AP® Physics C: Electricity and Magnetism
2005 Free-Response Questions
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TABLE OF INFORMATION FOR 2005
CONSTANTS AND CONVERSION FACTORS
1 unified atomic mass unit,
UNITS
= 1.66 ¥ 10
1u
-27
= 931 MeV/c
Proton mass,
Name
PREFIXES
Symbol
2
m p = 1.67 × 10 −27 kg
10 9
giga
G
kilogram
kg
10
6
mega
M
10
3
kilo
k
centi
c
milli
m
micro
µ
nano
n
pico
p
second
s
Electron mass,
me = 9.11 × 10 −31 kg
ampere
A
Avogadro’s number,
Universal gas constant,
e = 1.60 × 10
C
kelvin
N0 = 6.02 × 10 23 mol −1
R
= 8.31 J / ( mol ◊ K )
K
mole
mol
hertz
Hz
Boltzmann’s constant,
k B = 1.38 × 10 −23 J / K
Speed of light,
c = 3.00 × 10 8 m / s
newton
N
Planck’s constant,
h = 6.63 × 10 −34 J ⋅ s
pascal
Pa
= 4.14 × 10 −15 eV ⋅ s
hc = 1.99 × 10
−25
J⋅m
= 1.24 × 10 3 eV ⋅ nm
Vacuum permittivity,
Coulomb’s law constant,
Vacuum permeability,
Magnetic constant,
Universal gravitational constant,
Acceleration due to gravity
at the Earth’s surface,
1 atmosphere pressure,
⑀ 0 = 8.85 × 10
−12
C / N⋅m
2
2
k = 1 / 4π ⑀ 0 = 9.0 × 10 9 N ⋅ m 2 / C 2
µ 0 = 4π × 10 −7 (T ⋅ m) / A
k ' = µ 0 / 4π = 10 −7 (T ⋅ m) / A
G
= 6.67
¥
g = 9.8 m / s
10
-11
3
m / kg ◊ s
2
1 atm = 1.0 × 10 5 N / m 2
= 1.0 × 10 5 Pa
1 electron volt,
Symbol
m
mn = 1.67 × 10 −27 kg
Magnitude of the electron charge,
Prefix
meter
Neutron mass,
−19
Factor
kg
1 eV = 1.60 × 10 −19 J
2
10 −2
10
10
−3
−6
10 −9
10
−12
VALUES OF TRIGONOMETRIC
FUNCTIONS FOR COMMON ANGLES
joule
J
watt
W
θ
sin θ
cos θ
tan θ
coulomb
C
0
0
1
0
volt
V
ohm
Ω
30
1/2
3 /2
3 /3
henry
H
37
3/5
4/5
3/4
farad
F
tesla
T
45
2 /2
2 /2
1
degree
Celsius
C
53
4/5
3/5
4/3
electronvolt
eV
60
3 /2
1/2
3
90
1
0
∞
The following conventions are used in this examination.
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
ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2004 and 2005
MECHANICS
=
u
+ at
u0
1 2
at
2
+ 2 a ( x - x0 )
x = x0 + u0 t +
= u0 2
 F = Fnet = ma
u
2
dp
dt
J = Ú F dt = Dp
p = mv
F=
F fric £ mN
W = Ú F dr
1
K = mu 2
2
dW
P=
dt
P = Fⴢv
DUg = mgh
∑
ac =
u
2
=
r
2
w r
t=r¥F
 t = t net = I a
I = Ú r 2 dm = Â mr 2
rcm =  mr  m
= rw
L = r ¥ p = Iw
u
K =
w
q
=
=
1 2
Iw
2
w0
q0
=
=
=
=
=
=
=
=
=
L =
m=
N =
P =
p =
r =
r =
T =
t =
U=
u =
W=
x =
m =
q =
t =
w=
a =
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
∑
1 2
at
2
q1 q 2
4 p⑀ 0 r
1
UE = qV =
C=
C=
Q
V
k⑀ 0 A
d
∑i Ci
Cp =
∑
1
1
=
Cs
i Ci
dQ
dt
1
1
Uc = QV = CV 2
2
2
I=
R=
r
A
V = IR
Rs =
+ at
+ w0t +
a
F
f
h
I
J
K
k
ELECTRICITY AND MAGNETISM
1 q1 q 2
A = area
F=
2
B = magnetic field
4 p⑀ 0 r
C = capacitance
F
d = distance
E=
q
E = electric field
e = emf
Q
养 E • dA =
F = force
⑀0
I = current
dV
L = inductance
E=−
= length
dr
n
= number of loops of wire
qi
1
V=
per unit length
4 p⑀ 0 i ri
P = power
∑ Ri
1
=
Rp
i
∑ R1
i
i
Fs = - k x
P = IV
1
Us = kx 2
2
2p
1
=
T =
f
w
FM = qv × B
养 B • d 艎 = m0 I
m
Ts = 2 p
k
Bs = m0 nI
F = z I d艎 × B
fm = z B • dA
dfm
Tp = 2 p
FG = UG
g
Gm1m2
2
r
Gm m
=- 1 2
r
e=−
rˆ
dt
dI
e = −L
dt
1
U L = LI 2
2
3
Q=
q =
R =
r =
t =
U=
V =
u =
r =
fm =
k =
charge
point charge
resistance
distance
time
potential or stored energy
electric potential
velocity or speed
resistivity
magnetic flux
dielectric constant
ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2004 and 2005
GEOMETRY AND TRIGONOMETRY
Rectangle
A = bh
Triangle
1
A = bh
2
Circle
A = pr 2
C = 2 pr
Parallelepiped
V = wh
Cylinder
V = pr 2
S = 2 pr + 2 pr 2
Sphere
4
V = pr 3
3
S = 4 pr 2
Right Triangle
a 2 + b2 = c2
a
sin q =
c
cos q =
b
c
tan q =
a
b
A=
C=
V=
S =
b =
h =
=
w=
r =
CALCULUS
area
circumference
volume
surface area
base
height
length
width
radius
c
d f d f du
=
dx du dx
d n
n -1
( x ) = nx
dx
d x
x
(e ) = e
dx
d
1
(1n x) =
dx
x
d
(sin x) = cos x
dx
d
(cos x) = - sin x
dx
1 n +1
Ú xn dx =
x , n π -1
n +1
Ú ex dx = ex
dx
Ú x = ln x
Ú cos xdx = sin x
a
90°
q
Ú sin xdx = - cos x
b
4
