Unformatted text preview: AP® Physics C: Electricity and Magnetism 2010 FreeResponse Questions The College Board
The College Board is a notforprofit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the College Board is composed of more than 5,700 schools, colleges, universities and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,800 colleges through major programs and services in college readiness, college admission, guidance, assessment, financial aid and enrollment. Among its widely recognized programs are the SAT®, the PSAT/NMSQT®, the Advanced Placement Program® (AP®), SpringBoard® and ACCUPLACER®. The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities and concerns. © 2010 The College Board. College Board, ACCUPLACER, Advanced Placement Program, AP, AP Central, SAT, SpringBoard and the acorn logo are registered trademarks of the College Board. Admitted Class Evaluation Service is a trademark owned by the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. All other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at: www.collegeboard.com/inquiry/cbpermit.html. Visit the College Board on the Web: www.collegeboard.com. AP Central is the official online home for the AP Program: apcentral.collegeboard.com. TABLE OF INFORMATION FOR 2010 and 2011 CONSTANTS AND CONVERSION FACTORS 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 Avogadro’s number, N 0 = 6.02 ¥ 1023 mol1 Universal gas constant, Electron charge magnitude, e = 1.60 ¥ 10 19 C 1 electron volt, 1 eV = 1.60 ¥ 10 19 J Speed of light, Universal gravitational constant, Acceleration due to gravity at Earth’s surface, c = 3.00 ¥ 108 m s G = 6.67 ¥ 10 11 m 3 kgis2 R = 8.31 J (mol iK) g = 9.8 m s2 Boltzmann’s constant, k B = 1.38 ¥ 10 23 J K 1 unified atomic mass unit, Planck’s constant, Vacuum permittivity, Coulomb’s law constant, k = 1 4 p Vacuum permeability, 1 u = 1.66 ¥ 10 27 kg = 931 MeV c 2
h = 6.63 ¥ 10 34 J is = 4.14 ¥ 10 15 eV is hc = 1.99 ¥ 10 25 J im = 1.24 ¥ 103 eV i nm
0 0 = 8.85 ¥ 10 12 C2 N im 2 = 9.0 ¥ 109 N im 2 C2 m0 = 4 p ¥ 10 7 (T im) A Magnetic constant, k ¢ = m0 4 p = 1 ¥ 10 7 (T im) A 1 atmosphere pressure, meter, kilogram, second, ampere, kelvin, m kg s A K mole, hertz, newton, pascal, joule, mol Hz N Pa J 1 atm = 1.0 ¥ 105 N m 2 = 1.0 ¥ 105 Pa
watt, coulomb, volt, ohm, henry, W C V W H farad, tesla, degree Celsius, electronvolt, F T ∞C eV UNIT SYMBOLS PREFIXES Factor
10
9 VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES Symbol G M k c m Prefix giga mega kilo centi milli micro nano pico q sin q
cos q tan q 0 30 37 45 53 60 90 0 1 0 12
32 33 35 45 34 22 22
1 45 35 43 32 1 0 106 103 10 2 10 3 10 6 10 9 10
1 2 12
3 • m
n 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 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2010 and 2011 MECHANICS ELECTRICITY AND MAGNETISM u = u0 + at x = x0 + u0 t + 12 at 2 u 2 = u0 2 + 2 a ( x  x0 ) Â F = Fnet = ma
F= dp dt a F f h I J K k J = Ú F dt = Dp p = mv
Ffric £ m N W= K= P= Ú F i dr
1 mu 2 2 dW dt P = Fiv DUg = mgh = = = = = = = = = 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 F=
E= 1 q1q2 4p 0 r 2
F q Q
0 A B C d E Ú E i dA =
E=V= dV dr 1 4p 0 Â rii
i q = = = = = e= F= I= J= L= = n= N= UE = qV =
C= C= Q V k
0A 1 4p 0 q1q2 r d Cp = Â Ci
i 1 1 =Â Cs i Ci dQ I= dt Uc = 1 1 QV = CV 2 2 2 P= Q= q= R= r= t= U= V= u= r= 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 fm = magnetic flux k = dielectric constant ac = u2 = w2r r Fs =  kx t=r¥F
Â t = t net = I a I = Ú r 2 dm = Â mr 2 Ú Bid
dB =
F= = m0 I Us = T= 12 kx 2 R= 2p 1 = w f r A m0 I d ¥ r 4p r3
¥B E = rJ I = Neud A ÚI d rcm = Â mr Â m
u = rw Ts = 2 p
Tp = 2 p
FG =  m k
g ˆ r Bs = m0 nI
fm = Ú B i dA V = IR
Rs = L = r ¥ p = Iw
K=
12 Iw 2 Â Ri
i e
i = Gm1m2 r2 1 = Rp ÂR
i 1 Ú Eid
dI dt
12 LI 2 = d fm dt e = L w = w0 + at q = q0 + w0 t +
