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Unformatted text preview: Advanced Placement
Program AP® Physics C: Electricity
and Magnetism
Practice Exam The questions contained in this AP® Physics C: Electricity and Magnetism Practice Exam are written
to the content specifications of AP Exams for this subject. Taking this practice exam should provide
students with an idea of their general areas of strengths and weaknesses in preparing for the actual AP
Exam. Because this AP Physics C: Electricity and Magnetism Practice Exam has never been administered
as an operational AP Exam, statistical data are not available for calculating potential raw scores or
conversions into AP grades.
This AP Physics C: Electricity and Magnetism Practice Exam is provided by the College Board for AP
Exam preparation. Teachers are permitted to download the materials and make copies to use with their
students in a classroom setting only. To maintain the security of this exam, teachers should collect all
materials after their administration and keep them in a secure location. Teachers may not redistribute the
files electronically for any reason. © 2008 The College Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central,
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be trademarks of their respective owners. Visit the College Board on the Web: www.collegeboard.com. Contents
Directions for Administration ............................................................................................ ii
Section I: MultipleChoice Questions ................................................................................ 1
Section II: FreeResponse Questions .............................................................................. 13
Student Answer Sheet for MultipleChoice Section ...................................................... 20
MultipleChoice Answer Key........................................................................................... 21
FreeResponse Scoring Guidelines.................................................................................. 22 The College Board: Connecting Students to College Success
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Visit the College Board on the Web: www.collegeboard.com.
AP Central is the official online home for the AP Program: apcentral.collegeboard.com. i AP® Physics C: Electricity and Magnetism
Directions for Administration
The AP Physics C: Electricity and Magnetism Exam is one and onehalf hours in length and consists of a
multiplechoice section and a freeresponse section.
• The 45minute multiplechoice section contains 35 questions and accounts for 50 percent of the final
grade. • The 45minute freeresponse section contains 3 questions and accounts for 50 percent of the final grade. Students should be given a 10minute warning prior to the end of each section of the exam. A 10minute break
should be provided before Section I is begun if students are taking Physics C: Mechanics immediately before
Electricity and Magnetism.
The actual AP Physics C Exams are administered in one session, Mechanics first followed by Electricity and
Magnetism. Students taking only one of the exams will have the most realistic experience if both sections are
completed in one session. Similarly, students taking both Physics C exams will have the most realistic experience
if both exams are completed in one session and a complete morning or afternoon is available to administer them.
If a schedule does not permit one time period for administration, it would be acceptable to administer Mechanics
on one day and Electricity and Magnetism on a subsequent day, or to further break things up and administer
Section I and Section II of each exam on subsequent days.
Many students wonder whether or not to guess the answers to the multiplechoice questions about which they are
not certain. It is improbable that mere guessing will improve a score. However, if a student has some knowledge
of the question and is able to eliminate one or more answer choices as wrong, it may be to the student’s advantage
to answer such a question.
• The use of calculators is permitted only on Section II. Straightedges or rulers are allowed on both parts of
the exam. • It is suggested that the practice exam be completed using a pencil to simulate an actual administration. • Teachers will need to provide paper for the students to write their freeresponse answers. Teachers should
provide directions to the students indicating how they wish the responses to be labeled so the teacher will
be able to associate the student’s response with the question the student intended to answer. • The 2008–2009 AP Physics C table of information is included as a part of Section I. The table and the AP
Physics C equation lists are included with Section II. The equation lists are not allowed for Section I. If
you use these exams in subsequent years you should download the newer versions of the table and lists
from AP Central. • Remember that students are not allowed to remove any materials, including scratch work, from the testing
site. ii Section I
MultipleChoice Questions 1 TABLE OF INFORMATION FOR 2008 and 2009
CONSTANTS AND CONVERSION FACTORS
Proton mass, m p = 1.67 ¥ 10 27 kg Electron charge magnitude, Neutron mass, mn = 1.67 ¥ 10 27 kg 1 electron volt, 1 eV = 1.60 ¥ 10 19 J Electron mass, me = 9.11 ¥ 10 31 kg Speed of light,
Universal gravitational
constant,
Acceleration due to gravity
at Earth’s surface, Avogadro’s number, N 0 = 6.02 ¥ 10 23 mol 1 R = 8.31 J (mol iK) Universal gas constant, e = 1.60 ¥ 10 19 C c = 3.00 ¥ 108 m s G = 6.67 ¥ 10 11 m 3 kgis2 g = 9.8 m s2 Boltzmann’s constant, k B = 1.38 ¥ 10 23 J K
1 u = 1.66 ¥ 10 27 kg = 931 MeV c 2 1 unified atomic mass unit, h = 6.63 ¥ 10 34 J is = 4.14 ¥ 10 15 eV is Planck’s constant, hc = 1.99 ¥ 10 25 J im = 1.24 ¥ 103 eV i nm ⑀0 = 8.85 ¥ 10 12 C2 N im 2 Vacuum permittivity, Coulomb’s law constant, k = 1 4 p⑀0 = 9.0 ¥ 109 N im 2 C2
m0 = 4 p ¥ 10 7 (T im) A Vacuum permeability, Magnetic constant, k ¢ = m0 4 p = 10 7 (T im) A
1 atm = 1.0 ¥ 105 N m 2 = 1.0 ¥ 105 Pa 1 atmosphere pressure, UNIT
SYMBOLS Factor meter,
kilogram,
second,
ampere,
kelvin, PREFIXES
Prefix
Symbol m
kg
s
A
K mole,
hertz,
newton,
pascal,
joule, mol
Hz
N
Pa
J watt,
coulomb,
volt,
ohm,
henry, W
C
V
W
H farad,
tesla,
degree Celsius,
electronvolt, F
T
∞C
eV VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES
q
30
0
37
45
53
60
90 10 9 giga G sin q 0 12 35 2 2 45 3 2 1 106 mega M cosq 1 3 2 45 2 2 35 12 0 103 kilo k tan q 0 3 3 34 1 43 3 • 10 2 centi c 10 3 milli m 10 6 micro m 10 9 nano n 10 12 pico p The following conventions are used in this exam.
