Advanced Classical Electromagnetism

Description

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fashion, starting from concepts formulated in the eighteenth and nineteenth centuries, but this tends to promote outdated ways of thinking about the theory.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 studentsPresents electromagnetism from a modern, mathematically precise perspective, formulating key conceptual ideas and results clearly and conciselyWritten by a world-class physicist and proven in the classroomCovers 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 equationsAlso ideal as a supplementary text or for self-study Cover Contents Preface Chapter 1. Introduction: Electromagnetic Theory without Myths 1.1 The Fundamental Electromagnetic Variables Are the Potentials, Not the Field Strengths 1.2 Electromagnetic Energy, Momentum, and Stress Are an Integral Part of the Theory 1.3 Electromagnetic Fields Should Not Be Viewed as Being Produced by Charged Matter 1.4 At a Fundamental Level, Classical Charged Matter Must Be Viewed as Continuous Rather Than Point-Like Chapter 2. Electrostatics 2.1 Uniqueness of Solutions in Electrostatics 2.2 Point Charges and Green’s Functions 2.3 Interaction Energy and Force 2.4 Multipole Expansion of the Green’s Function 2.5 Conducting Cavities; Dirichlet and Neumann Green’s Functions Problems Chapter 3. Dielectrics 3.1 Macroscopic Description of Dielectrics 3.2 Force and Interaction Energy Problems Chapter 4. Magnetostatics 4.1 The Equations of Magnetostatics 4.2 Multipole Expansion 4.3 Interaction Energy and Force 4.4 Magnetic Materials Problems Chapter 5. Electrodynamics 5.1 The Equations of Electrodynamics 5.2 Retarded Green’s Function 5.3 Multipole Expansion 5.3.1 Cartesian Multipole Expansion of the Radiation Field for a Nonrelativistic Source 5.3.2 General Multipole Expansion for a Relativistic Source 5.4 The Initial Value Formulation for Maxwell’s Equations 5.5 Plane Waves 5.6 Conducting Cavities and Waveguides 5.6.1 Conducting Cavities 5.6.2 Waveguides Problems Chapter 6. Electrodynamics in Media 6.1 Linear, Homogeneous, Isotropic Medium with an Instantaneous Response 6.2 Linear, Homogeneous, Isotropic Medium with a Delayed Response 6.3 The Lorentz Model for ε (ω) 6.3.1 Nonconducting Medium 6.3.2 Plasma or Conducting Medium 6.4 Magnetohydrodynamics Problems Chapter 7. Geometric Optics, Interference, and Diffraction 7.1 Geometric Optics 7.2 Interference and Coherence 7.3 Diffraction 7.3.1 Scattering by a Dielectric Ball 7.3.2 Propagation of Waves through an Aperture Problems Chapter 8. Special Relativity 8.1 The Framework of Special Relativity 8.2 The Formulation of Electromagnetic Theory in the Framework of Special Relativity 8.3 Charged Particle Motion and Radiation 8.3.1 Charged Particle Motion 8.3.2 Radiation from a Point Charge in Arbitrary Motion Problems Chapter 9. Electromagnetism as a Gauge Theory 9.1 Lagrangian for the Electromagnetic Field and Its Interactions 9.2 Gauge Invariance and the Reinterpretation of the Electromagnetic Field as a Connection 9.3 Dirac Magnetic Monopoles Chapter 10. Point Charges and Self-Force 10.1 The Point Particle Limit 10.2 Lorentz Force 10.3 Corrections to Lorentz Force Motion 10.3.1 Self-force Corrections 10.3.2 Spin and Dipole Effects 10.4 Self-Consistent Motion Index