12 at 2 UG =  Gm1m2 r P = IV FM = qv ¥ B UL = 3 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2010 and 2011 GEOMETRY AND TRIGONOMETRY Rectangle A = bh Triangle A= C= V= S= b= h= = w= r= area circumference volume surface area base height length width radius CALCULUS df d f du = dx du dx
dn ( x ) = nx n 1 dx dx (e ) = e x dx d (ln x ) = 1 dx x d (sin x ) = cos x dx d (cos x ) =  sin x dx A=
Circle 1 bh 2 A = pr 2 C = 2pr Parallelepiped V = wh Cylinder
V = pr 2 S = 2pr + 2pr 2
Sphere Úx
Úe n dx = 1 x n + 1 , n π 1 n +1 x dx = e x V= 43 pr 3 Ú dx = ln x x S = 4pr 2
Right Triangle Ú cos x dx = sin x Ú sin x dx =  cos x
c q b 90° a a 2 + b2 = c2
sin q = cos q = tan q = a c b c a b 4 2010 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 charge +Q is uniformly distributed over a quarter circle of radius R, as shown above. Points A, B, and C are located as shown, with A and C located symmetrically relative to the xaxis. Express all algebraic answers in terms of the given quantities and fundamental constants. (a) Rank the magnitude of the electric potential at points A, B, and C from greatest to least, with number 1 being greatest. If two points have the same potential, give them the same ranking. ____ VA ____ VB ____ VC Justify your rankings. Point P is at the origin, as shown below, and is the center of curvature of the charge distribution. © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. 5 2010 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREERESPONSE QUESTIONS
(b) Determine an expression for the electric potential at point P due to the charge Q. (c) A positive point charge q with mass m is placed at point P and released from rest. Derive an expression for the speed of the point charge when it is very far from the origin. (d) On the dot representing point P below, indicate the direction of the electric field at point P due to the charge Q. (e) Derive an expression for the magnitude of the electric field at point P. E&M. 2. In the circuit illustrated above, switch S is initially open and the battery has been connected for a long time. (a) What is the steadystate current through the ammeter? (b) Calculate the charge on the 10 mF capacitor. (c) Calculate the energy stored in the 5.0 mF capacitor. The switch is now closed, and the circuit comes to a new steady state. (d) Calculate the steadystate current through the battery. (e) Calculate the final charge on the 5.0 mF capacitor. (f) Calculate the energy dissipated as heat in the 40 W resistor in one minute once the circuit has reached steady state. © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. 6 2010 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREERESPONSE QUESTIONS E&M. 3. The long straight wire illustrated above carries a current I to the right. The current varies with time t according to the equation I = I 0  Kt , where I 0 and K are positive constants and I remains positive throughout the time period of interest. The bottom of a rectangular loop of wire of width b and height a is located a distance d above the long wire, with the long wire in the plane of the loop as shown. A lightbulb with resistance R is connected in the loop. Express all algebraic answers in terms of the given quantities and fundamental constants. (a) Indicate the direction of the current in the loop. ____Clockwise Justify your answer. (b) Indicate whether the lightbulb gets brighter, gets dimmer, or stays the same brightness over the time period of interest. ____Gets brighter Justify your answer. (c) Determine the magnetic field at t = 0 due to the current in the long wire at distance r from the long wire. (d) Derive an expression for the magnetic flux through the loop as a function of time. (e) Derive an expression for the power dissipated by the lightbulb. ____Gets dimmer ____Remains the same ____Counterclockwise END OF EXAM © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. 7 ...
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 Electron, pH, Magnetic Field, Electric charge, The College Board

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