I. Unless otherwise stated, the frame of reference of any problem is
assumed to be inertial.
II. The direction of any electric current is the direction of flow of positive
charge (conventional current).
III. For any isolated electric charge, the electric potential is defined as zero at
an infinite distance from the charge. 2 PHYSICS C: ELECTRICITY AND MAGNETISM
SECTION I
Time—45 minutes
35 Questions
Directions: Each of the questions or incomplete statements below is followed by five suggested answers or
completions. Select the one that is best in each case and place the letter of your choice in the corresponding box on
the student answer sheet. 1. Two negative point charges are a distance x apart
and have potential energy U. If the distance
between the point charges increases to 3x, what is
their new potential energy?
(A)
(B)
(C)
(D)
(E) Questions 34 9U
3U
U
U 3
U 9 _______________________________________ Two concentric spherical surfaces are drawn
around an isolated positive charge +q located at their
center, as shown above. The inner surface has a radius
that is 1 2 that of the outer surface.
3. If the total electric flux passing through the inner
surface is f , what is the total electric flux passing
through the outer surface? 2. An electric field is produced by the very long,
uniformly charged rod drawn above. If the strength
of the electric field is E1 at a distance r1 from
the axis of the rod, at what distance from the axis is
E
the field strength 1 ?
4
(A) (A)
(B)
(C)
(D)
(E) r1
4 f 4
f 2
f
2f
4f 4. If the electric field strength at the inner surface
is E, what is the electric field strength at the outer
surface? r
(B) 1
2
(C) 2r1 (A)
(B)
(C)
(D)
(E) (D) 4r1
(E) 16r1 E 4
E 2
E
2E
4E GO ON TO THE NEXT PAGE.
3 6. A charge +q is placed at the center of a
tetrahedron whose faces are all equilateral
triangles, as shown above. What is the flux of
the electric field through one face of the
tetrahedron?
(A) 0
5. Sphere X of mass M and charge +q hangs from
a string as shown above. Sphere Y has an equal
charge +q and is fixed in place a distance d
directly below sphere X. If sphere X is in
equilibrium, the tension in the string is most
nearly (B)
(C) q ⑀0
q
4⑀ 0 (D) 4⑀0 q (A) Mg (E) The flux through one face cannot be
determined from the information given.
_______________________________________ kq
d
kq
(C) Mg d
kq 2
(D) Mg + 2
d
kq 2
(E) Mg  2
d (B) Mg + 7. Two concentric metal spheres X and Y are
shown above. X carries a positive charge, and Y
is connected to ground. True statements include
which of the following?
I. The electric field inside X is zero.
II. The electric field outside Y is zero.
III. The charge density on both spheres is
the same.
(A)
(B)
(C)
(D)
(E) I only
III only
I and II only
II and III only
I, II, and III GO ON TO THE NEXT PAGE.
4 9. The capacitor C in the circuit shown above is
initially uncharged. The switch S is then closed.
Which of the following best represents the voltage
VR across the resistor R as a function of time t ?
8. A small positively charged sphere is lowered by
a nonconducting thread into a grounded metal cup
without touching the inside surface of the cup, as
shown above. The grounding wire attached to the
outside surface is disconnected and the charged
sphere is then removed from the cup. Which of
the following best describes the subsequent
distribution of excess charge on the surface of
the cup? (A) (B) (A) Negative charge resides on the inside surface,
and no charge resides on the outside
surface.
(B) Negative charge resides on the outside
surface, and no charge resides on the inside
surface.
(C) Positive charge resides on the inside surface,
and no charge resides on the outside
surface.
(D) Positive charge resides on the outside surface,
and no charge resides on the inside surface.
(E) Negative charge resides on the inside surface,
and positive charge resides on the outside
surface. (C) (D) (E) GO ON TO THE NEXT PAGE.
