Advanced Classical Electromagnetism

"This is a concise, beginning graduate-level textbook on classical electromagnetism, the branch of physics that describes the interaction of electric currents or fields and magnetic fields. Electromagnetism (also called electrodynamics) is one of the pillars of modern physics and, as such, of the modern physics curriculum, with courses on electromagnetism required at the undergraduate and graduate levels. These courses traditionally proceed in a quasi-historical fashion, starting from equations and laws that were first formulated in the eighteenth and nineteenth centuries and still form the foundations of our understanding of electromagnetism. However, as Robert Wald argues, teaching in this way can be imprecise and tends to promote outdated ways of thinking about the subject. This book rethinks how electromagnetism is presented at the graduate level, offering a corrective that aims to bring teaching up to date with our more modern understanding of the topic. The book begins by debunking four common misconceptions, or "myths," that can hinder a deep conceptual understanding of electromagnetism. Wald then proceeds through the major topics first-year grad courses (and textbooks) in electromagnetism typically cover, including electrostatics, dielectrics, magnetostatics, electrodynamics, geometric optics, special relativity, gauge theory, and point charge. Wald's aim throughout is to explain to students how to think about electromagnetism from a modern and mathematically precise perspective, formulating all the key conceptual ideas and results in the field clearly and concisely, while forgoing extensive collections of examples and applications. The book could be used as the basis for or as a supplement to a course, or for self-study by students seeking a deeper understanding than traditional courses and books offer"-- Provided by publisher Cover 1 Contents 6 Preface 10 Chapter 1. Introduction: Electromagnetic Theory without Myths 14 1.1 The Fundamental Electromagnetic Variables Are the Potentials, Not the Field Strengths 17 1.2 Electromagnetic Energy, Momentum, and Stress Are an Integral Part of the Theory 18 1.3 Electromagnetic Fields Should Not Be Viewed as Being Produced by Charged Matter 21 1.4 At a Fundamental Level, Classical Charged Matter Must Be Viewed as Continuous Rather Than Point-Like 23 Chapter 2. Electrostatics 26 2.1 Uniqueness of Solutions in Electrostatics 26 2.2 Point Charges and Green’s Functions 29 2.3 Interaction Energy and Force 31 2.4 Multipole Expansion of the Green’s Function 35 2.5 Conducting Cavities; Dirichlet and Neumann Green’s Functions 40 Problems 47 Chapter 3. Dielectrics 51 3.1 Macroscopic Description of Dielectrics 51 3.2 Force and Interaction Energy 56 Problems 61 Chapter 4. Magnetostatics 63 4.1 The Equations of Magnetostatics 63 4.2 Multipole Expansion 66 4.3 Interaction Energy and Force 71 4.4 Magnetic Materials 78 Problems 79 Chapter 5. Electrodynamics 83 5.1 The Equations of Electrodynamics 83 5.2 Retarded Green’s Function 87 5.3 Multipole Expansion 93 5.3.1 Cartesian Multipole Expansion of the Radiation Field for a Nonrelativistic Source 93 5.3.2 General Multipole Expansion for a Relativistic Source 97 5.4 The Initial Value Formulation for Maxwell’s Equations 104 5.5 Plane Waves 110 5.6 Conducting Cavities and Waveguides 113 5.6.1 Conducting Cavities 114 5.6.2 Waveguides 115 Problems 120 Chapter 6. Electrodynamics in Media 126 6.1 Linear, Homogeneous, Isotropic Medium with an Instantaneous Response 127 6.2 Linear, Homogeneous, Isotropic Medium with a Delayed Response 130 6.3 The Lorentz Model for ε (ω) 133 6.3.1 Nonconducting Medium 135 6.3.2 Plasma or Conducting Medium 136 6.4 Magnetohydrodynamics 138 Problems 144 Chapter 7. Geometric Optics, Interference, and Diffraction 148 7.1 Geometric Optics 148 7.2 Interference and Coherence 153 7.3 Diffraction 160 7.3.1 Scattering by a Dielectric Ball 161 7.3.2 Propagation of Waves through an Aperture 163 Problems 166 Chapter 8. Special Relativity 171 8.1 The Framework of Special Relativity 172 8.2 The Formulation of Electromagnetic Theory in the Framework of Special Relativity 183 8.3 Charged Particle Motion and Radiation 188 8.3.1 Charged Particle Motion 188 8.3.2 Radiation from a Point Charge in Arbitrary Motion 191 Problems 196 Chapter 9. Electromagnetism as a Gauge Theory 201 9.1 Lagrangian for the Electromagnetic Field and Its Interactions 201 9.2 Gauge Invariance and the Reinterpretation of the Electromagnetic Field as a Connection 209 9.3 Dirac Magnetic Monopoles 212 Chapter 10. Point Charges and Self-Force 217 10.1 The Point Particle Limit 217 10.2 Lorentz Force 221 10.3 Corrections to Lorentz Force Motion 226 10.3.1 Self-force Corrections 231 10.3.2 Spin and Dipole Effects 233 10.4 Self-Consistent Motion 234 Index 240 Princeton,University,Press Princeton University Press **A modern approach to classical electromagnetism** Electromagnetism is one of the pillars of modern physics. Robert Wald provides graduate students with a clear, concise, and mathematically precise introduction to the subject, covering all the core topics while bringing the teaching of electromagnetism up to date with our modern understanding of the subject. Electromagnetism is usually taught in a quasi-historical fashion, starting from concepts formulated in the eighteenth and nineteenth centuries, but this tends to promote outdated ways of thinking about the theory. Wald begins with Maxwell’s equations―the foundation of electromagnetism―together with the formulas for the energy density, momentum density, and stress tensor of the electromagnetic field. He then proceeds through all the major topics in classical electromagnetism, such as electrostatics, dielectrics, magnetostatics, electrodynamics and radiation, diffraction, and special relativity. The last two chapters discuss electromagnetism as a gauge theory and the notion of a point charge―topics not normally treated in electromagnetism texts. * Completely rethinks how to teach electromagnetism to first-year graduate students * Presents electromagnetism from a modern, mathematically precise perspective, formulating key conceptual ideas and results clearly and concisely * Written by a world-class physicist and proven in the classroom * Covers all the subjects found in standard electromagnetism textbooks as well as additional topics such as the derivation of the initial value formulation for Maxwell’s equations * Also ideal as a supplementary text or for self-study