Fundamentals of Physics II: Electromagnetism, Optics, and Quantum Mechanics

563 Pages·2016·23.305 MB·English

by  Ramamurti Shankar

Fundamentals of Physics II
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Fundamentals of Physics II
Electromagnetism, Optics, and Quantum
Mechanics
R. SHANKAR
Yale
UNIVERSITY PRESS
New Haven and London
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Copyright © 2016 by Yale University.
All rights reserved.
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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).
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To Stella, Vesper, Matteo,
and the rest of G3.
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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.
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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
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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
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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
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14.2. Restricted Maxwell equations in vacuum
14.2.1. Maxwell equations involving infinitesimal cubes
14.2.2. Maxwell equations involving infinitesimal loops
14.3. The wave!
14.4. Sinusoidal solution to the wave equation
14.5. Energy in the electromagnetic wave
14.6. Origin of electromagnetic waves
14.7. Maxwell equations—the general case (optional)
14.7.1. Maxwell equations involving infinitesimal cubes
14.7.2. Maxwell equations involving infinitesimal loops
14.7.3. Consequences for the restricted E and B
14.8. From microscopic to macroscopic (optional)
14.8.1. Maxwell equations involving cubes
14.8.2. Maxwell equations involving loops
15. Electromagnetism and Relativity
15.1. Magnetism from Coulomb’s law and relativity
15.2. Relativistic invariance of electrodynamics
15.3. Review of Lorentz transformations
15.3.1. Implications for Newtonian mechanics
15.4. Scalar and vector fields
15.5. The derivative operator
15.6. Lorentz scalars and vectors
15.7. The four-current J
15.7.1. Charge conservation and the four-current J
15.8. The four-potential A
15.8.1. Gauge invariance
15.9. Wave equation for the four-vector A
15.9.1. Why work with V and A?
15.10. The electromagnetic tensor
15.10.1. Tensors
15.10.2. The electromagnetic field tensor
16. Optics I: Geometric Optics Revisited
16.1. Geometric or ray optics
16.2. Brief history of c
16.3. Some highlights of geometric optics
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