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This textbook provides a comprehensive one-semester course on advanced electromagnetic theory written from the modern perspective covering all important topics that a professional physicist needs to know. Starting from Maxwell's equations, electrostatics and magnetostatics, this book goes on to discuss such topics as relativistic electrodynamics, emission of electromagnetic radiation and plasma physics. It contains solved examples and exercises for students to highlight the concepts in each chapter.
Preface
Introduction
Why Electromagnetic Theory Again?
A Possible Axiomatic Formulation
Electrostatics and Magnetostatics
A Useful Representation of the Dirac δ-Function
General Solution of a Vector Field with Given Divergence and Curl
Concluding Remarks
References
Electrostatics
Coulomb's Law
Electrostatic Potential as Potential Energy
Poisson's and Laplace's Equations
Electric Field Due to a Dipole and a Surface Dipole Layer
Dipoles in Electromagnetic Theory
Gauss's Law in Electrostatics and Applications
Cylindrical and Spherical Coordinates
Boundary Value Problems and Uniqueness Theorem
Method of Images
Boundary Value Problems in Two-Dimensional Cartesian Coordinates
Boundary Value Problems in Polar Coordinates
Conducting Cylinder in a Uniform Electric Field
Wedge-Shaped Region Between Conductors
Boundary Value Problems in Spherical Coordinates
Some Properties of Legendre Polynomials
Boundary Value Problem Around a Sphere
Multipole Expansion
Polarization in Dielectric Medium
Boundary Conditions Between Dielectric Media
Dielectric Sphere Inside a Uniform Electric Field
Energy Density of an Electrostatic Field
Microscopic Theory of Dielectric Materials
References
Magnetostatics
Basic Principles
Biot–Savart Law
Ampere's Law in Magnetostatics
Techniques for Solving Magnetostatic Problems
Using the Biot–Savart Law
Using the Vector Potential
Using Ampere's Law
Using Scalar Potential
The Magnetic Dipole Moment of a Localized Current System
Polarization in a Magnetic Medium
A Boundary Value Problem in Magnetostatics: A Sphere of Magnetic Material
Microscopic Theory of Magnetic Materials
Analogy Between Electric Currents and Moving Charges
References
Electrodynamics and Electromagnetic Waves
Time Derivative Terms in Maxwell's Equations
The Displacement Current Term
The Electromagnetic Induction Term
Energy of Electromagnetic Fields
Momentum of Electromagnetic Fields
Electromagnetic Wave in an Infinite Medium
Polarization of Electromagnetic Waves
Energy Density and Energy Flux of Electromagnetic Waves
Electromagnetic Waves Inside Conductors
Reflection and Refraction of Electromagnetic Waves at an Interface
Electromagnetic Wave Propagation Through Waveguides
Rectangular Cavity Resonator
Theory of Optical Dispersion
Inhomogeneous Wave Equation
References
Relativity and Electrodynamics
Lorentz Transformation
Transformation of Velocity Between Frames
Proper Time
A Brief Note on Vectors and Tensors
Lorentz Four-Vectors
Doppler Effect of Light
Velocity and Momentum Four-Vectors
Conservation of Momentum and Energy
Covariant Formulation of Electrodynamics
Transformation of Electromagnetic Fields Between Inertial Frames
From the Electric Field of a Line Charge to the Magnetic Field of a Line Current
The Field of a Relativistically Moving Charged Particle
The Non-relativistic Limit
Covariant Formulation of the Lorentz Force Equation
Action Principle Formulation of Electrodynamics
Charged Particle in an Electromagnetic Field
Dynamics of the Electromagnetic Field
Some General Remarks
The Non-relativistic Hamiltonian for a Charged Particle in an Electromagnetic Field
References
Electromagnetic Fields of Time-Varying Sources
A Few Remarks on Inhomogeneous Equations
Solving the Inhomogeneous Wave Equation with the Green's …
The Lienard–Wiechert Potentials
Electromagnetic Fields Due to a Moving Charged Particle
The Fields Due to a Uniformly Moving Charge
References
Emission of Electromagnetic Radiation
Handling the Emission of Electromagnetic Radiation in Practical Situations
Electromagnetic Fields Due to a Non-relativistically Moving Charged Particle
Electromagnetic Fields Due to Oscillating Currents
Larmor's Formula of Radiation Emission from an Accelerated Charge
Radiation from a Centre-Fed Linear Antenna
The Dipole Approximation
Radiation Field from an Oscillating Electric Dipole
A Short Note on Multipole Radiation
Radiation Damping
Scattering of Electromagnetic Radiation by an Electron
The Case of Plane-Polarized Electromagnetic Radiation
The Case of Unpolarized Electromagnetic Radiation
The Case of Harmonically Bound Electrons
Cyclotron and Synchrotron Radiation from Charged Particle Moving in Magnetic Field
Bremsstrahlung
References
Basics of Plasma Physics and Magnetohydrodynamics
Introductory Remarks
Debye Shielding The Plasma Parameter
Electromagnetic Oscillations in Cold Plasmas
Electromagnetic Waves
Plasma Oscillations
Landau Damping
Basic Equations of MHD
The Equations of Fluid Mechanics
Extension to MHD
Alfvén's Theorem of Flux Freezing
Confining Plasmas with Magnetic Fields
MHD Waves in Magnetized Plasmas
Sunspots and Magnetic Buoyancy
References
Appendix A
Short Note on Gaussian Units
Electrostatic Units
Electromagnetic Units
Lorentz Force Equation
Maxwell's Equations
A Few Important Results
Appendix B Useful Vector Relations
General Identities
Integral Relations
Appendix C Formulae and Equations in Cylindrical and Spherical Coordinates
Vector Formulae in Cylindrical Coordinates
Vector Formulae in Spherical Coordinates
Appendix Suggestions for Further Reading
References
Index