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Electrodynamics

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Overview

Practically all of modern physics deals with fields—functions of space (or spacetime) that give the value of a certain quantity, such as the temperature, in terms of its location within a prescribed volume. Electrodynamics is a comprehensive study of the field produced by (and interacting with) charged particles, which in practice means almost all matter.

Fulvio Melia's Electrodynamics offers a concise, compact, yet complete treatment of this important branch of physics. Unlike most of the standard texts, Electrodynamics neither assumes familiarity with basic concepts nor ends before reaching advanced theoretical principles. Instead this book takes a continuous approach, leading the reader from fundamental physical principles through to a relativistic Lagrangian formalism that overlaps with the field theoretic techniques used in other branches of advanced physics. Avoiding unnecessary technical details and calculations, Electrodynamics will serve both as a useful supplemental text for graduate and advanced undergraduate students and as a helpful overview for physicists who specialize in other fields.

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Product Details

  • ISBN-13: 9780226519579
  • Publisher: University of Chicago Press
  • Publication date: 9/28/2001
  • Series: Chicago Lectures in Physics
  • Edition description: 1
  • Pages: 264
  • Product dimensions: 6.12 (w) x 9.52 (h) x 0.80 (d)

Meet the Author

Fulvio Melia is professor of physics and astronomy at the University of Arizona. He is coeditor of The Central Parsecs of the Galaxy and scientific editor of The Astrophysical Journal.

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Table of Contents

Preface
1 Introduction 1
1.1 The Physical Basis of Maxwell's Equations 1
1.2 Maxwell's Equations in Matter 14
1.3 The Mathematical Structure of Electrodynamics 17
1.3.1 Electrostatic Phenomena 17
1.3.2 Magnetostatic Phenomena 18
1.3.3 Wave Phenomena 19
1.3.4 The General Case 21
1.3.5 The Mathematical Apparatus 21
2 Time-Independent Fields 25
2.1 Electrostatics 25
2.1.1 Method 1: Guesses and Symmetries 26
2.1.2 Method 2: The Green Function 28
2.1.3 Expansions with Orthonormal Functions 42
2.2 Magnetostatics 50
2.2.1 Method 1: The Magnetic Scalar Potential 52
2.2.2 Method 2: The Magnetic Vector Potential 57
2.2.3 Method 3: Hard Ferromagnets 58
3 General Properties of Maxwell's Equations 61
3.1 Time-Varying Fields 61
3.2 The Time-Dependent Green Function 63
3.3 Conservation Laws 68
3.3.1 Field Energy Density and Poynting's Theorem 68
3.3.2 Conservation of Linear Momentum 71
3.3.3 The Maxwell Stress Tensor 73
3.3.4 Conservation of Angular Momentum 74
4 Electromagnetic Waves and Radiation 77
4.1 Electromagnetic Waves 77
4.2 Polarization and Stokes Parameters 80
4.3 Reflection and Refraction 83
4.4 Time Harmonic Fields in Matter 88
4.5 Wave Guides 93
4.6 Radiation 98
4.6.1 Point Currents and Lienard-Wiechert Potentials 98
4.6.2 The Radiation Fields 102
4.6.3 Simple Radiating Systems 107
5 A Need for the Special Theory of Relativity 115
5.1 Basic Principles and Transformations 115
5.2 Mathematical Structure of Four-Dimensional Spacetime 124
5.3 Lorentz Transformation Properties of Physical Quantities 128
5.4 Lorentz Transformation of Macroscopic Electrodynamics 133
5.5 Stress-Energy Momentum Tensor and Conservation Laws 139
6 The Lagrangian Formulation of Electrodynamics 145
6.1 Action Principles in Classical Field Theories 145
6.2 Relativistic Lagrangians of Point-Charge Motions 150
6.3 The Field Lagrangian 153
6.4 Invariances and Conservation Laws (Noether's Theorem) 156
7 Relativistic Treatment of Radiation 161
7.1 The Green Function in Four-Dimensional Spacetime 162
7.2 Lienard-Wiechert Potentials and Fields for a Point Charge 169
7.3 Angular Distribution of the Emitted Radiation 173
7.4 Bremsstrahlung Radiation 176
7.5 Radiative Motions of a Point Charge 183
7.6 Radiation Damping and the Relativistic Lorentz-Dirac Equation 188
8 Special Topics 195
8.1 Time-Independent Multipole Fields 195
8.2 Multipole Expansion of Time-Dependent Fields 199
8.3 Collisions between Charged Particles 206
8.4 Magnetohydrodynamics 210
8.5 Alfven Waves and Particle Acceleration 215
8.6 Synchrotron Emission 218
8.7 Echoes of the Big Bang 227
8.8 Cosmic Superluminal Sources 233
8.9 Polarized Radiation from the Black Hole at the Galactic Center 235
References 239
Index 245
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