2005 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREE-RESPONSE QUESTIONS
PHYSICS C
Section II, ELECTRICITY AND MAGNETISM
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. Show all your work in the
pink booklet in the spaces provided after each part, NOT in this green insert.
E&M. 1.
Consider the electric field diagram above.
(a) Points A, B, and C are all located at y = 0.06 m .
i. At which of these three points is the magnitude of the electric field the greatest? Justify your answer.
ii. At which of these three points is the electric potential the greatest? Justify your answer.
(b) An electron is released from rest at point B.
i. Qualitatively describe the electron’s motion in terms of direction, speed, and acceleration.
ii. Calculate the electron’s speed after it has moved through a potential difference of 10 V.
(c) Points B and C are separated by a potential difference of 20 V. Estimate the magnitude of the electric field
midway between them and state any assumptions that you make.
(d) On the diagram, draw an equipotential line that passes through point D and intersects at least three electric
field lines.
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2005 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREE-RESPONSE QUESTIONS
E&M. 2.
In the circuit shown above, resistors 1 and 2 of resistance R1 and R2 , respectively, and an inductor of
inductance L are connected to a battery of emf e and a switch S. The switch is closed at time t = 0.
Express all algebraic answers in terms of the given quantities and fundamental constants.
(a) Determine the current through resistor 1 immediately after the switch is closed.
(b) Determine the magnitude of the initial rate of change of current, dI dt , in the inductor.
(c) Determine the current through the battery a long time after the switch has been closed.
(d) On the axes below, sketch a graph of the current through the battery as a function of time.
Some time after steady state has been reached, the switch is opened.
(e) Determine the voltage across resistor 2 just after the switch has been opened.
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2005 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREE-RESPONSE QUESTIONS
E&M. 3.
A student performs an experiment to measure the magnetic field along the axis of the long, 100-turn
solenoid PQ shown above. She connects ends P and Q of the solenoid to a variable power supply and
an ammeter as shown. End P of the solenoid is taped at the 0 cm mark of a meterstick. The solenoid can be
stretched so that the position of end Q can be varied. The student then positions a Hall probe* in the center
of the solenoid to measure the magnetic field along its axis. She measures the field for a fixed current of
3.0 A and various positions of the end Q. The data she obtains are shown below.
Measured Magnetic Field (T)
(directed from P to Q)
1
Position of End Q
(cm)
40
2
50
7.70 ¥ 10 -4
3
60
6.80 ¥ 10 -4
4
80
4.90 ¥ 10 -4
5
100
4.00 ¥ 10 -4
Trial
n
(turns/m)
9.70 ¥ 10 -4
(a) Complete the last column of the table above by calculating the number of turns per meter.
* A Hall Probe is a device used to measure the magnetic field at a point.
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2005 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREE-RESPONSE QUESTIONS
(b) On the axes below, plot the measured magnetic field B versus n. Draw a best-fit straight line for the data
points.
(c) From the graph, obtain the value of m0 , the magnetic permeability of vacuum.
(d) Using the theoretical value of m0 = 4 p ¥ 10 -7 (T im ) A , determine the percent error in the experimental
value of m0 computed in part (c).
END OF SECTION II, ELECTRICITY AND MAGNETISM
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Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents).
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