Electrodynamics: A Concise Introduction

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.- 6Radiation 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.