Unformatted text preview: AP® Physics C: Electricity & Magnetism
2003 FreeResponse Questions The materials included in these files are intended for use by AP teachers
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For the College Board’s online home for AP professionals, visit AP Central at apcentral.collegeboard.com. TABLE OF INFORMATION FOR 2003
UNITS CONSTANTS AND CONVERSION FACTORS
1 unified atomic mass unit, 1 u = 1.66 10 27 = 931 MeV/c
Proton mass, PREFIXES Name Symbol meter
kilogram Factor Prefix Symbol m 10 9 giga G kg 10 6 mega M 10 3 kilo k kg 2 m p = 1.67 × 10 −27 kg Neutron mass, mn = 1.67 × 10 −27 kg second s Electron mass, me = 9.11 × 10 −31 kg ampere A 10 −2 centi c Magnitude of the electron charge, e = 1.60 × 10 −19 C kelvin K 10 −3 milli m micro µ Avogadro’s number, N0 = 6.02 × 10 mol
23 −1 mol hertz Hz 10 −9 nano n 10 −12 pico p 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 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 k = 1 / 4π = 8.85 × 10 C / N⋅m 0 k = µ 0 / 4π = 10 (T ⋅ m ) / A
G = 6.67 10 11 m 3 / kg ¼ s 2 g = 9.8 m / s V
Ω H farad −7 0 henry µ 0 = 4π × 10 −7 (T ⋅ m ) / A C ohm = 9.0 × 10 N ⋅ m 2 / C 2 θ volt 9 W coulomb
2 J watt = 1.24 × 10 3 eV ⋅ nm
2 VALUES OF TRIGONOMETRIC FUNCTIONS
FOR COMMON ANGLES joule hc = 1.99 × 10 −25 J ⋅ m −12 10 mole R = 8.31 J / ( mol ¼ K ) Universal gas constant, −6 F tesla T 45o o = 1.0 × 10 Pa tan θ 0 1 0 3 /2 3 /3 1/2 37o 3/5 degree
Celsius o C 53o eV 60 o
90o 1 atm = 1.0 × 10 5 N / m 2 cos θ 30o electronvolt 2 sin θ 2 /2 4/5 4/5
2 /2 3/4
1 3/5 4/3 3 /2 1/2 3 1 0 ∞ 5 1 electron volt, 1 eV = 1.60 × 10 −19 J 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.
IV. For mechanics and thermodynamics equations, W represents the work done on a system. 2 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2003
MECHANICS
a = acceleration
F = force
1
x = x 0 + u 0 t + at 2
f = frequency
2
2
2
h = height
u = u 0 + 2a x  x 0
I = rotational inertia
Ê F = Fnet = ma
J = impulse
dp
K = kinetic energy
F=
dt
k = spring constant
l = length
J = F dt = Dp
L = angular momentum
p = mv
m = mass
F fric mN
N = normal force
W = F dr
P = power
p = momentum
1
2
K = mu
r = radius or distance
2
r = position vector
dW
P=
T = period
dt
t = time
P=F v
U = potential energy
DUg = mgh
u = velocity or speed
u 2 = w2r
W = work done on a system
ac =
r
x = position
t=rF
m = coefficient of friction
Ê t = t net = Ia
q = angle
t = torque
I = r 2 dm = Ê mr 2
w = angular speed
rcm = Ê mr Ê m
a = angular acceleration
u = rw
L = r p = Iw
1
K = Iw 2
2
w = w0 + at
q = q 0 + w0 t + 1 at 2
2
Fs =  kx
1
Us = kx 2
2
2p
1
T=
=
f
w
m
Ts = 2 p
k
l
Tp = 2 p
g
Gm1m2
$
FG = r
r2
Gm1m2
UG = r u = u 0 + at 0 I I I 5 ELECTRICITY AND MAGNETISM
q1 q 2
A = area
2
B = magnetic field
r
0
C = capacitance
F
E=
d = distance
q
E = electric field
Q
e = emf
E • dA =
F = force
0
I = current
dV
E=−
L = inductance
dr
l = length
qi
1
n = number of loops of wire per
V=
unit length
4 p 0 i ri
P = power
1 q1 q 2
Q = charge
UE = qV =
4p 0 r
q = point charge
Q
R = resistance
C=
r = distance
V
t = time
kA
C= 0
U = potential or stored energy
d
V = electric potential
C p = ∑ Ci
υ = velocity or speed
i
r = resistivity
1
1
fm = magnetic flux
=∑
Cs
i Ci
k = dielectric constant
dQ
I=
dt
1
1
Uc = QV = CV 2
2
2
rl
R=
A
V = IR
1
F=
4p ∑ Rs = ∑ Ri
i 1
1
=∑
Rp
i Ri
P = IV
FM = qv × B
B • d ø = m0 I I F = I dø × B
Bs = m0 nI I fm = B • dA dfm
dt
dI
e = −L
dt
12
U L = LI
2 e=− 3 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2003
GEOMETRY AND TRIGONOMETRY
Rectangle
A = bh
Triangle
1
A = bh
2
Circle
A = pr 2
C = 2 pr
Parallelepiped
V = lwh
Cylinder
V = pr 2 l
S = 2 prl + 2 pr 2
Sphere
4
V = pr 3
3
S = 4 pr 2
Right Triangle
a 2 + b2 = c2
a
sin q =
c A=
C=
V=
S=
b=
h=
l=
w=
r= area
circumference
volume
surface area
base
height
length
width
radius c a
90 q
b b
cos q =
c
tan q = a
b CALCULUS
df
d f du
=
dx
du dx 27
27 dn
n 1
x = nx
dx
dx
e = ex
dx
d
1
(1n x) =
dx
x
d
(sin x) = cos x
dx
d
(cos x) =  sin x
dx
1 n +1
xn dx =
x
, n 1
n +1
e x dx = e x I
I I dx
= 1n x
x
cos x dx = sin x I
I sin x dx =  cos x
4 2003 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREERESPONSE 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.