5 Questions 1011 13. The three lightbulbs in the circuit above are
identical, and the battery has zero internal
resistance. When switch S is closed to cause
bulb 1 to light, which of the other two bulbs
increase(s) in brightness? An electric circuit consists of a 12 V battery, an
ideal 10 A fuse, and three 2 W resistors connected
as shown above. (A)
(B)
(C)
(D)
(E) 10. What would be the reading on a voltmeter
connected across points A and C ?
(A) 12 V
(B) 6 V
(C) 3 V
(D) 2 V
(E) 0 V, since the fuse would break the circuit 14. A length of wire of resistance R is connected
across a battery with zero internal resistance. The
wire is then cut in half and the two halves are
connected in parallel. When the combination is
reconnected across the battery, what happens to
the resultant power dissipated and the current
drawn from the battery? 11. What would be the reading on an ammeter
inserted at point B ?
(A) 9 A
(B) 6 A
(C) 3 A
(D) 2 A
(E) 0 A, since the fuse would break the circuit
_________________________________________ Power Current (A) No change
No change
(B) Doubles
Doubles
(C) Quadruples
Doubles
(D) Doubles
Quadruples
(E) Quadruples
Quadruples
________________________________________ 12. A fixed voltage is applied across the length of a
tungsten wire. An increase in the power dissipated
by the wire would result if which of the following
could be increased?
(A)
(B)
(C)
(D)
(E) Neither bulb
Bulb 2 only
Bulb 3 only
Both bulbs
It cannot be determined without knowing
the emf of the battery. The resistivity of the tungsten
The crosssectional area of the wire
The length of the wire
The temperature of the wire
The temperature of the wire’s surroundings 15. In the circuit shown above, the 10 mF capacitor
is initially uncharged. After the switch S has been
closed for a long time, how much energy is stored
in the capacitor?
(A)
0 mJ
(B) 100 mJ
(C) 250 mJ
(D) 500 mJ
(E) 1000 mJ
GO ON TO THE NEXT PAGE.
6 Questions 1819 16. An electron e  moving in the plane of the page is
injected into a uniform magnetic field B that is
perpendicular to the page, as shown above. Upon
entering the field, the electron takes a path that is
(A) straight through the field
(B) clockwise, circular, and in the plane of
the page
(C) counterclockwise, circular, and in the
plane of the page
(D) circular and curved out of the page
(E) circular and curved into the page
_________________________________________ A fixed charge distribution produces the
equipotential lines shown in the figure above.
18. Which of the following expressions best
represents the magnitude of the electric field at
point P ?
(A)
(B) 10 V
0.04 m (C) 25 V
0.14 m (D) 25 V
0.04 m (E) 17. In the figure above, two long, straight, insulated
wires at right angles in the plane of the page
carry currents of I and 2I, as shown. What is the
direction of the magnetic field at point P, which
is equidistant from the wires and coplanar
with them? 10 V
0.14 m 40 V
0.25 m 19. The direction of the electric field at point P is
most nearly (A) Into the page (A)
(B)
(C)
(D)
(E) (B) Out of the page
(C) toward the left
toward the right
toward the bottom of the page
toward the top of the page
perpendicular to the plane of the page (D)
(E) GO ON TO THE NEXT PAGE.
7 20. A helium nucleus (charge +2q and mass 4m) and Questions 2324 a lithium nucleus (charge +3q and mass 7m) are A cloud contains spherical drops of water
of radius R and charge Q. Assume the drops are
far apart. accelerated through the same electric potential
difference, V0. What is the ratio of their resultant
K
kinetic energies, lithium ?
K helium
(A) 2
3 (B) 23. The electric field E0 and potential V0 at the
surface of each drop is given by which of the
following? 6
7 E0 V0 (A) 0 0 (C) 1
(D) 7
6 (B) kQ
R kQ
R2 (E) 3
2 (C) kQ
R2 kQ
R (D) 0 kQ
R (E) kQ
R 0 21. The electric potential in the xyplane in a certain
region of space is given by V ( x, y) = 6 x 2 y  2 y3 ,
where x and y are in meters and V is in volts.
What is the magnitude of the ycomponent of the
electric field at the point ( 1, 2) ? 24. If two droplets happen to combine into a single
larger droplet, the new potential V at the surface
of the larger droplet is most nearly equal to (A)
0 V/m
(B)
4 V/m
(C) 18 V/m
(D) 24 V/m
(E) 30 V/m
_________________________________________ (A) 3V0
(B) 2 V0
(C) 2
1/ 3 2 V0 (D) 21/ 3 V0 22. Two protons and an electron are assembled along
a line, as shown above. The distance between the
electron and each proton is a. What is the work
done by an external force in assembling this
configuration of charges?
(A)  2 (E) V0 ke2
a (B)  3 ke2
2 a (C) 1 ke2
2 a (D) 3 ke2
2 a (E) 3 ke2
a
GO ON TO THE NEXT PAGE.
