1999 Electricity

1999 Electricity - AP Physics C: Electricity &...

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Unformatted text preview: AP Physics C: Electricity & Magnetism 1999 Free-Response Questions The materials included in these files are intended for non-commercial 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. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. This permission does not apply to any third-party copyrights contained herein. 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 dedicated to preparing, inspiring, and connecting students to college and opportunity. Founded in 1900, the association is composed of more than 3,900 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 admission, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT™, the Advanced Placement Program® (AP®), and Pacesetter®. 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. Copyright © 2001 by College Entrance Examination Board. All rights reserved. College Board, Advanced Placement Program, AP, and the acorn logo are registered trademarks of the College Entrance Examination Board. 1999 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. a E&M 1. An isolated conducting sphere of radius a = 0.20 m is at a potential of -2,000 V . (a) Determine the charge Q0 on the sphere. b a c r The charged sphere is then concentrically surrounded by two uncharged conducting hemispheres of inner radius b = 0.40 m and outer radius c = 0.50 m , which are joined together as shown above, forming a spherical capacitor. A wire is connected from the outer sphere to ground, and then removed. (b) Determine the magnitude of the electric field in the following regions as a function of the distance r from the center of the inner sphere. i. ii. iii. iv. r a b r < < < > a r<b r<c c (c) Determine the magnitude of the potential difference between the sphere and the conducting shell. (d) Determine the capacitance of the spherical capacitor. 1999 PHYSICS C—E & M B (out of page) O P a r E&M 2. A uniform magnetic field B exists in a region of space defined by a circle of radius a = 0.60 m as shown above. The magnetic field is perpendicular to the page and increases out of the page at a constant rate of 0.40 T/s . A single circular loop of wire of negligible resistance and radius r = 0.90 m is connected to a lightbulb with a resistance R = 5.0 W , and the assembly is placed concentrically around the region of magnetic field. (a) Determine the emf induced in the loop. (b) Determine the magnitude of the current in the circuit. On the figure above, indicate the direction of the current in the loop at point O. (c) Determine the total energy dissipated in the lightbulb during a 15 s interval. b a The experiment is repeated with a loop of radius b = 0.40 m placed concentrically in the same magnetic field as before. The same lightbulb is connected to the loop, and the magnetic field again increases out of the page at a rate of 0.40 T/s . Neglect any direct effects of the field on the lightbulb itself. (d) State whether the brightness of the bulb will be greater than, less than, or equal to the brightness of the bulb in part (a). Justify your answer. 1999 PHYSICS C—E & M y Q R z E&M 3. x The nonconducting ring of radius R shown above lies in the yz-plane and carries a uniformly distributed positive charge Q. (a) Determine the electric potential at points along the x-axis as a function of x. (b) i. Show that the x-component of the electric field along the x-axis is given by Ex = Qx 3 22 . 4π ò0 ( R + x ) 2 ii. What are the y- and z- components of the electric field along the x-axis? (c) Determine the following. i. The value of x for which E x is a maximum ii. The maximum electric field E x max 1999 PHYSICS C—E & M (d) On the axes below, sketch E x versus x for points on the x-axis from x = −2 R to x = +2 R . Ex 2R (e) R R 2R x An electron is placed at x = R /2 and released from rest. Qualitatively describe its subsequent motion. STOP END OF SECTION II, ELECTRICITY AND MAGNETISM ...
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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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