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Unformatted text preview: AP® Physics C: Electricity and Magnetism
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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 2004 and 2005
CONSTANTS AND CONVERSION FACTORS
27 = 1.66 = 931 MeV/c ¥ 1 unified atomic mass unit, 10  1u UNITS
Name Symbol 10 9 giga G kilogram kg 10 6 mega M 10 3 kilo k centi c milli m micro µ nano n pico p mn = 1.67 × 10 −27 kg second s Electron mass, me = 9.11 × 10 −31 kg ampere A e = 1.60 × 10 C kelvin N0 = 6.02 × 10 23 mol −1
R = Universal gas constant, K mole mol hertz 8.31 J / ( mol K )
◊ Avogadro’s number, 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 k = 1 / 4π J
W θ sin θ cos θ tan θ C 0 0 1 0 V
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 k = µ 0 / 4π = 10 −7 (T ⋅ m) / A = G 6.67 ¥ 1 atmosphere pressure, VALUES OF TRIGONOMETRIC
FUNCTIONS FOR COMMON ANGLES volt 2 = 9.0 × 10 9 N ⋅ m 2 / C 2 g = 9.8 m / s 10 11  Acceleration due to gravity
at the Earth’s surface, 10 −12 1 0 ∞ ' Universal gravitational constant, 10 −9 ohm C / N⋅m
2 µ 0 = 4π × 10 −7 (T ⋅ m) / A Vacuum permeability,
Magnetic constant, 0 = 8.85 × 10 10 −6 coulomb 3 m / kg s
◊ Coulomb’s law constant, 0 10 −3 watt J⋅m −12 10 −2 joule = 1.24 × 10 3 eV ⋅ nm Vacuum permittivity, Symbol m Neutron mass, Magnitude of the electron charge, Prefix meter 2 −19 Factor kg m p = 1.67 × 10 −27 kg Proton mass, PREFIXES 2 1 atm = 1.0 × 10 5 N / m 2 2 = 1.0 × 10 5 Pa 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. 2 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2004 and 2005 = q
t a= = w = w q = q + = w + 0t 12
t
2 w 1
Ri FM = qv × B
B•d = 1
f m
k Bs = =
= = p m ˆ
r e r2
Gm1m2
r 0 nI = B • dA dm
dt
dI
= −L
dt
12
U L = LI
2 e p g
Gm1m2 0I F= Id ×B f = FG i 3 =− f w
p 2 = Tp 1
=
Rp Ri z =
2 i P = IV 12
kx
2 2 = UG Rs = t
a + 0 a Ts w= T A
V = IR z u Us R= I kx Fs 0 dQ
dt
1
1
Uc = QV = CV 2
2
2
I= m ¥=
w=
Â=
Ú= K rp
12
I
2 1
1
=
Cs
i Ci m t = tÂ
=t ¥ r m Ci i ∑ Â
Â= mr mr 2 Cp = d ∑ = r 2 dm a
w u = w I net rcm
L m D = F 0A r u I r Q
V ∑ = r 2 0 q1 q 2
r Q
q
R
r
t
U
V =
=
=
=
=
=
=
=
=
m=
= k = u r C= 4 1 f Ú= ∑ 2 C= ∑ £ m ac UE = qV = r
u =
Ú= F dr
12
K
m
2
dW
P
dt
P Fv
Ug
mgh k N p D= = W = F fric p 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 p =Â
=u u dp
dt
F dt
mv ma =
=
=
=
=
=
=
=
=
L=
m=
N=
P=
p=
r=
r=
T=
t=
U=
=
W=
x=
=
=
=
=
= ∑ + J
p ( F Fnet  F ) = 2 0 a
F
f
h
I
J
K
k e + u u
2 12
at
2
2 a x x0 0t + = u x0 at + x 0 ELECTRICITY AND MAGNETISM
1 q1 q 2
A = area
F=
2
B = magnetic field
40r
C = capacitance
F
d = distance
E=
q
E = electric field
= emf
Q
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 0 i ri
P = power
p MECHANICS 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
area
circumference
volume
surface area
base
height
length
width
radius d f d f du
dx du dx
dn
x
nxn 1
dx
dx
e
ex
dx
1
d
1n x
dx
x
d
sin x cos x
dx
d
cos x
sin x
dx
1 n1
xn dx
x ,n
n1
ex dx ex
dx
ln x
x
cos xdx sin x
(
(
( =) ( =) = Ú = Ú Ú
Ú
4 sin xdx =
= p q a
b = p
p p Ú
b + p
p p 90° q + a cos x 1 π ( =) c b
c = =) q
q tan = =) cos  A=
C=
V=
S=
b=
h=
=
w=
r= = Rectangle
A = bh
Triangle
1
A = bh
2
Circle
A = r2
C=2r
Parallelepiped
V = wh
Cylinder
V = r2
S = 2 r + 2 r2
Sphere
43
V=
r
3
S = 4 r2
Right Triangle
a 2 + b2 = c2
a
sin =
c CALCULUS 2004 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
booklet in the spaces provided after each part, NOT in this green insert. E&M. 1.