8 Questions 2728 An emf of 20 V is induced around a metal ring by
increasing a uniform magnetic field at a constant rate
from zero to a final magnitude of 1.0 ¥ 10 2 T
throughout the region enclosed by the ring. The field
direction is perpendicular to the plane of the ring. 25. A point charge −Q is located at the origin, while
a second point charge +2Q is located at x = d on
the xaxis, as shown above. A point on the xaxis
where the net electric field is zero is located in
which of the following regions? 27. If the area enclosed by the ring is 4.0 ¥ 10 3 m 2 ,
what is the time interval during which the field
is increased? (A)  • < x < 0
(B) 0 < x <
(C) d
2 (A) 2.0 ms
(B) 5.0 ms
(C) 10 ms
(D) 20 ms
(E) 50 ms d
< x<d
2 (D) d < x < •
(E) No region on the xaxis
__________________________________________ 28. If the electrical resistance of the ring is 500 Ω,
what is the rate at which energy is dissipated in
the ring as the field is increased?
(A) 0.040 W
(B)
0.80 W
(C)
1.25 W
(D) 25 W
(E)
1.0 ¥ 10 4 W 26. An inductor of inductance L is connected in
series with a resistor of resistance R, a battery of
emf e , and a switch, as shown above. When the
switch is closed, the current I in the circuit
increases with time, approaching the value I max .
What is Imax ?
(A) R L e
(B) RL e
(C) e RL
(D) e R
(E) L e GO ON TO THE NEXT PAGE.
9 29. Two long, straight wires are parallel to and equidistant from the yaxis, as shown above left. Each carries current I
in opposite directions, resulting in a magnetic field of magnitude B0 at the origin. If the wires are each bent into
right angles and placed as shown above right, what is the magnitude of the magnetic field at the origin?
(A) Zero
(B) Between zero and
(C) B0
2 B0
2 (D) Between B0
and B0
2 (E) B0
__________________________________________________________________________________ 30. A length of wire carrying a steady clockwise current I is bent
to form the triple circular loop X above. An identical length of
the same wire is bent less tightly to form the single loop Y of
larger radius, which carries the same current I. The ratio of
the magnetic field strength at the center of loop Y to the
magnetic field strength at the center of loop X is
(A) 1
9 (B) 1
3 (C) 1
(D) 3
(E) 9
GO ON TO THE NEXT PAGE.
10 32. A long wire of radius R carries a current I, as
shown above, with a current density J = ar that
increases linearly with the distance r from the
center of the wire. Which of the following graphs
best represents the magnitude of the magnetic
field B as a function r ? 31. The diagram above shows the cross section of a
long cable that has an inner wire of radius R
surrounded by a conducting sheath of outer radius
2R. The wire and the sheath carry currents in
opposite directions but with the same uniform
current density J. What is the magnitude of the
magnetic field at the surface of the outer
conductor? (A) (A) Zero
1
m RJ
(B)
4 0
1
(C)
m RJ
2 0
3
(D)
m RJ
4 0
(E) m0 RJ (B) (C) (D) (E) GO ON TO THE NEXT PAGE.
11 34. Which of the following statements contradicts one
of Maxwell’s equations?
(A) A changing magnetic field produces an
electric field.
(B) A changing electric field produces a magnetic
field.
(C) The net magnetic flux through a closed
surface depends on the current inside.
(D) The net electric flux through a closed surface
depends on the charge inside.
(E) The electric field due to an isolated stationary
point charge is inversely proportional to the
square of the distance from the charge. 33. In the circuit drawn above, the switch S is
initially open, and the capacitor C is charged
with the polarity indicated. The switch is then
closed, and the capacitor begins discharging
through the resistor. Which of the following is
true of the current that is subsequently induced
in the circular wire loop near the long, straight
wire AB ? 35. A student building a circuit wishes to increase the
frequency of an oscillator consisting of a capacitor
of capacitance C and an inductor of inductance L.
Which of the following would accomplish this
objective? (A) It is counterclockwise and constant.
(B) It is counterclockwise and increases
with time.
(C) It is counterclockwise and decreases
with time.
(D) It is clockwise and increases with time.
(E) It is clockwise and decreases with time. I.
II.
III.
IV.
(A)
(B)
(C)
(D)
(E) Increase L
Increase C
Decrease L
Decrease C
I only
I or II
I or IV
II or III
III or IV STOP
END OF ELECTRICITY AND MAGNETISM SECTION I
IF YOU FINISH BEFORE TIME IS CALLED,
YOU MAY CHECK YOUR WORK ON ELECTRICITY AND MAGNETISM SECTION I ONLY.
