2004 Electricity

2004 Electricity - AP® Physics C Electricity and Magnetism...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: AP® Physics C: Electricity and Magnetism 2004 Free-Response Questions The materials included in these files are intended for noncommercial 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 face-to-face teaching purposes but may not mass distribute the materials, electronically or otherwise. This permission does not apply to any third-party copyrights contained herein. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 4,500 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 23,000 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 excellence and equity, and that commitment is embodied in all of its programs, services, activities, and concerns. For further information, visit www.collegeboard.com Copyright © 2004 College Entrance Examination Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, AP Vertical Teams, APCD, Pacesetter, Pre-AP, SAT, Student Search Service, and the acorn logo are registered trademarks of 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 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 = t =t ¥ r m Ci i ∑  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 = =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 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 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. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). GO ON TO THE NEXT PAGE. 5 2004 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE 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. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). GO ON TO THE NEXT PAGE. 6 2004 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE 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. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). GO ON TO THE NEXT PAGE. 7 2004 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE 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. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). GO ON TO THE NEXT PAGE. 8 2004 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE 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. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 9 ...
View Full Document

Ask a homework question - tutors are online