INTRODUCTION TO ELECTRODYNAMICS

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Cover; An Introduction to Electrodynamics; Copyright; Dedication; PREFACE; CONTENTS; COMMONLY USED SYMBOLS; Geometry; Polar Coordinates; Electrical Circuits; Physical and Material Constants; Fields; Charge and Current; Energy and Force; Velocities and Waves; Epigraph; PART I Mathematical Preliminaries; 1 Vector Calculus; 1.1 Vectors and Vector Algebra; 1.1.1 Elementary Definitions and Properties of Vectors; 1.1.2 Vectors in Cartesian Coordinate Systems; 1.1.3 Mirror Reflections: Polar Versus Axial Vectors Revisited; 1.1.4 From Point Vectors to Vector Fields; 1.2 Line and Surface Integrals 1.2.1 Line Integrals, Conservative Fields and the Scalar Potential1.2.2 Surface Integrals and Solenoidal Fields; 1.3 The Gradient, Divergence and Curl; 1.3.1 The Gradient and the Scalar Potential Revisited; 1.3.2 The Divergence, Gauss' Theorem and the Laplacian; 1.3.3 The Curl; 1.4 Stokes' Theorem and Conservative Fields Revisited; 1.5 Solenoidal Fields Revisited: The Vector Potential and Helmholtz's Decomposition; 1.6 An Aside: The Troubled History of Vector Calculus; Exercises; References; 2 The Physical Signatures of Three Important Partial Differential Equations 2.1 Three Important Second-Order Partial Differential Equations2.1.1 The Classification of Linear Second-Order Partial Differential Equations; 2.1.2 A Key Property of the Diffusion Equation: The Idea of Diffusion Length; 2.1.3 A Key Property of the Wave Equation: d'Alembert's Solution; 2.1.4 A Key Property of Poisson's Equation: Green's Inversion Formula; 2.2 The Diffusion Equation Revisited; 2.2.1 More on Self-Similar Solutions; 2.2.2 The Diffusion of Oscillatory Fields; 2.2.3 Spherically Symmetric Diffusion, Kelvin and the Core of the Earth; 2.3 Waves and the Wave Equation Revisited 2.3.1 From Waves on a String to Alfvén Waves in a Plasma2.3.2 Spherically Symmetric Solutions of the Wave Equation; 2.3.3 SomeWave-Bearing Systems Not Governed by the Wave Equation; 2.3.4 Dispersive Versus Non-Dispersive Waves and d'Alembert Explained; 2.3.5 The Concept of Group Velocity for Dispersive Waves; 2.4 More on Inverting Poisson's Equation; 2.4.1 An Example of the Use of Green's Function; 2.4.2 A Glimpse at Gauss' Law of Electrostatics; 2.4.3 A Glimpse at the Biot-Savart Law of Magnetostatics; 2.4.4 Information Propagation and Hidden Physics 2.5 Inverting the Inhomogeneous Wave Equation: Retarded Potentials2.5.1 Retarded Potentials in Acoustics; 2.5.2 Retarded Potentials and Moving Sources; Exercises; References; PART II The Fundamentals of Electrodynamics; 3 A Bird's Eye View of Electromagnetism; 3.1 The Lorentz Force, the Electric Field and Charge Conservation; 3.2 Ampère's Law, the Biot-Savart Law and the Ampère-Maxwell Equation; 3.3 Faraday's Law in Differential and Integral Form; 3.4 The Vector Potential; 3.5 Maxwell's Equations, Electromagnetic Energy and the Poynting Vector