Introduction to Electromagnetic Theory

Contents: 

Preface • Introduction

Chapter 1: Mathematical Preliminaries • Dimensions, Units, and Dimensional Analysis • Vector Algebra • The Scalar Product of Two Vectors • The Vector Product of Two Vectors • The Triple Scalar Product • The Triple Vector Product • Coordinate Systems • Cylindrical Polar Coordinates (p, f, z) • Spherical Polar Coordinates (r, ???,f) • Vector Differentiation • The Gradient • The Divergence of a Vector • The Laplacian Operator s2 • The Curl of a Vector • Vector Integration and Integral Theorems • Volume Integrals and Line Integrals • Surfaces and Surface Integrals • The Divergence Theorem and Stokes' Theorem • Dirac's Delta Function • Analytical Mechanics • Problem

Chapter 2: Electrostatics • Coulomb's Law • Principle of Superposition • The Electric Field • Earnshaw Theorem • The Electrostatic Potential • Equipotentials and Field Lines • Gauss' Law: Integral and Differential Forms • Applications of Gauss' Law • Is the Field of a Point Charge Exactly 1/r2? • Energy of Electrostatic Systems • Conductors in the Electrostatic Field • Electrical Shielding • Force on a Charged Conducting Surface • High- Voltage Breakdown • Capacitors • The Energy of a Capacitor • Electric Dipole • Electric Dipole in an External Electric Field • Electric Double Layers • Multipole Expansion of Potentials • Minimum Energy Theorem • Applications of Electrostatic Fields • Electrostatic Particle Precipitators • Photoduplication (Xerography) • Electrostatic Lenses • Problems

Chapter 3: Electrostatic Boundary Value Problems • Introduction • Solution of Laplace's Equation • Principle of Superposition • Uniqueness Theorem • Laplace's Equation in Rectangular Coordinates • Method of Variable Separation • Laplace's Equation in Spherical Polar Coordinates • Legendre's Equation and Legendre Polynomials • Laplace's Equation in Cylindrical Polar Coordinates • Solution of Poisson's Equation • Formal (Green's Function) Solution to Poisson's Equation • Green's Function • Method of Image Charges • Conjugate Functions and Two-Dimensional Electrostatic Problems • Problems

Chapter 4: Magnetostatics • Electric Current • The Lorentz Force and Magnetic Fields • Gauss' Law for the Magnetic Field • Forces on Current-Carrying Conductors • The Magnetic Field of Steady Current: Ampere's Circuital Law • The Vector Potential • Field of a Small Current Loop: The Magnetic Dipole • Magnetic Dipole in an External Magnetic Field • The Law of Biot-Savart • The Laws of Magnetostatics From the Biot-Savart Law • The Magnetic Scalar Potential • A Comparison Between Electrostatics and Magnetostatics • Magnetic Dipole Moments at the Atomic Level • Problems

Chapter 5: Time-Dependent Magnetic Fields and Faraday's Law of Induction • Magnetic Flux • Electromotive Force • Motional Electromotive Force and Lenz's Law • Faraday's Law of Induction for a Moving Circuit • Integral and Differential Forms of Faraday's Law of Induction • Applications of Faraday's Law of Induction • The Betatron • Electric Generators • Faraday's Disc • Electromagnetic Potentials • Self-Inductance • Mutual Inductance and Neumann's Formula • Magnetic Energy • Magnetic Energy in Terms of Circuit Parameters • Magnetic Energy in Terms of Field Vectors • Forces and Torques on Linear Magnetic Materials • The Transformer • Eddy Current and Magnetic Levitation • Problems

Chapter 6: Maxwell Equations and Electromagnetic Waves in Vacuum • Displacement Current • Maxwell Equations • Magnetic Monopoles • Decay of Free Charge • Electromagnetic Potentials and Wave Equations in Vacuum • Plane Electromagnetic Waves • Polarization • Waves in Three Dimensions, Spherical Waves • Energy and Momentum in Electromagnetic Waves • Poynting Theorem and Poynting Vector • Electromagnetic Field Momentum • Angular Momentum • Problems

Chapter 7: Electrostatics of Dielectric Media • Macroscopic Aspects of Dielectric Polarization • Induced Dipoles • Electric Field at an Exterior Point • The Polarization Charge Densities and Pp and sp • Electric Field at an Interior Point • Gauss' Law for Charges in Dielectric • Electric Displacement Vector  • Poisson's Equation for Dielectrics • Boundary Conditions for and  • Energy of the Electrostatic Field • Forces on Dielectrics • Stresses in a Dielectric • Stress on Surface of Dielectric • Microscopic Aspects of Dielectrics • The Local Field  • Evaluation of the Depolarizing Field  • Evaluation of Due To the Dipoles in the Sphere • Linear Dielectrics and the Clausius-Mossotti Equation • Polar Molecules and the Langevin Equation • The Debye Equation • Permanent Polarization: Ferroelectricity • Frequency-Dependent Linear Response • Kramers-Kronig Relations • Problems