DO NOT TURN TO ANY OTHER TEST MATERIALS. 12 Section II
FreeResponse Questions 13 TABLE OF INFORMATION FOR 2008 and 2009
CONSTANTS AND CONVERSION FACTORS
Proton mass, m p = 1.67 ¥ 10 27 kg Electron charge magnitude, Neutron mass, mn = 1.67 ¥ 10 27 kg 1 electron volt, 1 eV = 1.60 ¥ 10 19 J Electron mass, me = 9.11 ¥ 10 31 kg Speed of light,
Universal gravitational
constant,
Acceleration due to gravity
at Earth’s surface, Avogadro’s number, N 0 = 6.02 ¥ 10 23 mol 1 R = 8.31 J (mol iK) Universal gas constant, e = 1.60 ¥ 10 19 C c = 3.00 ¥ 108 m s
G = 6.67 ¥ 10 11 m 3 kgis2 g = 9.8 m s2 Boltzmann’s constant, k B = 1.38 ¥ 10 23 J K 1 u = 1.66 ¥ 10 27 kg = 931 MeV c 2 1 unified atomic mass unit, h = 6.63 ¥ 10 34 J is = 4.14 ¥ 10 15 eV is Planck’s constant, hc = 1.99 ¥ 10 25 J im = 1.24 ¥ 103 eV i nm ⑀0 = 8.85 ¥ 10 12 C2 N im 2 Vacuum permittivity, Coulomb’s law constant, k = 1 4 p⑀0 = 9.0 ¥ 109 N im 2 C2
m0 = 4 p ¥ 10 7 (T im) A Vacuum permeability, Magnetic constant, k ¢ = m0 4 p = 10 7 (T im) A
1 atm = 1.0 ¥ 105 N m 2 = 1.0 ¥ 105 Pa 1 atmosphere pressure, UNIT
SYMBOLS meter,
kilogram,
second,
ampere,
kelvin, PREFIXES m
kg
s
A
K mole,
hertz,
newton,
pascal,
joule, mol
Hz
N
Pa
J watt,
coulomb,
volt,
ohm,
henry, W
C
V
W
H farad,
tesla,
degree Celsius,
electronvolt, F
T
∞C
eV VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES Prefix Symbol q 0 30 37 45 53 60 giga G sin q 0 12 35 2 2 45 3 2 1 106 mega M cosq 1 3 2 45 2 2 35 12 0 103 kilo k tan q 0 3 3 34 1 43 3 • 10 2 centi c 3 milli m 10 6 micro m 10 9 nano n 12 pico p Factor
10 10 10 9 90 The following conventions are used in this exam.
I. Unless otherwise stated, the frame of reference of any problem is
assumed to be inertial.
II. The direction of any electric current is the direction of flow of positive
charge (conventional current).
III. For any isolated electric charge, the electric potential is defined as zero at
an infinite distance from the charge. 14 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2008 and 2009
MECHANICS
u = u0 + at 1 2
at
2 x = x0 + u0 t + u 2 = u0 2 + 2 a ( x  x0 )
Â F = Fnet = ma F= dp
dt J = Ú F dt = Dp p = mv
Ffric £ m N
W = ÚF K = 1 2
mu
2 P = dW
dt ∑ dr P = Fؒv
DUg = mgh ac = =
=
=
=
=
=
=
=
=
L =
m=
N =
P =
p =
r =
r =
T =
t =
U=
u =
W=
x =
m=
q =
t =
w=
a=
a
F
f
h
I
J
K
k ELECTRICITY AND MAGNETISM acceleration
force
frequency
height
rotational inertia
impulse
kinetic energy
spring constant
length
angular momentum
mass
normal force
power
momentum
radius or distance
position vector
period
time
potential energy
velocity or speed
work done on a system
position
coefficient of friction
angle
torque
angular speed
angular acceleration u2
= w2r
r Fs =  kx Â t = t net = I a E= F
q ÚE UE Us = 1 2
kx
2 rcm = Â mr Â m Ts = 2 p L = r ¥ p = Iw Tp = 2 p
FG =  Gm1m2 UG =  Gm1m2
r w = w0 + at 1 2
at
2 1 q1q2
= qV =
4 p⑀0 r C = Q
V C = k ⑀0 A
d Â Ci Cp = i 1
1
=Â
Cs
i Ci r2 area
magnetic field
capacitance
distance
electric field
emf
force
current
current density
inductance
length
number of loops of wire
per unit length
number of charge carriers
per unit volume
power
charge
point charge
resistance
distance
time
potential or stored energy
electric potential
velocity or speed
resistivity N =
P =
Q=
q =
R =
r =
t =
U=
V=
u =
r= fm = magnetic flux k = dielectric constant dQ
dt
1
1
QV = CV 2
2
2 ÚB ∑ d ᐉ = m0 I
m0 I d ᐉ ¥ r
4p r 3 dB =
F= I = Neud A Bs = m0 nI V = IR g 1 2
Iw
2 i =
=
=
=
=
e=
F =
I =
J =
L =
=
n = E = rJ m
k u = rw q Â rii 1
4 p⑀0 A
B
C
d
E r
R=
A 2p
1
=
f
w T = ⑀0 dV
dr E =V = Q dA = ∑ Uc = I = Ú r 2 dm = Â mr 2 q = q0 + w0 t + 1 q1q2
4 p⑀0 r 2 I = t=r¥F K = F = fm = Ú B ∑ dA Rs = ˆ
r Â Ri 1
=
Rp = e = L 1 ÂR
i d fm
dt e i i P = IV FM = qv ¥ B 15 Ú I dᐉ ¥ B UL = dI
dt 1 2
LI
2 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2008 and 2009
GEOMETRY AND TRIGONOMETRY
Rectangle
A = bh
Triangle A= 1
bh
2 Circle A = pr 2
C = 2pr
Parallelepiped
V = wh
Cylinder A=
C=
V=
S =
b =
h =
=
w=
r = CALCULUS area
circumference
volume
surface area
base
height
length
width
radius df
d f du
=
dx
du dx
d n
( x ) = nx n 1
dx
d x
(e ) = e x
dx
d
(1n x ) = 1
dx
x
d
(sin x ) = cos x
dx
d
(cos x ) =  sin x
dx V = pr 2 Úx S = 2pr + 2pr 2 Úe Sphere V = 4 3
pr
3 Ú Right Triangle a
c
b
c tan q = x dx = e x dx
= ln x
x Ú sin x dx =  cos x a 2 + b2 = c2 cos q = dx = Ú cos x dx = sin x S = 4pr 2 sin q = 1
x n + 1 , n π 1
n +1 n c a
90° q a
