2003 Electricity

2003 Electricity - AP® Physics C Electricity& Magnetism...

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Unformatted text preview: AP® Physics C: Electricity & Magnetism 2003 Free-Response Questions The materials included in these files are intended for use by AP teachers for course and exam preparation; permission for any other use must be sought from the Advanced Placement Program®. Teachers may reproduce them, in whole or in part, in limited quantities for noncommercial, face-to-face teaching purposes. This permission does not apply to any third-party copyrights contained herein. This material may not be mass distributed, electronically or otherwise. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. These materials were produced by Educational Testing Service® (ETS®), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and their programs, services, and employment policies are guided by that principle. The College Board is a national nonprofit membership association whose mission is to prepare, inspire, and connect students to college and opportunity. Founded in 1900, the association is composed of more than 4,300 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 22,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of equity and excellence, and that commitment is embodied in all of its programs, services, activities, and concerns. For further information, visit www.collegeboard.com Copyright © 2003 College Entrance Examination Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Vertical Teams, APCD, Pacesetter, Pre-AP, SAT, Student Search Service, and the acorn logo are registered trademarks of the College Entrance Examination Board. AP Central is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service. Other products and services may be trademarks of their respective owners. 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 ˆ 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=r™F 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 œ 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 ž -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 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. 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 ˆ 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 ˆ R . 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. 5 2003 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE 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 data-fitting program finds that the current decays according to the equation i(t ) = e e-t 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 students and parents at www.collegeboard.com/apstudents. GO ON TO THE NEXT PAGE. 6 2003 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE 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 FREE-RESPONSE 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 students and parents at www.collegeboard.com/apstudents. GO ON TO THE NEXT PAGE. 8 2003 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE 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.

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