Classical Theory of Electromagnetism

Description

The topics treated in this book are essentially those that a graduate student of physics or electrical engineering should be familiar with in classical electromagnetism. Each topic is analyzed in detail, and each new concept is explained with examples. The text is self-contained and oriented toward the student. It is concise and yet very detailed in mathematical calculations; the equations are explicitly derived, which is of great help to students and allows them to concentrate more on the physics concepts, rather than spending too much time on mathematical derivations. The introduction of the theory of special relativity is always a challenge in teaching electromagnetism, and this topic is considered with particular care. A large number of exercises are included. Contents Foreword Preface to the Third Edition Preface to the Second Edition Preface to the First Edition 1. Mathematical Introduction 1.1. Vector Notation 1.2. Fields 1.3. Vector Differential Operator 1.4. Gauss's Theorem and Related Theorems CHAPTER 1 EXERCISES 2. Charges and Electrostatics 2.1. Basic Phenomena 2.2. Units 2.3. The Gauss Flux Theorem and the First Maxwell Equation 2.4. Singular and General Charge Distributions 2.5 Some Potential Theory 2.6. Properties of Spherical Harmonics 2.7. The Mean Value Theorem 2.8. Conductors and Insulators 2.9. General Electrostatic Problems 2.10. Forces and the Stress Tensor 2.11. The Field Energy 2.12. Earnshaw's Theorem 2.13. Thompson's Theorem 2.14. Polarization 2.15. Field Energy in a Dielectric with Constant K 2.16. Field Energy in a Dielectric for Which K = K(x) 2.17. Forces on a Dielectric 2.18. The Stress Tensor 2.19. Capacitance CHAPTER 2 EXERCISES 3. Stationary Currents and Magnetostatics 3.1. Lorentz Force and the Biot and Savart Law 3.2. Forces between Current Loops 3.3. Units 3.4. The Vector Potential 3.5. Forces and the Magnetic Stress Tensor 3.6. Magnetic Media 3.7. B and H CHAPTER 3 EXERCISES 4. Induction and Quasi-Stationary Phenomena 4.1. Effect of Time Variations on ∇×B and ∇×H 4.2. Induction Phenomena 4.3. Temporal Variation of a Flux through a Moving Surface Element 4.4. Differential Formulation.of the Law of Induction 4.5 Quasi-Stationary Phenomena 4.6. Self-Inductance and Mutual Inductance 4.7. About Units CHAPTER 4 EXERCISES 5. General Discussion of Maxwell Equations 5.1. Introduction 5.2. Field Equations, Forces Acting on Charged Matter, and Conservation Laws 5.3. Conservation Laws for the Macroscopic Case 5.4. Energy and Momentum Conservation in General 5.5. Complex Field 5.6. Electromagnetic Waves in Vacuum and in Continuous Media 5.7. Radiation Pressure 5.8. Reflection and Refraction of Waves 5.9. Electromagnetic Waves in a Conducting Medium 5.10. Electromagnetic Potentials and Gauge Transformations CHAPTER 5 EXERCISES 6. Theory of Relativity: I 6.1. Princℙle of Relativity in Mechanics and Electrodynamics 6.2. The Search for an Absolute Frame Tied to the Ether 6.3. Einstein's Postulates 6.4. Lorentz Transformation 6.5. Lorentz Contraction, Time Dilation, and Addition of Velocities 6.6. Minkowski Notation 6.7. General Lorentz Transformation 6.8. Scalars, Vectors, and Tensors in Four Dimensions 6.9. Four-Velocity, Four-Acceleration, and Proper Time 6.10. Lorentz-Covariant Form of the Potential Equations 6.11. Plane Waves 6.12. The Twin Paradox CHAPTER 6 EXERCISES 7. Theory of Relativity: II 7.1. Lorentz Transformation and E and B Fields 7.2. Charged Mass Point in Electromagnetic Field Minkowski Force 7.3. Gauss's Theorem in Four Dimensions 7.4. Electromagnetic Energy-Momentum Tensor 7.5. Green's Functions for the Potential Equations 7.6. Retarded, Advanced, and Symmetrical Potentials CHAPTER 7 EXERCISES 8. Radiation from a Moving Point Charge 8.1. Liénard-Wiechert Potentials of a Moving Point Charge 8.2. Fields of a Moving Point Charge 8.3. Fields of a Slow-Moving Point Charge 8.4. Radiation from a Moving Charged Particle CHAPTER 8 EXERCISES 9. Radiation Damping and Electromagnetic Mass 9.1. Introduction 9.2. Evaluation of the Self-Force and Radiation Damping 9.3. Energy Loss by Radiation. Application to Periodic Motion 9.4. Forced Vibrations 9.5. Scattering of Radiation CHAPTER 9 EXERCISES 10. Radiation from Periodic Charge and Current Distributions 10.1. Multipole Expansion 10.2. Electric and Magnetic Multipoles 10.3. Multipole Expansion Using Spherical Harmonics 10.4. Angular Distribution of Multipole Radiation CHAPTER 10 EXERCISES 11. Lagrangian and Hamiltonian Formulations of Electrodynamics 11.1. Outline of Classical Mechanics 11.2. Lagrangian Formulation of the Motion of a Charged Particle in Given Fields 11.3. Hamiltonian Formulation of the Motion of a Charged Particle in Given Fields 11.4. Lagrangian Formulation of the Maxwell Equations 11.5. Hamiltonian Formulation of the Maxwell Equations 11.6. Poisson Bracket Method 11.7. Hamiltonian of a Closed System CHAPTER 11 EXERCISES 12. Electromagnetic Properties of Matter 12.1. Normal and Anomalous Dispersion 12.2. Multiple Scattering Theory of the Index of Refraction 12.3. Kramers-Kronig Relations 12.4. General Observations on the Kramers-Kronig Relations 12.5. Relaxation 12.6. Plasma Frequency CHAPTER 12 EXERCISES Appendix A Appendix B Bibliography Index Solutions Manual Preface 1.1. 1.3. 1.5. 1.7. 1.11. 1.13. 1.15. 1.19. 2.1. 2.3. 2.5. 2.7. 2.9. 2.11. 2.15. 2.17. 2.19. 2.21. 2.23. 2.25. 2.27. 2.29. 2.31. 2.33. 2.35. 2.37. 3.1. 3.3. 3.5. 3.7. 3.9. 3.11. 3.13. 3.15. 3.17. 3.19. 3.23. 3.25. 4.1. 4.3. 4.5. 4.7. 4.9. 4.13. 4.17. 4.19. 4.21. 5.1. 5.5. 5.11. 5.13. 5.15. 5.19. 5.23. 6.1. 6.5. 6.7. 6.9. 6.13. 6.17. 6.19. 6.23. 6.25. 6.27. 7.1. 7.3. 7.5. 7.7. 7.9. 7.11. 7.13. 7.15. 7.17. 7.19. 7.21. 7.23. 7.25. 8.1. 8.3. 8.5. 8.7. 8.9. 8.11. 9.1. 9.3. 9.5. 10.1. 10.3. 10.5. 10.7. 11.1. 12.1. 12.3. 12.5.