b b 16 PHYSICS C: ELECTRICITY AND MAGNETISM
SECTION II
Time—45 minutes
3 Questions
Directions: Answer all three questions. The suggested time is about 15 minutes for answering each of the questions,
which are worth 15 points each. The parts within a question may not have equal weight. All final numerical answers
should include appropriate units. Credit depends on the quality of your solutions and explanations, so you should
show your work. Credit also depends on demonstrating that you know which physical principles would be
appropriate to apply in a particular situation. Therefore, you should clearly indicate which part of a question your
work is for. E&M. 1.
A parallelplate capacitor X, with plate area A and plate separation d, is filled with air and charged by connecting
the capacitor through a switch to a power supply of emf e , as shown above.
(a) Determine the magnitude of the charge q0 on each plate of the capacitor, in terms of the given quantities and
fundamental constants.
The switch is now flipped to the right, so that capacitor X is disconnected from the power supply and is instead
connected to an uncharged parallelplate capacitor Y. Capacitor Y has the same plate separation but twice the
plate area and is filled with a material having dielectric constant 3.
(b) Calculate the equilibrium charges qX and qY on capacitors X and Y, expressing your answers in terms of
the initial charge q0 .
Once the charges on the two capacitors have reached equilibrium, they are disconnected from one another. The
dielectric is then removed from capacitor Y.
(c) Indicate whether the energy stored in capacitor Y as the dielectric is removed increases, decreases or remains
the same.
___ Increases ___ Decreases ___ Remains the same Justify your answer.
(d) Indicate whether your answer to (c) requires that the electric force on the dielectric as it is removed pulls the
dielectric into the capacitor, pushes it out, or is zero.
___ Pulls it in ___ Pushes it out ___ Is zero Justify your answer.
(e) A resistor of resistance R is now connected to the two sides of capacitor Y. The capacitor is allowed to
discharge through the resistor. Derive the equation describing the charge on capacitor Y as a function of
time, expressed in terms of R, d, A, the initial charge qY on capacitor Y, and fundamental constants. GO ON TO THE NEXT PAGE.
17 E&M. 2.
Electrons created at the filament at the left end of the tube represented above are accelerated through a voltage V0
and exit the tube. The electrons then move with constant speed to the right, as shown, before entering a region in
which there is a uniform electric field between two parallel plates separated by a distance D. The electrons enter
the field at point P, which is a distance y0 from the bottom plate, and are deflected toward that plate. Express
your answers to the following in terms of V0 , D, y0 , and fundamental constants.
(a) Calculate the speed of the electrons as they exit the tube.
(b) i. Calculate the magnitude of the electric field required to cause the electrons to land the distance y0 from
the edge of the plate.
ii. Indicate the direction of the electric field.
____ To the left
____ Toward the top of the page
____ Into the page ____ To the right
____ Toward the bottom of the page
____ Out of the page Justify your answer.
(c) Calculate the potential difference between the two plates required to produce the electric field determined in
part (b).
Suppose the electric field between the plates is replaced by a magnetic field and the electrons are to strike the
lower plate at the same distance y0 from the edge of the plate.
(d) i. Calculate the magnitude of the magnetic field.
ii. Indicate the direction of the required magnetic field.
____ To the left
____ Toward the top of the page
____ Into the page ____ To the right
____ Toward the bottom of the page
____ Out of the page Justify your answer. GO ON TO THE NEXT PAGE.
18 E&M. 3.
An astronaut on another planet erects a tall, thin, vertical, nonconducting, frictionless cylinder of radius r0 at one
of the planet’s magnetic poles. Assume the magnetic field has an upward vertical component with a magnitude
that varies with altitude z as Bz = B0 (1  kz ) , where k is a constant. The horizontal component of the field has
the constant value BH at the surface of the cylinder and points radially outward from the axis of the cylinder.
