Advanced Electromagnetic Theory

Preface
Contents
1 Introduction
1.1 Why Electromagnetic Theory Again?
1.2 A Possible Axiomatic Formulation
1.3 Electrostatics and Magnetostatics
1.4 A Useful Representation of the Dirac δ-Function
1.5 General Solution of a Vector Field with Given Divergence and Curl
1.6 Concluding Remarks
References
2 Electrostatics
2.1 Coulomb's Law
2.2 Electrostatic Potential as Potential Energy
2.3 Poisson's and Laplace's Equations
2.4 Electric Field Due to a Dipole and a Surface Dipole Layer
2.5 Dipoles in Electromagnetic Theory
2.6 Gauss's Law in Electrostatics and Applications
2.7 Cylindrical and Spherical Coordinates
2.8 Boundary Value Problems and Uniqueness Theorem
2.9 Method of Images
2.10 Boundary Value Problems in Two-Dimensional Cartesian Coordinates
2.11 Boundary Value Problems in Polar Coordinates
2.11.1 Conducting Cylinder in a Uniform Electric Field
2.11.2 Wedge-Shaped Region Between Conductors
2.12 Boundary Value Problems in Spherical Coordinates
2.12.1 Some Properties of Legendre Polynomials
2.12.2 Boundary Value Problem Around a Sphere
2.13 Multipole Expansion
2.14 Polarization in Dielectric Medium
2.15 Boundary Conditions Between Dielectric Media
2.16 Dielectric Sphere Inside a Uniform Electric Field
2.17 Energy Density of an Electrostatic Field
2.18 Microscopic Theory of Dielectric Materials
References
3 Magnetostatics
3.1 Basic Principles
3.2 Biot–Savart Law
3.3 Ampere's Law in Magnetostatics
3.4 Techniques for Solving Magnetostatic Problems
3.4.1 Using the Biot–Savart Law
3.4.2 Using the Vector Potential
3.4.3 Using Ampere's Law
3.4.4 Using Scalar Potential
3.5 The Magnetic Dipole Moment of a Localized Current System
3.6 Polarization in a Magnetic Medium
3.7 A Boundary Value Problem in Magnetostatics: A Sphere of Magnetic Material
3.8 Microscopic Theory of Magnetic Materials
3.9 Analogy Between Electric Currents and Moving Charges
References
4 Electrodynamics and Electromagnetic Waves
4.1 Time Derivative Terms in Maxwell's Equations
4.1.1 The Displacement Current Term
4.1.2 The Electromagnetic Induction Term
4.2 Energy of Electromagnetic Fields
4.3 Momentum of Electromagnetic Fields
4.4 Electromagnetic Wave in an Infinite Medium
4.4.1 Polarization of Electromagnetic Waves
4.4.2 Energy Density and Energy Flux of Electromagnetic Waves
4.5 Electromagnetic Waves Inside Conductors
4.6 Reflection and Refraction of Electromagnetic Waves at an Interface
4.7 Electromagnetic Wave Propagation Through Waveguides
4.8 Rectangular Cavity Resonator
4.9 Theory of Optical Dispersion
4.10 Inhomogeneous Wave Equation
References
5 Relativity and Electrodynamics
5.1 Lorentz Transformation
5.2 Transformation of Velocity Between Frames
5.3 Proper Time
5.4 A Brief Note on Vectors and Tensors
5.5 Lorentz Four-Vectors
5.6 Doppler Effect of Light
5.7 Velocity and Momentum Four-Vectors
5.8 Conservation of Momentum and Energy
5.9 Covariant Formulation of Electrodynamics
5.10 Transformation of Electromagnetic Fields Between Inertial Frames
5.10.1 From the Electric Field of a Line Charge to the Magnetic Field of a Line Current
5.10.2 The Field of a Relativistically Moving Charged Particle
5.10.3 The Non-relativistic Limit
5.11 Covariant Formulation of the Lorentz Force Equation
5.12 Action Principle Formulation of Electrodynamics
5.12.1 Charged Particle in an Electromagnetic Field
5.12.2 Dynamics of the Electromagnetic Field
5.12.3 Some General Remarks
5.13 The Non-relativistic Hamiltonian for a Charged Particle in an Electromagnetic Field
References
6 Electromagnetic Fields of Time-Varying Sources
6.1 A Few Remarks on Inhomogeneous Equations
6.2 Solving the Inhomogeneous Wave Equation with the Green's …
6.3 The Lienard–Wiechert Potentials
6.4 Electromagnetic Fields Due to a Moving Charged Particle
6.5 The Fields Due to a Uniformly Moving Charge
References
7 Emission of Electromagnetic Radiation
7.1 Handling the Emission of Electromagnetic Radiation in Practical Situations
7.1.1 Electromagnetic Fields Due to a Non-relativistically Moving Charged Particle
7.1.2 Electromagnetic Fields Due to Oscillating Currents
7.2 Larmor's Formula of Radiation Emission from an Accelerated Charge
7.3 Radiation from a Centre-Fed Linear Antenna
7.4 The Dipole Approximation
7.5 Radiation Field from an Oscillating Electric Dipole
7.6 A Short Note on Multipole Radiation
7.7 Radiation Damping
7.8 Scattering of Electromagnetic Radiation by an Electron
7.8.1 The Case of Plane-Polarized Electromagnetic Radiation
7.8.2 The Case of Unpolarized Electromagnetic Radiation
7.8.3 The Case of Harmonically Bound Electrons
7.9 Cyclotron and Synchrotron Radiation from Charged Particle Moving in Magnetic Field
7.10 Bremsstrahlung
References
8 Basics of Plasma Physics and Magnetohydrodynamics
8.1 Introductory Remarks
8.2 Debye Shielding. The Plasma Parameter
8.3 Electromagnetic Oscillations in Cold Plasmas
8.3.1 Electromagnetic Waves
8.3.2 Plasma Oscillations
8.3.3 Landau Damping
8.4 Basic Equations of MHD
8.4.1 The Equations of Fluid Mechanics
8.4.2 Extension to MHD
8.5 Alfvén's Theorem of Flux Freezing
8.6 Confining Plasmas with Magnetic Fields
8.7 MHD Waves in Magnetized Plasmas
8.8 Sunspots and Magnetic Buoyancy
References
Appendix A A Short Note on Gaussian Units
A.1 Electrostatic Units
A.2 Electromagnetic Units
A.3 Lorentz Force Equation
A.4 Maxwell's Equations
A.5 A Few Important Results
Appendix B Useful Vector Relations
B.1 General Identities
B.2 Integral Relations
Appendix C Formulae and Equations in Cylindrical and Spherical Coordinates
C.1 Vector Formulae in Cylindrical Coordinates
C.2 Vector Formulae in Spherical Coordinates
Appendix Suggestions for Further Reading
References
Index