The figure above left shows a hollow, infinite, cylindrical, uncharged conducting shell of inner radius r1 and
outer radius r2 . An infinite line charge of linear charge density
is parallel to its axis but off center. An
enlarged cross section of the cylindrical shell is shown above right. l+ (a) On the cross section above right,
i. sketch the electric field lines, if any, in each of regions I, II, and III and  ii. use + and signs to indicate any charge induced on the conductor. (b) In the spaces below, rank the electric potentials at points a, b, c, d, and e from highest to lowest
(1 = highest potential). If two points are at the same potential, give them the same number.
____ Va ____ Vb ____ Vc
____ Vd ____ Ve Copyright © 2004 by College Entrance Examination Board. All rights reserved.
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5 2004 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREERESPONSE QUESTIONS (c) The shell is replaced by another cylindrical shell that has the same dimensions but is nonconducting and
. The infinite line charge, still of charge density
, is located
carries a uniform volume charge density
at the center of the shell as shown above. Using Gauss’s law, calculate the magnitude of the electric field as
a function of the distance r from the center of the shell for each of the following regions. Express your
answers in terms of the given quantities and fundamental constants. r+ r1 £ r > r2 £ iii. r < ii. r1 l+ i. r r2 Copyright © 2004 by College Entrance Examination Board. All rights reserved.
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6 2004 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREERESPONSE QUESTIONS E&M. 2.
In the circuit shown above left, the switch S is initially in the open position and the capacitor C is initially
uncharged. A voltage probe and a computer (not shown) are used to measure the potential difference across the
capacitor as a function of time after the switch is closed. The graph produced by the computer is shown above
right. The battery has an emf of 20 V and negligible internal resistance. Resistor R1 has a resistance of 15 k
and the capacitor C has a capacitance of 20 µF. W (a) Determine the voltage across resistor R2 immediately after the switch is closed.
(b) Determine the voltage across resistor R2 a long time after the switch is closed.
(c) Calculate the value of the resistor R2.
(d) Calculate the energy stored in the capacitor a long time after the switch is closed. Copyright © 2004 by College Entrance Examination Board. All rights reserved.
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7 2004 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREERESPONSE QUESTIONS
(e) On the axes below, graph the current in R2 as a function of time from 0 to 15 s. Label the vertical axis with
appropriate values. Resistor R2 is removed and replaced with another resistor of lesser resistance. Switch S remains closed for a
long time.
(f) Indicate below whether the energy stored in the capacitor is greater than, less than, or the same as it was
with resistor R2 in the circuit.
____ Greater than ____ Less than ____ The same as Explain your reasoning. Copyright © 2004 by College Entrance Examination Board. All rights reserved.
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8 2004 AP® PHYSICS C: ELECTRICITY AND MAGNETISM
FREERESPONSE QUESTIONS E&M. 3.
A rectangular loop of dimensions 3 and 4 lies in the plane of the page as shown above. A long straight wire
also in the plane of the page carries a current I.
(a) Calculate the magnetic flux through the rectangular loop in terms of I, , and fundamental constants. Starting at time t = 0, the current in the long straight wire is given as a function of time t by
I0e  = It kt , where I 0 and k are constants. )( (b) The current induced in the loop is in which direction?
____ Clockwise ____ Counterclockwise Justify your answer.
The loop has a resistance R. Calculate each of the following in terms of R, I 0 , k,
(c) The current in the loop as a function of time t , and fundamental constants. (d) The total energy dissipated in the loop from t = 0 to t = ∞ END OF SECTION II, ELECTRICITY AND MAGNETISM Copyright © 2004 by College Entrance Examination Board. All rights reserved.
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 Physics, Electricity And Magnetism, Magnetism

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