A gold ring of resistance R that just fits around the cylinder is released from rest at some height above the
ground. Assume air friction is negligible. Express all algebraic answers in terms of B0 , BH , k, r0 , R, and
fundamental constants.
(a) Determine the magnetic flux through the ring as a function of z .
(b) Indicate whether the direction of the induced current in the ring, as seen from above the cylinder, is clockwise
or counterclockwise.
___ Clockwise ___ Counterclockwise Justify your answer.
(c) Calculate the power dissipated in the ring at the instant it is falling with speed u .
(d) Calculate the magnitude of the net upward force on the ring due to the horizontal component of the field at
the instant the ring is falling with speed u .
(e) Is there a net force on the ring due to the vertical component of the field? Explain your reasoning. STOP
END OF EXAM 19 Name: ____________________________________ AP® Physics C: Electricity and Magnetism
Student Answer Sheet for MultipleChoice Section
No.
1 Answer No.
31 2 32 3 33 4 34 5 35 6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30 20 Answer AP® Physics C: Electricity and Magnetism
MultipleChoice Answer Key No.
1 Correct
Answer
D No.
31 Correct
Answer
C 2 D 32 C 3 C 33 E 4 A 34 C 5 E 35 E 6 C 7 C 8 B 9 D 10 A 11 C 12 B 13 C 14 E 15 D 16 B 17 B 18 B 19 A 20 E 21 C 22 B 23 C 24 C 25 A 26 D 27 A 28 B 29 C 30 A 21 AP® Physics C: Electricity and Magnetism
FreeResponse Scoring Guidelines
General Notes about AP Physics Practice Exam Scoring Guidelines
1. The solutions contain a common method of solving the freeresponse questions and the allocation of
points for the solutions. Some also contain a common alternate solution. They are typical of draft
guidelines developed before student solutions are available. Teachers should feel free to make
modifications based on their students’ responses. 2. The scoring guidelines typically show numerical results using the value g = 9.8 m s2 , but use of 10 m s2 is of course also acceptable. Solutions usually show numerical answers using both values
when they are significantly different.
The following rules apply to the official scoring of AP Physics Exams.
3. All correct methods of solution receive appropriate credit for correct work. 4. Generally, double penalty for errors is avoided. For example, if an incorrect answer to part (a) is
correctly substituted into an otherwise correct solution to part (b), full credit will usually be awarded.
One exception to this may be cases when the numerical answer to a later part should be easily
recognized as wrong, e.g., a speed faster than the speed of light in vacuum.
5. Implicit statements of concepts normally receive credit. For example, if use of the equation expressing a
particular concept is worth 1 point, and a student’s solution contains the application of that equation to
the problem but the student does not write the basic equation, the point is still awarded. However, when
students are asked to derive an expression, it is normally expected that they will begin by writing one or
more fundamental equations, such as those given on the AP Physics Exam equation sheet. For a
description of the use of such terms as “derive” and “calculate” on the exams, and what is expected for
each, see “The FreeResponse Sections⎯Student Presentation” in the AP Physics Course Description.
6. Strict rules regarding significant digits are usually not applied to numerical answers. However, in some
cases answers containing too many digits may be penalized. In general, two to four significant digits are
acceptable. Numerical answers that differ from the published answer due to differences in rounding
throughout the question typically receive full credit. Exceptions to these guidelines usually occur when
rounding makes a difference in obtaining a reasonable answer. For example, suppose a solution requires
subtracting two numbers that should have five significant figures and that differ starting with the fourth
digit (e.g., 20.295 and 20.278). Rounding to three digits will lose the accuracy required to determine the
difference in the numbers, and some credit may be lost. 22 AP® Physics C: Electricity and Magnetism
FreeResponse Scoring Guidelines
Question 1
15 points total
(a) Distribution
of points 2 points
For using the expressions relating charge to emf and capacitance to capacitor dimensions
q0 = C e
C = ⑀0 A d
For the correct answer
⑀ A
q0 = 0 e
d (b) 1 point 1 point 5 points
For correct use of conservation of charge
q X + qY = q0
For indicating that at equilibrium the voltage is the same across each capacitor
q
q
VX = VY = X = Y
CX
CY 1 point For a correct relationship between C X and CY
3⑀ (2 A) 6⑀0 A
CY = 0
=
= 6C X
d
d
Combining these relationships to solve for q X
q  qX
qX
= 0
CX
6C X 1 point 6q X = (q0  q X )
For correct answers for both capacitors
1
q X = q0
7
6
qY = q0
7
Note: 1 point partial credit will be given if the correct charge for only one of the capacitors
is given. 23 1 point 2 points AP® Physics C: Electricity and Magnetism
FreeResponse Scoring Guidelines
Question 1 (continued)
Distribution
of points
(c) 2 points
For correctly indicating that the stored energy increases as the dielectric is removed
For a valid justification
For example:
Removing the dielectric will decrease the capacitance of capacitor Y by a factor of 3. 1 point
1 point The charge on the capacitor stays the same. So the stored energy U = q 2 2C will
increase by a factor of 3.
