
(c) If the electric potential at infinity is taken to be zero, what is the electric potential at point A?
(A)
(B)
(C)
(D)
(E)
ke ed / a (d  a )
ke ed / a(d  a)
k e e( d  2 a ) / a ( d  a )
 k e e( d  2 a ) / a ( d  a )
 k e e( a  2 d ) / a ( d  a )
(d) What is the potential energy of positronium?
(A) ke e / d
(B)  ke e / d
(C) ke e2 / d
(D) ke e2 / d
(E) ke e2 / d 2
(F) ke e2 / d 2
7
PH2200 Practice Final Exam
Spring 2004
2. In addition to a magnetic field, the Earth also has an electric field. During days of fair weather (no thunderclouds),
the atmospheric electric field has a magnitude of 135 V/m at the Earth's surface, and it points toward the center of the
Earth. Treat the Earth as an isolated, uniformly charged conducting sphere of radius 6.37 106 m , and take the zero
of electric potential to be at infinity.
E = 135 V/m
(a) What is the net charge (sign and magnitude) on the Earth?
(A)
(B)
(C)
(D)
(E)
(F)
-0.0957 C
+0.0957 C
6.09 105 C
6.09 105 C
4.92 1025 C
4.92 1025 C
(b) What is the magnitude of the flux of the electric field through a sphere concentric with the Earth but having only
half its radius?
(A)
(B)
(C)
(D)
(E)
0
5.38 1014
4.30 1015
1.72 1016
6.88 1016
Vm
Vm
Vm
Vm
(c) What is the electric energy density near the surface of the Earth?
(A)
(B)
(C)
(D)
(E)
5.98 1010 J/m3
8.07 108 J/m3
6.77 106 J/m3
3.93 104 J/m3
9.11103 J/m3
(d) What is the magnitude of the electric potential of the surface of the Earth?
(A)
(B)
(C)
(D)
(E)
1.06 107
3.49 107
7.75 107
8.60 108
9.60 109
V
V
V
V
V
8
PH2200 Practice Final Exam
Spring 2004
3. The cable connecting the positive terminal of an automobile battery to the starter motor is 0.600 m long and
0.250 cm in radius. The resistance of the cable is 5.26 104  .
(a) What is the resistivity of this cable?
(A)
(B)
(C)
(D)
(E)
6.20 109   m.
1.72 108   m.
5.27 107   m.
6.89 106   m.
9.98 106   m.
(b) When the motor is stalled, the current in the cable may be as much as 600 A. What is the potential difference
between the ends of the cable under this condition?
(A)
(B)
(C)
(D)
(E)
0.316 V
0.547 V
4.57 V
11.7 V
12.0 V
(c) At what rate is heat dissipated in the cable under the condition of part (b), that is, what is the power?
(A)
(B)
(C)
(D)
(E)
0.316 W
4.82 W
23.6 W
112 W
189 W
9
PH2200 Practice Final Exam
Spring 2004
4. To protect service personnel against shock, large capacitors in the power supplies of electronic equipment are
usually connected in parallel with "bleeder resistors" whose job is to discharge ("bleed") the capacitors after the
equipment is turned off. Suppose a 2.00  104 F capacitor with an initial charge of 7.10 102 C is in parallel with
a 5.60 104  bleeder resistor.
2.00  104 F
5.60 104 
(a) What is the initial electric potential difference across the capacitor?
(A)
(B)
(C)
(D)
(E)
1.42 105 V
2.82 103 V
4.56 V
123 V
355 V
(b) How much charge is on the capacitor after a time corresponding to one time constant?
(A)
(B)
(C)
(D)
(E)
2.34 102 C
2.61102 C
2.75 102 C
2.83 102 C
2.97 102 C
(c) How much time will it take for the capacitor voltage to reach the safe value of 30.0 V?
(A)
(B)
(C)
(D)
(E)
8.85 s
11.2 s
19.2 s
27.7 s
35.0 s
10
PH2200 Practice Final Exam
Spring 2004
5. At the surface of a pulsar or neutron star the magnetic field may be as strong as 108 T. A proton with a speed of
2.20 106 m/s is on the surface of such a pulsar. Consult the figure below for the direction of the magnetic field and
the proton’s initial velocity. Assume that in the region of interest the magnetic field is uniform with a magnitude of
1.00 x 108 T.
z

