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Unformatted text preview: AP® Physics C: Electricity and Magnetism
2007 FreeResponse Questions The College Board: Connecting Students to College Success
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AP Central is the official online home for the AP Program: apcentral.collegeboard.com. TABLE OF INFORMATION FOR 2006 and 2007
UNITS
CONSTANTS AND CONVERSION FACTORS PREFIXES 1 u = 1.66 ¥ 10 27 kg Name = 931 MeV c 2 1 unified atomic mass unit, meter m kilogram kg Proton mass, m p = 1.67 ¥ 10 27 kg Neutron mass, mn = 1.67 ¥ 10 27 kg Electron mass, me = 9.11 ¥ 10 31 kg Boltzmann’s constant, second kelvin K 10 R = 8.31 J (mol iK) mole mol k B = 1.38 ¥ 10 23 J /K hertz Hz h = 6.63 ¥ 10 34 J is newton N pascal Pa joule J = 1.24 ¥ 103 eV i nm watt W 8.85 ¥ 10 12 C2 N im 2 coulomb = 9.0 ¥ 109 N im 2 C2 hc = 1.99 ¥ 10 25 J im Magnetic constant,
Universal gravitational constant,
Acceleration due to gravity
at Earth’s surface,
1 atmosphere pressure, mega 10 12 m nano 10 9 m micro 6 c milli 3 k centi 2 M kilo 3 n pico p VALUES OF
TRIGONOMETRIC
FUNCTIONS FOR COMMON
ANGLES k = 1 4p 0 m0 = 4 p ¥ 10 7 (T im) A
k ¢ = m0 /4 p = 10 7 (T ◊ m) A
G = 6.67 ¥ 10 11 m 3 kgis2
g = 9.8 m s 2 1 atm = 1.0 ¥ 105 N m 2
1 eV = 1.60 ¥ 10 19 J q sin q C 0 0 1 0 volt V 30 1/2 3 /2 3 /3 ohm W henry H 37 3/5 4/5 3/4 farad F 45 2 /2 2 /2 1 tesla 0= = 1.0 ¥ 105 Pa 1 electron volt, 10 N 0 = 6.02 ¥ 1023 mol 1 = 4.14 ¥ 10 15 eVis Vacuum permeability, 10 s 10 c = 3.00 ¥ 108 m s Prefix Symbol
giga
G 9 106 A Planck’s constant, Coulomb’s law constant, 10 ampere Speed of light, Vacuum permittivity, Factor e = 1.60 ¥ 10 19 C Electron charge magnitude,
Avogadro’s number,
Universal gas constant, Symbol cos q tan q T 53 4/5 3/5 4/3 degree
Celsius ∞C 60 3 /2 1/2 3 electronvolt eV 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 2006 and 2007
MECHANICS
u = u0 + at
x = x0 + u0 t + 12
at
2 u 2 = u02 + 2 a ( x  x0 )
Â F = Fnet = ma F= dp
dt J = Ú F dt = Dp
p = mv
F fric £ m N
W= ÚF K= 12
mu
2 P= dW
dt ∑ dr P=Fv DUg = mgh
ac = a
F
f
h
I
J
K
k =
=
=
=
=
=
=
=
=
L=
m=
N=
P=
p=
r=
r=
T=
t=
U=
u=
W=
x=
m=
q=
t=
w=
a= 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 u
= w2 r
r Fs =  k x
Us = Â t = t net = I a
I = Ú r dm = Â mr
2 2 rcm = Â mr Â m E= F
q ÚE T= 12
kx
2 L = r ¥ p = Iw
12
Iw
2 FG =  w = w0 + at UG = 12
at
2 r2
Gm1m2
r q Â rii 1
4p 0 V= i UE = qV = 1 q1q2
4p 0 r Q
V C= 0A k C= d Â Ci Cp = i 1
1
=Â
Cs
Ci
i
dQ
dt r
A V = IR
Rs =
ˆ
r Â Ri 1
=
Rp 1 ÂR i P = IV
FM = qv ¥ B 3 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
magnetic flux
dielectric constant N=
P
Q
q
R
r
t
U =
=
=
=
=
=
=
V=
u=
r=
fm =
k= ÚB ∑ d = m0 I dB = m0 I d ¥ r
4p r 3 ÚI d ¥B Bs = m0 nI fm = Ú B ∑ d A
d fm
dt e i i n =
=
=
=
=
=
=
=
=
=
=
= F= I = Neud A g Gm1m2 dV
dr E= E = rJ m
k Tp = 2 p F
I
J
L 0 R= 2p
1
=
f
w Ts = 2 p dA= ∑ A
B
C
d
E e Q 1
1
Uc = QV = CV 2
2
2 u = rw q = q0 + w0t + 1 q1q2
4p 0 r 2 I= 2 t=r¥F K= F= = e = L UL = dI
dt 12
LI
2 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2006 and 2007
GEOMETRY AND TRIGONOMETRY
Rectangle
A = bh
Triangle
A= 1
bh
2 Circle
A = pr2
C = 2p r
Parallelepiped
V = wh
Cylinder A=
C=
V=
S=
b=
h=
=
w=
r= CALCULUS
df
d f du
=
dx
du dx area
circumference
volume
surface area
base
height
length
width
radius dn
( x ) = nxn  1
dx
dx
(e ) = e x
dx
d
(1n x ) = 1
dx
x
d
(sin x ) = cos x
dx
d
(cos x ) =  sin x
dx V = pr2 Sphere
43
pr
3 a
c tan q = dx = e x dx
= ln x
x Ú sin x dx =  cos x a 2 + b2 = c 2 b
c x Ú cos x dx = sin x Right Triangle cos q = dx = Ú S = 4p r 2 sin q = n Úe S = 2p r + 2p r 2
V= 1
x n + 1 , n π 1
n +1 Úx c a
90° q a
b b 4 2007 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREERESPONSE QUESTIONS
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. Show all your work in the
pink booklet in the spaces provided after each part, NOT in this green insert. E&M 1. A student sets up the circuit above in the lab. The values of the resistance and capacitance are as shown, but the
