AP Physics C: Electricity and Magnetism 2004 Free-Response Questions

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1 AP Physics C: Electricity an Magnetism 004 Free-Response Questions The materials inclue in these files are intene for noncommercial use by AP teachers for course an exam preparation; permission for any other use must be sought from the Avance Placement Program. Teachers may reprouce them, in whole or in part, in limite quantities, for face-to-face teaching purposes but may not mass istribute the materials, electronically or otherwise. This permission oes not apply to any thir-party copyrights containe herein. These materials an any copies mae of them may not be resol, an the copyright notices must be retaine as they appear here. The College Boar is a not-for-profit membership association whose mission is to connect stuents to college success an opportunity. Foune in 900, the association is compose of more than 4,500 schools, colleges, universities, an other eucational organizations. Each year, the College Boar serves over three million stuents an their parents, 3,000 high schools, an 3,500 colleges through major programs an services in college amissions, guiance, assessment, financial ai, enrollment, an teaching an learning. Among its best-known programs are the SAT, the PSAT/NMSQT, an the Avance Placement Program (AP ). The College Boar is committe to the principles of excellence an equity, an that commitment is emboie in all of its programs, services, activities, an concerns. For further information, visit Copyright 004 College Entrance Examination Boar. All rights reserve. College Boar, Avance Placement Program, AP, AP Central, AP Vertical Teams, APCD, Pacesetter, Pre-AP, SAT, Stuent Search Service, an the acorn logo are registere traemarks of the College Entrance Examination Boar. PSAT/NMSQT is a registere traemark jointly owne by the College Entrance Examination Boar an the National Merit Scholarship Corporation. Eucational Testing Service an ETS are registere traemarks of Eucational Testing Service. Other proucts an services may be traemarks of their respective owners. For the College Boar s online home for AP professionals, visit AP Central at apcentral.collegeboar.com.

2 TABLE OF INFORMATION FOR 004 an 005 CONSTANTS AND CONVERSION FACTORS - unifie atomic mass unit, u kg 93 MeV/ c Proton mass, m p kg Neutron mass, m n kg Electron mass, m e kg Magnitue of the electron charge, e C Avogaro s number, N mol Universal gas constant, R 83. J/ ( mol K ) Boltzmann s constant, k B J/K Spee of light, c ms / Planck s constant, h Js ev s 5 hc J m ev nm Vacuum permittivity, C / N m 9 Coulomb s law constant, k / 4π Nm / C 7 Vacuum permeability, µ 0 4π 0 ( Tm) / A Magnetic constant, k' µ / 4π 0 7 ( T m) / A 0 Universal gravitational constant, G m 3 / kg s Acceleration ue to gravity at the Earth s surface, g 98. m/s atmosphere pressure, atm N / m Pa electron volt, ev J UNITS Name Symbol meter kilogram secon ampere kelvin mole hertz newton pascal joule watt coulomb volt ohm henry fara tesla egree Celsius electronvolt m kg s A K mol Hz N Pa J W C V Ω H F T C ev PREFIXES Factor Prefix Symbol 0 9 giga G 0 6 mega M 0 3 kilo k 0 centi c 0 milli m 0 6 micro µ 0 9 nano n 0 pico p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES θ sin θ cos θ tan θ / 3 / 33 / 37 3/5 4/5 3/4 45 / / 53 4/5 3/5 4/ / / The following conventions are use in this examination. I. Unless otherwise state, the frame of reference of any problem is assume to be inertial. II. The irection of any electric current is the irection of flow of positive charge (conventional current). III. For any isolate electric charge, the electric potential is efine as zero at an infinite istance from the charge.

3 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 004 an 005 MECHANICS u u0 + at a acceleration F force x x0 + u0t + at f frequency h height u u0 + a( x - x0) I rotational inertia Â F Fnet ma J impulse K kinetic energy p F k spring constant t l length J Ú Ft Dp L angular momentum m mass p mv N normal force Ffric mn P power p momentum W ÚF r r raius or istance K m r position vector u T perio W t time P t U potential energy u P Fv velocity or spee W work one on a system DUg mgh x position m coefficient of friction u ac w r r q angle t torque t r F w angular spee Â t tnet Ia a angular acceleration I Ú r m Â mr rcm Âmr Âm u r w L r p Iw K w w w0 + a q q0 + w0t + at F U T T T s s s F U p G G I t kx kx p w f m p k - p g Gm m r Gm m r - - l rˆ ELECTRICITY AND MAGNETISM qq A area F 4p r B magnetic fiel 0 E F C capacitance istance q E electric fiel Q e emf E A F force 0 I current V E L inuctance r l length q n number of loops of wire i V per unit length 4p 0 i ri P power qq Q charge UE qv 4p 0 r q point charge C Q R resistance r istance V t time k 0 A U potential or store energy C V electric potential u velocity or spee Cp Ci r resistivity i f m magnetic flux k ielectric constant Cs i Ci Q I t Uc QV CV rl R A V IR R R s i i R R p i i P IV FM qv B B m I 0 F z I B Bs m0ni fm z B A fm e t e L I t UL LI 3

