Modern Problems in Classical Electrodynamics

by Brau, Charles A.

• ISBN13: 9780195146653
• ISBN10: 0195146654
• Format: Hardcover
• Copyright: 2003-09-18
• Publisher: Oxford University Press

Summary

Designed as an upper-level undergraduate/beginning graduate text and as a reference for research scientists, Modern Problems in Classical Electrodynamics addresses a wide range of topics in modern physics--including lasers and nonlinear optics--that are not found in other texts. The bookbegins with relativistic mechanics and field theory, partly because they lend unity and beauty to electrodynamics, and also because relativistic concepts appear frequently throughout the book. Electrostatics and magnetostatics, waves, continuous media, nonlinear optics, diffraction, and radiation bymoving particles are then covered in depth. The book concludes by returning to basics, discussing the fundamental problems inherent in the classical theory of electrons. Modern Problems in Classical Electrodynamics features examples and homework exercises drawn from condensed-matter physics, particle physics, optics, and atomic physics. Many of these are experimentally oriented and help to make the book interesting and relevant to a broad audience. An instructor'smanual including answers to the homework exercises is available to adopters. An accompanying website, http://www.physics.vanderbilt.edu/brau/book/Index.html, contains errata and additional homework exercises that instructors can use to supplement the exercises in the text.

Author Biography

Charles A. Brau received his B.A. in Engineering from Cornell University and his M.A. (in Engineering) and Ph.D. in Applied Physics from Harvard University. In the course of his career, he has been a theorist, an experimenter, a manager, and currently a professor of physics at the Vanderbilt University in Nashville, Tennessee. He focuses his research on free-electron lasers (FEL) and electron beams. He became a program manager of the FEL program at Los Alamos National Laboratory and then a director of the FEL Center at Vanderbilt University. In 1988 he was a visiting scientist in the Department of Nuclear Physics at the University of Oxford in England. He is an author of 7 patents and numerous publications, including 2 books. He is also a fellow of American Physical Society.

Table of Contents

Preface	p. 0
Prologue
Introduction
Electrostatics
Charges
Forces and Electric Fields
Magnetostatics
Currents
Forces and Fields
Vector Potential
Electrodynamics
Conservation of Charge
Faraday''s Law
Energy in the Magnetic Field
The Maxwell Equations and Electromagnetic Waves
The Maxwell--Ampere Law
Electromagnetic Waves
Potentials and Gauges
Conservation Laws
Poynting''s Theorem
Conservation of Momentum
Relativistic Kinematics
The Principles of Special Relativity
Historical Overview
Einstein''s Postulate
Intervals
Proper Time
The Lorentz Transformation
Rotation in 4-Spave
Time Dilation and Length Contraction
Velocity Transformation
4-Vectors and 4-Tensors
Cartesian Tensors
Relativistic Metric and Lorentz Transformation
4-Vector Calculus
Electromagnetic Fields
The 4-Tensor Electromagnetic Field
Transformation of Electromagnetic Fields
Relativistic Mechanics and Field Theory
Relativistic Free Particle
Hamilton''s Principle and the Calculus of Variations
Langrangian for a Free Particle
Energy and Momentum
de Broglie Waves
Rotational Invariance and Angular Momentum
Charged Particle in a Vector Potential
Langrangian Mechanics
Canonical Momentum
Canonical Equations of Motion
The Maxwell Equations
Equations of Motion of a Vector Field
Proca Mass Term
Invariance and Conservation Laws
Gauge Transformations
Symmetric Stress Tensor for the Electromagnetic Field
Time-Independent Electromagnetic Fields
Electrostatics
Coulomb''s Law
Energy in Electrostatic Fields
Multipole Moments
Boundary-Value Problems with Conductors
Boundary Conditions and Uniqueness Theorems
Energy and Capacitance
Method of Images
Separation of Variables
Spheroidal Coordinates
Spherical Harmonics
Variational Methods
Numerical Methods
Green Functions
Magnetostatics
Biot-Savart Law
Forces and Energy
Multipole Moments
Magnetic Scalar Potential
Electromagnetic Waves
Plane Waves
Electric and Magnetic Fields in Plane Waves
Charged Particle in a Plane Wave
Canonical Equations of an Electromagnetic Field
Fourier Decomposition of the Field
Spontaneous Emission by a Harmonic Oscillator
Canonical Equations of the Electromagnetic Field
Blackbody Radiation and the Einstein Coefficients
Waves in Plasmas
Transverse Electromagnetic Waves
Longitudinal Electrostatic Waves
Fourier Techniques and Virtual Quanta
Fourier Transformation
Fourier''s Theorem
Asymptotic Behavior of Fourier Transforms
-Functions
Autocorrelation Functions and the Wiener-Khintchine Theorem
Pulse Compression
Method of Virtual Quanta
Fourier Decomposition of the Field of a Relativistic Charge
Bremsstrahlung
Excitation by a Fast Charged Particle
Transition Radiation
Macroscopic Materials
Polarization and Magnetization
The Macroscopic Form of the Maxwell Equations
The Constitutive Relations
Boundary Conditions
Magnetic Scalar Potentia
Conservation of Energy, and Poynting''s Theorem
Properties of Dielectric and Magnetic Materials
Dielectric Materials
Magnetic Materials
Linear, Dispersive Media
Linear Media
Waves in a Nondispersive Medium
Constitutive Relations in Dispersive Media
Kramers-Kronig Relations
Plane Waves in Dispersive Media
Phase Velocity and Group Velocity
Conservation of Energy in Dispersive Media
Lorentz-Drude Model
Reflection and Refraction at Surfaces
Boundary Conditions
Dielectric Reflection
Metallic Reflection
Surface Waves
Energy Loss by Fast Particles Traveling Through Mat
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