Classical Electrodynamics

Julian Schwinger, Lester L. Deraad Jr., Kimball Milton, Wu-Yang Tsai

• Éditeur: CRC Press
• Année: 2019
• ISBN:
  9780429983177
• Édition: 1
• Sujet: Physical Sciences
• Sous-sujet: Physics

Classical Electrodynamics captures Schwinger's inimitable lecturing style, in which everything flows inexorably from what has gone before. Novel elements of the approach include the immediate inference of Maxwell's equations from Coulomb's law and (Galilean) relativity, the use of action and stationary principles, the central role of Green's functions both in statics and dynamics, and, throughout, the integration of mathematics and physics. Thus, physical problems in electrostatics are used to develop the properties of Bessel functions and spherical harmonics. The latter portion of the book is devoted to radiation, with rather complete treatments of synchrotron radiation and diffraction, and the formulation of the mode decomposition for waveguides and scattering. Consequently, the book provides the student with a thorough grounding in electrodynamics in particular, and in classical field theory in general, subjects with enormous practical applications, and which are essential prerequisites for the study of quantum field theory.An essential resource for both physicists and their students, the book includes a?Reader's Guide,? which describes the major themes in each chapter, suggests a possible path through the book, and identifies topics for inclusion in, and exclusion from, a given course, depending on the instructor's preference. Carefully constructed problems complement the material of the text, and introduce new topics. The book should be of great value to all physicists, from first-year graduate students to senior researchers, and to all those interested in electrodynamics, field theory, and mathematical physics.The text for the graduate classical electrodynamics course was left unfinished upon Julian Schwinger's death in 1994, but was completed by his coauthors, who have brilliantly recreated the excitement of Schwinger's novel approach.

Chapter 1

Maxwell’s Equations

The teaching of electromagnetic theory is something like that of American History in school; you get it again and again. Well, this is the end of the line. Here is where we put it all together, and yet, not quite, since it is still classical electrodynamics and the final goal is quantum electrodynamics. This preoccupation reflects the all-pervasive nature of electromagnetism, with implications ranging from the farthest galaxies to the interiors of the fundamental particles. In particular, the properties of ordinary matter, including those properties classified as chemical and biological, depend only on electromagnetic forces, in conjunction with the microscopic laws of quantum mechanics.

1.1 Electrostatics

Our intention is to move toward the general picture as quickly as possible, starting with a review of electrostatics. We take for granted the phenomenology of electric charge, including the Coulomb law of force between charges of dimensions that are small in comparison with their separation. This is expressed by the interaction energy, E, of a system of such charges in otherwise empty space, a vacuum:

E=12∑a,ba≠beaebrab,(1.1)

where e_α is the charge of the at h particle while

rab=| ra−rb |(1.2)

is the separation between the αth and bth particles. (Throughout this book we use the Gaussian system of units. Connection with the SI units will be given in Appendix A.) As we shall see, this starting point, the Coulomb energy (1.1), summarizes all the experimental facts of electrostatics. The energy of interaction of an individual charge with the rest of the system can be emphasized by rewriting (1.1) as

E=12∑aea∑b≠aebrab=12∑aebϕa,(1.3)

where we have introduced the electrostatic potential at the location of the αth charge that is due to all the other charges,

ϕa=∑b≠aebrab.(1.4)

This is an action-at-a-distance point of view, in which the charge at a given point interacts with charges at other...

Table des matières

• Cover
• Title page
• Copyright Page
• Dedication Page
• Table of Contents
• Preface
• Reader’s Guide
• 1 Maxwell’s Equations
• 2 Magnetic Charge I
• 3 Conservation Laws
• 4 Macroscopic Electrodynamics
• 5 Simple Model for Constitutive Relations
• 6 Magnetic Properties of Matter
• 7 Macroscopic Energy and Momentum
• 8 Review of Action Principles
• 9 Action Principle for Electrodynamics
• 10 Einsteinian Relativity
• 11 Stationary Principles for Electrostatics
• 12 Introduction to Green’s Functions
• 13 Electrostatics in Free Space
• 14 Semi-Infinite Dielectric
• 15 Application of Green’s Function
• 16 Bessel Functions
• 17 Parallel Conducting Plates
• 18 Modified Bessel Functions
• 19 Cylindrical Conductors
• 20 Spherical Harmonics
• 21 Coulomb’s Potential
• 22 Multipoles
• 23 Conducting and Dielectric Spheres
• 24 Dielectrics and Conductors
• 25 Modes and Variations
• 26 Magnetostatics
• 27 Macroscopic Current Distributions
• 28 Magnetic Multipoles
• 29 Magnetic Scalar Potential
• 30 Magnetic Charge II
• 31 Retarded Green’s Function
• 32 Radiation—Field Point of View
• 33 Radiation—Source Point of View
• 34 Models of Antennas
• 35 Spectral Distribution of Radiation
• 36 Power Spectrum and Čerenkov Radiation
• 37 Constant Acceleration and Impulse
• 38 Synchrotron Radiation I
• 39 Synchrotron Radiation II—Polarization
• 40 Synchrotron Radiation III—High Energies
• 41 Propagation in a Dielectric Medium
• 42 Reflection by an Imperfect Conductor
• 43 Cylindrical Coordinates
• 44 Waveguides
• 45 Scattering by Small Obstacles
• 46 Partial-Wave Analysis of Scattering
• 47 Diffraction I
• 48 Diffraction II
• 49 Babinet’s Principle
• 50 General Scattering
• 51 Dispersion Relations for the Susceptibility
• 52 Charged Particle Energy Loss
• A Units
• B Bibliography
• Index