B

v
y
x (out of page)
(a) What is the direction of the magnetic force on the proton?
(A)
(B)
(C)
(D)
(E)
(F)
+x
-x
+y
-y
+z
-z
(b) What is the magnitude of the magnetic force on the proton?
(A)
(B)
(C)
(D)
(E)
3.52 106 N
3.52 105 N
3.52 104 N
3.52 103 N
3.52 102 N
(c) What is the shape of the path or trajectory of the proton?
(A)
(B)
(C)
(D)
(E)
straight line
ellipse
circle
parabola
hyperbola
(d) What is the cyclotron frequency of the proton in the given field?
(A)
(B)
(C)
(D)
(E)
9.58 1015 rad/s
2.20 1016 rad/s
1.36 1017 rad/s
7.45 1018 rad/s
1.76 1019 rad/s
11
PH2200 Practice Final Exam
Spring 2004
6. A long cylindrical conductor having a radius of 5.00 102 m carries a current of 10.0 A uniformly distributed over
its cross-section. A long thin wire lies parallel to the cylinder, a distance of 0.500 m from its center, and carries a
current of 2.00 A in the same direction as that in the cylinder. In the figure below, both currents are out of the page.
10.0 A (out)
2.00 A (out)
0.500 m
(a) What is the magnitude of the magnetic field produced by the cylindrical conductor a distance of 0.500 m from its
center?
(A)
(B)
(C)
(D)
(E)
0.500 106 T
1.00 106 T
2.00 106 T
4.00 106 T
8.00 106 T
(b) What is the magnitude of the magnetic force per unit length experienced by the long thin wire?
(A)
(B)
(C)
(D)
(E)
8.00 106 N/m
8.25 106 N/m
8.50 106 N/m
8.75 106 N/m
9.00 106 N/m
(c) Suppose the long thin wire is now removed. What is the magnitude of the magnetic field at a point inside the
cylindrical conductor, a distance of 2.50 102 m from its center?
(A)
(B)
(C)
(D)
(E)
1.00 105 T
2.00 105 T
4.00 105 T
8.00 105 T
1.60 104 T
12
PH2200 Practice Final Exam
Spring 2004
7. A car alternator consists of a 250-turn coil 5.00 cm in radius in a magnetic field of 0.100 T. The alternator is turning
with a constant angular speed of 105 rad/s. This implies that angle  shown in the figure below is given by
  105t where t is time expressed in seconds.

B


(a) Find the induced emf in the coil as a function of time.
(A)
(B)
(C)
(D)
(E)
 8.25 10
 1.96 10
2
1
V  sin105t
V  sin105t
 20.6 V  sin105t
 120 V  sin105t
 170 V  sin105t
(b) If the angular speed of the coil were doubled, by what factor would the maximum induced emf increase?
(A)
(B)
(C)
(D)
(E)
2
4
8
16
There would be no change.
(c) What is the orientation of the coil with respect to the magnetic field when the maximum induced emf
occurs, that is, for what angle  is the induced emf maximum?
(A)
(B)
(C)
(D)
(E)
0
22.5
45.0
67.6
90.0
13
PH2200 Practice Final Exam
Spring 2004
8. A laser beam of wavelength 632 nm and cross-sectional diameter d = 2.00 mm is incident at an angle of  = 40.0 on
a glass plate having a thickness of t = 2.00 cm. The index of refraction of the glass is 1.55.
d

t
glass
(a) At what angle is the laser beam refracted as it passes from air into the glass?
(A)
(B)
(C)
(D)
(E)
17.4
21.3
24.5
35.6
85.0
(b) What is the wavelength of the laser beam inside the glass?
(A)
(B)
(C)
(D)
(E)
408 nm
556 nm
632 nm
825 nm
980 nm
(c) What is the cross-sectional diameter of the laser beam after it has passed through the glass plate?
(A)
(B)
(C)
(D)
(E)
1.02 mm
1.24 mm
1.69 mm
1.80 mm
2.00 mm
14
PH2200 Practice Final Exam
Spring 2004
9. When a woman's hand mirror is held 20.0 cm from her face, a virtual image is formed 30.0 cm from the mirror. The
mirror is spherical.
(a) What is the radius of curvature of the mirror?
(A)
(B)
(C)
(D)
(E)
-12.0 cm
+12.0 cm
+24.0 cm
+60.0 cm
+120 cm
(b) What is the magnification provided by the mirror for the given object and image distances?
(A)
(B)
(C)
(D)
(E)
-3.00
-1.50
+1.00
+1.50
+3.00
(c) If the mirror were flat, how far from the woman's face would the image be formed if the mirror were held
20.0 cm from her face?
(A)
(B)
(C)
(D)
(E)
20.0 cm
40.0 cm
80.0 cm
120 cm
The image would be formed at the same position as the woman's face.
15
PH2200 Practice Final Exam
Spring 2004
Name: ____________________________________
Recitation Section: 8:00 Zhou _____
12:00 Yap _____
Concept Questions
ID#
___________________________________________
9:00 Zhou _____
10:00 Teboh _____
1:00 Roy _____
2:00 Roy _____
11:00 Teboh _____
Problems
D
1. _______
A
11. _______
C
1. (a) _______
B
2. _______
A
12. _______
A
(b) _______
B
3. _______
A
13. _______
B
4. _______
B
3. (a) _______
D
6. (a) _______
E
9.(a) _______
A
(b) _______
A
(b) _______
D
(b) _______
B
(c) _______
E
(c) _______
B
(c) _______
B
(c) _______
B
14. _______
D
(d) _______
E
4. (a) _______
C
7. (a) _______
B
5. _______
C
15. _______
C
2. (a) _______
B
(b) _______
A
(b) _______
A
6. _______
B
16. _______
A
(b) _______
D
(c) _______
E
(c) _______
B
7. _______
C
17. _______
B
(c) _______
A
5. (a) _______
C
8. (a) _______
B
8. _______
C
18. _______
D
(d) _______
B
(b) _______
A
(b) _______
B
9. _______
B
19. _______
C
(c) _______
E
(c) _______
C
10. _______
C
20. _______
A
(d) _______
10
_______
10
_______
8
_______
10
_______
Column Subtotals
50  6  300
Exam Score ___________
16
9
_______
3
_______