constant voltage e delivered by the ideal battery is unknown. At time t = 0, the capacitor is uncharged and the
student closes the switch. The current as a function of time is measured using a computer system, and the following
graph is obtained. (a) Using the data above, calculate the battery voltage e. (b) Calculate the voltage across the capacitor at time t = 4.0 s.
(c) Calculate the charge on the capacitor at t = 4.0 s. © 2007 The College Board. All rights reserved.
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5 2007 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREERESPONSE QUESTIONS
(d) On the axes below, sketch a graph of the charge on the capacitor as a function of time. (e) Calculate the power being dissipated as heat in the resistor at t = 4.0 s.
(f) The capacitor is now discharged, its dielectric of constant k = 1 is replaced by a dielectric of constant k = 3 ,
and the procedure is repeated. Is the amount of charge on one plate of the capacitor at t = 4.0 s now greater than,
less than, or the same as before? Justify your answer.
_____Greater than _____Less than _____The same © 2007 The College Board. All rights reserved.
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6 2007 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREERESPONSE QUESTIONS E&M 2. In the figure above, a nonconducting solid sphere of radius a with charge +Q uniformly distributed throughout
its volume is concentric with a nonconducting spherical shell of inner radius 2a and outer radius 3a that has a
charge Q uniformly distributed throughout its volume. Express all answers in terms of the given quantities and
fundamental constants.
(a) Using Gauss’s law, derive expressions for the magnitude of the electric field as a function of radius r in the
following regions.
i. Within the solid sphere ( r < a )
ii. Between the solid sphere and the spherical shell ( a < r < 2 a )
iii. Within the spherical shell ( 2 a < r < 3a )
iv. Outside the spherical shell ( r > 3a )
(b) What is the electric potential at the outer surface of the spherical shell ( r = 3a )? Explain your reasoning.
(c) Derive an expression for the electric potential difference VX  VY between points X and Y shown in the figure. © 2007 The College Board. All rights reserved.
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7 2007 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREERESPONSE QUESTIONS E&M 3. In the diagram above, a nichrome wire of resistance per unit length l is bent at points P and Q to form horizontal
conducting rails that are a distance L apart. The wire is placed within a uniform magnetic field of magnitude B
pointing into the page. A conducting rod of negligible resistance, which was aligned with end PQ at time t = 0, slides
to the right with constant speed u and negligible friction. Express all algebraic answers in terms of the given
quantities and fundamental constants.
(a) Indicate the direction of the current induced in the circuit.
______Clockwise ______Counterclockwise Justify your answer.
(b) Derive an expression for the magnitude of the induced current as a function of time t.
(c) Derive an expression for the magnitude of the magnetic force on the rod as a function of time.
(d) On the axes below, sketch a graph of the external force Fext as a function of time that must be applied to the rod
to keep it moving at constant speed while in the field. Label the values of any intercepts. (e) The force pulling the rod is now removed. Indicate whether the speed of the rod increases, decreases, or remains
the same.
______Increases _____Decreases ______Remains the same Justify your answer. END OF EXAM
© 2007 The College Board. All rights reserved.
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 Spring '10
 mr.donald
 Physics, Electricity And Magnetism, Magnetism

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