Table Of Content

Fundamentals of Physics II THE OPEN YALE COURSES SERIES is designed to bring the depth and breadth of a Yale education to a wide variety of readers. Based on Yale’s Open Yale Courses program (http://oyc.yale.edu), these books bring outstanding lectures by Yale faculty to the curious reader, whether student or adult. Covering a wide variety of topics across disciplines in the social sciences, physical sciences, and humanities, Open Yale Courses books offer accessible introductions at affordable prices. The production of Open Yale Courses for the Internet was made possible by a grant from the William and Flora Hewlett Foundation. TITLES IN THIS SERIES Paul H. Fry, Theory of Literature Roberto González Echevarría, Cervantes’ “Don Quixote” Christine Hayes, Introduction to the Bible Shelly Kagan, Death Dale B. Martin, New Testament History and Literature Giuseppe Mazzotta, Reading Dante R. Shankar, Fundamentals of Physics: Mechanics, Relativity, and Thermodynamics R. Shankar, Fundamentals of Physics II: Electromagnetism, Optics, and Quantum Mechanics Ian Shapiro, The Moral Foundations of Politics Steven B. Smith, Political Philosophy Fundamentals of Physics II Electromagnetism, Optics, and Quantum Mechanics R. SHANKAR Yale UNIVERSITY PRESS New Haven and London Copyright © 2016 by Yale University. All rights reserved. This book may not be reproduced, in whole or in part, including illustrations, in any form (beyond that copying permitted by Sections 107 and 108 of the U.S. Copyright Law and except by reviewers for the public press), without written permission from the publishers. Yale University Press books may be purchased in quantity for educational, business, or promotional use. For information, please e-mail [email protected] (U.S. office) or [email protected] (U.K. office). Set in Minion type by Newgen North America. Printed in the United States of America. ISBN: 978-0-300-21236-5 (pbk. : alk. paper) Library of Congress Control Number: 2015956862 A catalogue record for this book is available from the British Library. This paper meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). 10 9 8 7 6 5 4 3 2 1 To Stella, Vesper, Matteo, and the rest of G3. Deep and original, but also humble and generous, the physicist Josiah Willard Gibbs spent much of his life at Yale University. His father was a professor of sacred languages at Yale, and Gibbs received his bachelor’s and doctorate degrees from the university before teaching there until his death in 1903. The sculptor Lee Lawrie created the memorial bronze tablet pictured above, which was installed in Yale’s Sloane Physics Laboratory in 1912. It now resides in the entrance to the J. W. Gibbs Laboratories, Yale University. His life and work continue to inspire the author as they do everyone who is familiar with them. Contents Preface 1. Electrostatics I 1.1. Review of F = ma 1.2. Enter electricity 1.3. Coulomb’s law 1.4. Properties of charge 1.4.1. Superposition principle 1.5. Verifying Coulomb’s law 1.6. The ratio of gravitational to electric forces 1.7. Coulomb’s law for continuous charge density 2. The Electric Field 2.1. Review of key ideas 2.2. Digression on nuclear forces 2.3. The electric field E 2.4. Visualizing the field 2.5. Field of a dipole 2.5.1. Far field of dipole: general case 2.6. Response to a field 2.6.1. Dipole in a uniform field 3. Gauss’s Law I 3.1. Field of an infinite line charge 3.2. Field of an infinite sheet of charge 3.3. Spherical charge distribution: Gauss’s law 3.4. Digression on the area vector dA 3.4.1. Composition of areas 3.4.2. An application of the area vector 3.5. Gauss’s law through pictures 3.5.1. Continuous charge density 4. Gauss’s Law II: Applications 4.1. Applications of Gauss’s law 4.2. Field inside a shell 4.3. Field of an infinite charged wire, redux 4.4. Field of an infinite plane, redux 4.5. Conductors 4.5.1. Field inside a perfect conductor is zero 4.5.2. The net charge on a conductor will reside at the surface 4.5.3. A conductor with a hole inside 4.5.4. Field on the surface of a conductor 5. The Coulomb Potential 5.1. Conservative forces and potential energy 5.2. Is the electrostatic field conservative? 5.3. Path independence through pictures 5.4. Potential and field of a dipole 6. Conductors and Capacitors 6.1. Cases where computing V from E is easier 6.2. Visualizing V 6.3. Equipotentials 6.4. Method of images 6.4.1. Proof of uniqueness (optional section) 6.4.2. Additional properties of the potential V(r) 6.5. Capacitors 6.6. Energy stored in a capacitor 6.7. Energy of a charge distribution 7. Circuits and Currents 7.1. Energy in the electric field 7.2. Circuits and conductivity 7.3. Circuits 7.4. The battery and the EMF 7.5. The RC circuit with a battery 7.6. Miscellaneous circuits 8. Magnetism I 8.1. Experiments pointing to magnetism 8.2. Examples of the Lorentz force, the cyclotron 8.3. Lorentz force on current-carrying wires 8.4. The magnetic dipole 8.5. The DC motor 9. Magnetism II: Biot-Savart Law 9.1. Practice with Biot-Savart: field of a loop 9.2. Microscopic description of a bar magnet 9.3. Magnetic field of an infinite wire 9.4. Ampère’s law 9.5. Maxwell’s equations (static case) 10. Ampère II, Faraday, and Lenz 10.1. Field of an infinite wire, redux 10.2. Field of a solenoid 10.3. Faraday and Lenz 10.4. Optional digression on Faraday’s law 11. More Faraday 11.1. Betatron 11.2. Generators 11.3. Inductance 11.4. Mutual inductance 11.5. Self-inductance 11.6. Energy in the magnetic field 12. AC Circuits 12.1. Review of inductors 12.2. The LC circuit 12.2.1. Driven LC circuit 12.3. The LCR circuit 12.3.1. Review of complex numbers 12.3.2. Solving the LCR equation 12.3.3. Visualizing Z 12.4. Complex form of Ohm’s law 13. LCR Circuits and Displacement Current 13.1. Analysis of LCR results 13.1.1. Transients and the complementary solution 13.2. Power of the complex numbers 13.3. Displacement current 14. Electromagnetic Waves 14.1. The wave equation