4 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 004 an 005 GEOMETRY AND TRIGONOMETRY CALCULUS Rectangle A bh Triangle A bh Circle A pr C pr Parallelepipe V lwh Cyliner V pr l S prl + pr Sphere V 4 3 pr 3 S 4pr Right Triangle a + b c sin q a c b cos q c tan q a b A area C circumference V volume S surface area b base h height l length w with r raius q c b 90 a f f u x u x ( x n ) nx n- x ( e x x ) e x ( n x) x x ( sin x) cos x x ( cos x) -sinx x, n n+ Ú xx x n π - n + x x Ú ex x ln x x cos xx sin x Ú sin xx e Ú Ú - cos x 4

004 AP PHYSICS C: ELECTRICITY AND MAGNETISM PHYSICS C Section II, ELECTRICITY AND MAGNETISM Time 45 minutes 3 Questions Directions: Answer all three questions.

5 004 AP PHYSICS C: ELECTRICITY AND MAGNETISM PHYSICS C Section II, ELECTRICITY AND MAGNETISM Time 45 minutes 3 Questions Directions: Answer all three questions. The suggeste time is about 5 minutes for answering each of the questions, which are worth 5 points each. The parts within a question may not have equal weight. Show all your work in the booklet in the spaces provie after each part, NOT in this green insert. E&M.. The figure above left shows a hollow, infinite, cylinrical, uncharge conucting shell of inner raius r an outer raius r. An infinite line charge of linear charge ensity + l is parallel to its axis but off center. An enlarge cross section of the cylinrical shell is shown above right. (a) On the cross section above right, i. sketch the electric fiel lines, if any, in each of regions I, II, an III an ii. use + an - signs to inicate any charge inuce on the conuctor. (b) In the spaces below, rank the electric potentials at points a, b, c,, an e from highest to lowest ( highest potential). If two points are at the same potential, give them the same number. V a V b V c V V e Copyright 004 by College Entrance Examination Boar. All rights reserve. 5 GO ON TO THE NEXT PAGE.

6 004 AP PHYSICS C: ELECTRICITY AND MAGNETISM (c) The shell is replace by another cylinrical shell that has the same imensions but is nonconucting an carries a uniform volume charge ensity + r. The infinite line charge, still of charge ensity + l, is locate at the center of the shell as shown above. Using Gauss s law, calculate the magnitue of the electric fiel as a function of the istance r from the center of the shell for each of the following regions. Express your answers in terms of the given quantities an funamental constants. i. r < r ii. r r r iii. r > r Copyright 004 by College Entrance Examination Boar. All rights reserve. 6 GO ON TO THE NEXT PAGE.

7 004 AP PHYSICS C: ELECTRICITY AND MAGNETISM E&M.. In the circuit shown above left, the switch S is initially in the open position an the capacitor C is initially uncharge. A voltage probe an a computer (not shown) are use to measure the potential ifference across the capacitor as a function of time after the switch is close. The graph prouce by the computer is shown above right. The battery has an emf of 0 V an negligible internal resistance. Resistor R has a resistance of 5 kw an the capacitor C has a capacitance of 0 µf. (a) Determine the voltage across resistor R immeiately after the switch is close. (b) Determine the voltage across resistor R a long time after the switch is close. (c) Calculate the value of the resistor R. () Calculate the energy store in the capacitor a long time after the switch is close. Copyright 004 by College Entrance Examination Boar. All rights reserve. 7 GO ON TO THE NEXT PAGE.

8 004 AP PHYSICS C: ELECTRICITY AND MAGNETISM (e) On the axes below, graph the current in R as a function of time from 0 to 5 s. Label the vertical axis with appropriate values. Resistor R is remove an replace with another resistor of lesser resistance. Switch S remains close for a long time. (f) Inicate below whether the energy store in the capacitor is greater than, less than, or the same as it was with resistor R in the circuit. Greater than Less than The same as Explain your reasoning. Copyright 004 by College Entrance Examination Boar. All rights reserve. 8 GO ON TO THE NEXT PAGE.

9 004 AP PHYSICS C: ELECTRICITY AND MAGNETISM E&M. 3. A rectangular loop of imensions 3 l an 4 l 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, l, an funamental constants. Starting at time t 0, the current in the long straight wire is given as a function of time t by I ( t) I0e -kt, where I 0 an k are constants. (b) The current inuce in the loop is in which irection? Clockwise Counterclockwise Justify your answer. The loop has a resistance R. Calculate each of the following in terms of R, I 0, k, l, an funamental constants. (c) The current in the loop as a function of time t () The total energy issipate in the loop from t 0 to t END OF SECTION II, ELECTRICITY AND MAGNETISM Copyright 004 by College Entrance Examination Boar. All rights reserve. 9

AP Physics C: Mechanics 2004 Free-Response Questions

AP Physics C: Mechanics 2004 Free-Response Questions AP Physics C: Mechanics 004 Free-Response Questions The materials inclue in these files are intene for noncommercial use by AP teachers for course an exam preparation; permission for any other use must