A spherical cloud of charge of radius R contains a total charge +Q with a nonuniform volume charge density that
varies according to the equation
r
r(r ) = r0 1 for r R and
R
r = 0 for r > R , where r is the distance from the center of the cloud. Express all algebraic answers in terms of Q, R, and
fundamental constants.
(a) Determine the following as a function of r for r > R .
i. The magnitude E of the electric field
ii. The electric potential V
(b) A proton is placed at point P shown above and released. Describe its motion for a long time after its release.
(c) An electron of charge magnitude e is now placed at point P, which is a distance r from the center of the sphere,
and released. Determine the kinetic energy of the electron as a function of r as it strikes the cloud.
(d) Derive an expression for r0 .
(e) Determine the magnitude E of the electric field as a function of r for r R . Copyright © 2003 by College Entrance Examination Board. All rights reserved.
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5 2003 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREERESPONSE QUESTIONS
E&M. 2.
In the laboratory, you connect a resistor and a capacitor with unknown values in series with a battery of emf
e = 12 V . You include a switch in the circuit. When the switch is closed at time t = 0, the circuit is completed,
and you measure the current through the resistor as a function of time as plotted below. A datafitting program finds that the current decays according to the equation i(t ) = e et 4.
R (a) Using common symbols for the battery, the resistor, the capacitor, and the switch, draw the circuit that you
constructed. Show the circuit before the switch is closed and include whatever other devices you need to
measure the current through the resistor to obtain the above plot. Label each component in your diagram.
(b) Having obtained the curve shown above, determine the value of the resistor that you placed in this circuit.
(c) What capacitance did you insert in the circuit to give the result above? Copyright © 2003 by College Entrance Examination Board. All rights reserved.
Available to AP professionals at apcentral.collegeboard.com and to
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6 2003 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREERESPONSE QUESTIONS
You are now asked to reconnect the circuit with a new switch in such a way as to charge and discharge the capacitor.
When the switch in the circuit is in position A, the capacitor is charging; and when the switch is in position B, the
capacitor is discharging, as represented by the graph below of voltage VC across the capacitor as a function of time. (d) Draw a schematic diagram of the RC circuit that you constructed that would produce the graph above. Clearly
indicate switch positions A and B on your circuit diagram and include whatever other devices you need to
measure the voltage across the capacitor to obtain the above plot. Label each component in your diagram. Copyright © 2003 by College Entrance Examination Board. All rights reserved.
Available to AP professionals at apcentral.collegeboard.com and to
students and parents at www.collegeboard.com/apstudents. GO ON TO THE NEXT PAGE.
7 2003 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREERESPONSE QUESTIONS E&M. 3.
An airplane has an aluminum antenna attached to its wing that extends 15 m from wingtip to wingtip. The plane is
traveling north at 75 m/s in a region where Earth’s magnetic field has both a vertical component and a northward
component, as shown above. The net magnetic field is at an angle of 55 degrees from horizontal and has a magnitude
of 6.0 10 5 T .
(a) On the figure below, indicate the direction of the magnetic force on electrons in the antenna. Justify your
answer. (b) Determine the magnitude of the electric field generated in the antenna.
(c) Determine the potential difference between the ends of the antenna.
(d) On the figure below, indicate which end of the antenna is at higher potential. Copyright © 2003 by College Entrance Examination Board. All rights reserved.
Available to AP professionals at apcentral.collegeboard.com and to
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8 2003 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREERESPONSE QUESTIONS
(e) The ends of the antenna are now connected by a conducting wire so that a closed circuit is formed.
i. Describe the condition(s) that would be necessary for a current to be induced in the circuit. Give a
specific example of how the condition(s) could be created.
ii. For the example you gave in i. above, indicate the direction of the current in the antenna on the
figure below. END OF SECTION II, ELECTRICITY AND MAGNETISM Copyright © 2003 by College Entrance Examination Board. All rights reserved.
Available to AP professionals at apcentral.collegeboard.com and to
students and parents at www.collegeboard.com/apstudents. 9 ...
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This note was uploaded on 08/05/2009 for the course PHYS 101 taught by Professor Reich during the Spring '08 term at Johns Hopkins.
 Spring '08
 Reich
 Physics, Magnetism

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