1 Origins and Concepts 1.1 Introduction 1.2 Magnetism 1.3 Gravitation 1.4 Faraday, Thomson, and Maxwell 1.5 Gravitation a Vector Field 1.6 Charges and Electric Fields 1.7 Priestly's Speculation 1.8 Voltaic Cell 1.9 Currents and Magnetic Fields 1.9.1 Oersted 1.9.2 Ampere 1.9.3 Electrical current 1.10 Induced Electric Field 1.11 The Mathematical Theory 1.11.1 The field equations 1.11.2 Maxwell 1.12 Experimental Evidence 1.12.1 Waves in the laboratory 1.12.2 Wave energy and momentum 1.13 Michelson and Morley Experiment 1.14 Relativity 1.15 Summary Questions 2 Mathematical Background 2.1 Introduction 2.2 Vectors 2.2.1 The Vector Space 2.2.2 Representation 2.2.3 Scalar Product 2.2.4 Vector Product 2.3 Multivariate Functions 2.3.1 Differentials 2.3.2 Cylindrical Coordinates 2.3.3 Spherical Coordinates 2.4 Analytic Functions 2.4.1 Taylor Series 2.4.2 Analyticity 2.5 Vector Calculus 2.5.1 Field Quantities 2.5.2 The Gradient 2.5.3 The Divergence 2.5.4 The Curl 2.5.5 The Laplacian Operator 2.6 Differential Equations 2.6.1 Helmholtz' Theorem 2.6.2 The Del Operator 2.6.3 Dirac Delta Function 2.7 Summary Exercises
3 Electrostatics 3.1 Introduction 3.2 Coulomb's Law 3.2.1 Coulomb's Experiment 3.2.2 Units 3.3 Superposition 3.4 Distributions of'Charges 3.4.1 Distribution of Point Charges 3.4.2 Volume Charge Density 3.4.3 Surface Charge Density 3.5 The Field Concept 3.6 Divergence and Curl of E 3.7 Integral Electrostatic Field Equations 3.7.1 Gauss' Theorem 3.7.2 Stokes' Theorem 3.8 Summary Exercises 4 The Scalar Potential 4.1 Introduction 4.2 Potential Energy 4.3 Potential Surfaces 4.4 Poisson's Equation 4.5 Multipole Expansion 4.6 Energy Storage 4.6.1 Electrostatic Energy Density 4.6.2 Energy of a Set of Conductors …… 5 Magnetostatics 6 Applications of Magnetostatics 7 Particle Motion 8 Green's Functions 9 Laplace's Equation 10 Time Dependence 11 Electromagnetic Waves 12 Energy and Momentum 13 Special Relativity 14 Radiation 15 Fields in Matter 16 Waves in Dispersive Media Appendix References Index
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