Chapter 8: The Physics of Electric Conductivity • Electrical Conductivity of Solids • Energy Loss and Joule Heating • Equations of the Static Field and Flow • Insufficiency of the Classical Theory of Electrical Conductivity  • Magnetic Field Effects • Frequency-Dependent Conductivity • Skin Effect • Electrical Conductivity of Gases and Liquids • Superconductivity • The Meissner Effect • Electromagnetic Properties of Superconductors • The London Equations • The London Equations and the Meissner Effect • Flux Quantization • Josephson Junctions • Problems

Chapter 9: Magnetic Properties of Matter • Magnetic Materials • Magnetization and Magnetization Current • Ampere's Law in Magnetic Materials and the Auxiliary Field  • Magnetic Susceptibility and Permeability • Boundary Conditions • Boundary-Value Problems • Magnetic Shielding • Cavities • Origin of Diamagnetism and Paramagnetism • Diamagnetism • Paramagnetism • Ferromagnetic Materials • Maxwell Equations in Matter • Problems

Chapter 10: Relativity and Electromagnetism • Elements of Special Theory of Relativity • Space and Time Before Einstein • The Search of Ether • The Michelson-Morley Experiment • The Postulates of the Special Theory of Relativity • Time Is Not Absolute • The Lorentz Transformations • Relativity of Simultaneity: Causality • Time Dilation: Relativity of Colocality • Length Contraction • Velocity Transformation • The Doppler Effect • Relativistic Space-Time and Minkowski Space • Four-Velocity and Four-Acceleration • Equivalence of Mass and Energy • Four-Energy and Four-Momentum Vectors • The Conservation Laws of Energy and Momentum • Generalization of Newton's Equation of Motion • The Force Transformation • Particles of Zero Rest Mass • Relativistic Electrodynamics • Relativistic Nature of Magnetism • The Four-Current Density J???? • The Contravariant Four-Vector A???? • Covariance and Tensors • Electromagnetic Field Tensor F????v • Covariant Form of Maxwell Equations • Transformations of and  • Field of a Uniformly Moving Point Charge • Electromagnetic Field Invariants • Problems

Chapter 11: Electromagnetic Waves in Matter • The Wave Equation • Propagation of Plane Electromagnetic Waves in Nonconducting Media • Propagation of Plane Electromagnetic Waves in Conducting Media • The Skin Depth • The Poynting Vector • and Are Not in Phase • Propagation of Plane Electromagnetic Waves in a Uniform Plasma • Effective Dielectric Constant • Wave Propagation at Frequencies Higher Than ?p • Problems

Chapter 12: Electromagnetic Waves in Bounded Media • Introduction • Reflection and Refraction of Plane Waves at a Dielectric Boundary • Laws of Reflection and Snell's Law (Law of Refraction) • The Fresnel Equations • Total (Internal) Reflection • Reflection from the Surface of a Conductor: Normal Incidence Problems

Chapter 13: Electromagnetic Radiation • Retarded Potentials • Radiation from an Oscillating Electric Dipole • The Field • The Field • Electric Dipole Radiation: Generalization • Magnetic Dipole Radiation • Radiation from a Linear Antenna • The Lienard-Weichert Potential: Fast-Moving Point Charges  • Fields of an Accelerated Point Charge • The Fields of a Point Charge in Uniform Motion • Radiation from an Accelerated Charge • Radiation Damping • Scattering of Radiation • Problems

Chapter 14: Motion of Charged Particles in Electric and Magnetic Fields • Motion of a Charged Particle in Electromagnetic Field • Equations of Motion • Motion in Magnetic Field • Motion in a Constant Electric Field • Drift of Charged Particle in Crossed  and Fields • Particle Drift in a Converging Magnetic Field • Magnetic Moment, a Constant of the Motion • Magnetic Lens with Axial Symmetry • The Cyclotron • Hydromagnetics • Magnetic Pressure • Alfven Waves • Magnetic Confinement • Pinch Effect • Kink and Sausage Instabilities • Problems • Appendix: Solutions of Laplace's Equation in Spherical Polar Coordinates • Index

About the Author: 

Tai Chow, PhD-California State University, California
Dr. Chow is a professor of Physics at California State University, Stanislaus, where he also served as the department chairman. He was previously visiting professor of Physics at University of California, Davis and Berkeley and worked as Summer Faculty Research Fellow at Stanford University and at NASA"s Ames Research Center. Dr. Chow has published more than 36 articles in refereed physics journals and is the author of four textbooks.