(d) 3 points
For correctly indicating that the dielectric will be pulled in
For a valid justification
For example: Removing the dielectric increases the stored energy. This means that positive
work was done on the system to remove it. This requires an external force to pull the
dielectric material out, acting opposite to the electric force. So the electric force pulls
the dielectric in.
Note: Full credit can be given if correct reasoning is used, even if an incorrect conclusion is
reached based on an incorrect answer in part (c). (e) 1 point
2 points 3 points
For a correct expression of the voltage loop equation for the circuit
q
= IR
CY q
dq
= R
CY
dt
A general form for the solution of this equation can be determined by integration or deduced
by inspection.
For giving the proper exponential form of the solution
q(t ) = qi e  t RC
Using the initial condition at t = 0
q(0) = qi = qY
For the correct answer q(t ) = qY e td 2⑀0 RA 24 1 point 1 point 1 point AP® Physics C: Electricity and Magnetism
FreeResponse Scoring Guidelines
Question 2
15 points total
(a) Distribution
of points 2 points
For correct application of conservation of energy
1
m u 2 = eV0
2 e
For the correct answer
2eV0
u =
me 1 point 1 point (b)
(i) 4 points
For a correct application of the kinematic equation and Newton’s second law in the vertical
direction
1
eE
Dy = at 2 where Dy = y0 , a =
2
me
Combining these equations and solving for t
1 eE 2
y0 =
t
2 me 1 point t = 2 y0 me eE
For a correct application of the kinematic equation in the horizontal direction
Dx = u0 x t where Dx = y0 1 point For indicating that u0 x is the answer from part (a) 1 point 2eV0 2 y0 me
me
eE
For the correct answer
4V
E = 0
y0 1 point y0 = (ii) 2 points For correctly indicating that the electric field is directed toward the top of the page
For a correct justification
For example: Negative charges are accelerated in the direction opposite the electric field.
Since the acceleration here is downward, the field must be upward. 25 1 point
1 point AP® Physics C: Electricity and Magnetism
FreeResponse Scoring Guidelines
Question 2 (continued)
Distribution
of points
(c) 1 point V = Ed
For the correct answer
4V0 D
V =
y0 1 point (d)
(i) 4 points
For equating the magnetic force to the centripetal force
m u2
eu B = e
y0
me u
ey0
For using the result for u from part (a)
m 2eV0
B= e
ey0 me
For the correct answer
2 meV0
B=
2
ey0 2 points B= (ii) 1 point 1 point 2 points For correctly indicating that the magnetic field must be directed into the page
For a correct justification
For example: Using the righthand rule, a field out of the page would produce an initial
downward force on positively charged particles. Since these are electrons, the field must
be in the opposite direction. 26 1 point
1 point AP® Physics C: Electricity and Magnetism
FreeResponse Scoring Guidelines
Question 3
15 points total
(a) Distribution
of points 2 points
fm = Bz A
For using the correct area 1 point A=
For the correct answer
fm = B0 (1  kz ) p r02
p r02 (b) 1 point 3 points
For correctly indicating that the current is clockwise
For a correct justification
For example: The vertical component of the magnetic field and thus the flux is increasing
with time because the magnetic field increases with decreasing z. The induced current
will act to oppose the change in flux and create a downward field. 1 point
2 points Note: 1 point partial credit can be earned for stating just one of the two ideas above. (c) 5 points
For indicating the need to take the derivative of the flux to calculate the induced emf
For correctly taking the derivative
df
e =  dtm = p r02 B0 k dz
dt
dz
For correctly equating
with the velocity u
dt
df
e =  dtm = p r02 B0 ku
For applying a valid power equation P = e 1 point
1 point 1 point 1 point 2 R
For the correct answer
2
p 2 r04 B0 k 2 u 2
P =
R 1 point 27 AP® Physics C: Electricity and Magnetism
FreeResponse Scoring Guidelines
Question 3 (continued)
Distribution
of points
(d) 3 points
F = I Bradial
For the correct determination of the path length
= 2 p r0
For the correct substitution of the current I
e = p r 2 B0 ku
I =
0
R
R
B ku
F = p r02 0 (2 p r0 ) BH
R
For the correct answer
3 kB B u
F = 2 p 2 r0 0 H
R (e) 1 point
1 point 1 point 2 points
For correctly indicating that there is no net force due to the vertical component of the
magnetic field
For a correct justification
For example: For any pair of points on the ring located opposite each other, there are equal
but opposite forces acting on the ring that cancel. 28 1 point
1 point ...
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 Spring '08
 Boudreaux
 Electricity And Magnetism

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