Electrodynamics: A Concise Introduction

ISBN-13: 9781461275145 / Angielski / Miękka / 2011 / 435 str.

James B. Westgard

Opis

This textbook is intended for advanced undergraduates or beginning graduates. It is based on the notes from courses I have taught at Indiana State University from 1967 to the present. The preparation needed is an introductory calculus-based course in physics and its prerequisite calculus courses. Courses in vector analysis and differential equations are useful but not required, since the text introduces these topics. In writing this book, I tried to keep my own experience as a stu dent in mind and to write the kind of book I liked to read. That goal determined the choice of topics, their order, and the method of presentation. The organization of the book is intended to encourage independent study. Accordingly, I have made every effort to keep the material self-contained, to develop the mathematics as it is needed, and to present new material by building incrementally on preceding material. In organizing the text, I have taken care to give explicit cross references, to show the intermediate steps in calculations, and to give many examples. Provided they are within the mathematical scope of this book, I have preferred elegant mathematical treatments over more ad hoc ones, not only for aesthetic reasons, but because they are often more profound and indicate connections to other branches of physics. I have emphasized physical understanding by presenting mechanical models. This book is organized somewhat differently from the traditional textbook at this level."

Spis treści

1 Introduction to Electrodynamics.- 1-1 A Brief History of Electromagnetism.- 1-2 Vectors.- 1 -3 Vector Calculus.- 1-4 Curvilinear Coordinate Systems.- 1 -5 Integration of Vectors.- 1-6 Delta Functions.- 1-7 Selected Bibliography.- 1-8 Problems.- App. 1-1 Vector Operators.- App. 1-2 Curvilinear Coordinates.- 2 Experimental Foundation.- 2-1 Fields.- 2-2 Coulomb’s Law.- 2-3 Ampère’s Laws for the Magnetic Field.- 2-4 Faraday’s Induction Law.- 2-5 Maxwells Equations.- 2-6 A Mechanical Model of the Electromagnetic Field.- 2-7 The Michelson—Morley Experiment.- 2-8 Systems of Units.- 2-9 Selected Bibliography.- 2-10 Problems.- App. 2-1 Field Plotter in 2-D.- 3 Dielectric and Magnetic Materials and Boundary Conditions.- 3-1 Dielectric Materials.- 3-2 Currents.- 3-3 Magnetic Materials.- 3-4 Boundary Conditions.- 3-5 Some Mathematical Aspects of Boundary Conditions.- 3-6 Selected Bibliography.- 3-7 Problems.- 4 Electromagnetic Equations.- 4-1 Tensor Notation.- 4-2 Integral Theorems.- 4-3 Relativity: A New Kinematics.- 4-4 The Electromagnetic Field.- 4-5 Electromagnetic Potentials and Gauge Conditions.- 4-6 Lorentz Transformed Fields.- 4-7 The Lagrangian Method.- 4-8 Selected Bibliography.- 4-9 Problems.- App. 4-1 Lorentz Transformation of the Field Tensor.- 5 Electromagnetic Fields in Steady States.- 5-1 Steady-State Equations.- 5-2 Multipole Expansion.- 5-3 Laplace’s Equation: Separation of Variables.- 5-4 The Cauchy—Riemann Equations and Conformal Mapping.- 5-5 Numerical Solutions by Finite-Element Analysis.- 5-6 Magnetic Fields.- 5-7 Selected Bibliography.- 5-8 Problems.- App. 5-1 Relaxation Solution of Laplaces Equation.- App. 5-2 Gram—Schmidt Orthogonalization.- App. 5-3 Schwartz Transformations.- App. 5-4 Fourier Series.- App. 5-5 Laplace Equation.- 6 Radiation and Optics in Dielectric Media.- 6-1 Wave Equation in Uniform Media.- 6-2 Spherical Waves.- 6-3 Radiation in Conductive and Dispersive Media.- 6-4 Refraction and Reflection at a Dielectric Boundary.- 6-5 Momentum and Energy.- 6-6 Huygens’ Principle and Diffraction.- 6-7 Selected Bibliography.- 6-8 Problems.- App. 6-1 Bessel and Legendre Functions.- App. 6-2 Multipole Radiation Patterns.- App. 6-3 Single Slit Diffraction by Helmholtz Integral.- App. 6-4 The Electromagnetic Stress Tensor.- 7 Particle Motion in Electromagnetic Fields.- 7-1 Uniform Fields.- 7-2 Numerical Solutions.- 7-3 An Example: Particle Optics.- 7-4 Velocity Field Model of Single Particle Kinematics.- 7-5 Cross Sections.- 7-6 Selected Bibliography.- 7 Problems.- App. 7-1 Finite-Element Solution of a Differential Equation Using a Spreadsheet.- App. 7-2 Taylor Series Solutions of Differential Equations.- 8 Radiation by Moving Charges.- 8-1 Multipole Expansion.- 8-2 A Physical Model.- 8-3 Frequency Analysis of Radiation.- 8-4 Calculating with Delta Functions.- 8-5 Radiation by Charged Particles.- 8-6 Selected Bibliography.- 7 Problems.- App. 8-1 Radiation by a Fast Charged Particle.- App. 8-2 Tensor Potentials.- 9 Beyond the Classical Theory.- 9-1 Radiation Reaction.- 9-2 Classical Models of the Electron.- 9-3 Quantization.- 9-4 Unification with Weak Interactions.- 9-5 Selected Bibliography.