Electrodynamics: An Introduction Including Quantum Effects

The following sections are included:

• Contents

• Preface

The following sections are included:

• What is Electrodynamics?

• Presentation of Macroscopic Electrodynamics

• On the Choice of Units

The following sections are included:

• Introductory Remarks

• The Coulomb Law

• The Electrostatic Potential

• The Equations of Electrostatics

• Dirac's Delta Distribution

• Potential Energy of Charges in Electric Fields

• The Electric Field at Charged Surfaces

• Examples

• Conductors and Electrical Screening

• Energy of Charge Distributions

The following sections are included:

• Introductory Remarks

• Method I: The Gauss Law

• Method II: Poisson and Laplace Equations

• Method III: Direct Integration

• Method IV: Kelvin's Method of Image Charges

• Theoretical Aspects of Image Charges
  • The Induced Charge
  • Green's Theorems
  • Green's Function and Image Potential
  • The Image Potential in an Example

• Method V: Conjugate Functions

• Orthogonal Functions
  • Orthogonal Functions in General
  • Fourier Series, Fourier Expansions
  • Spherical Functions (Legendre, Associated Legendre, Hyperspherical Functions)

• The Multipole Expansion

The following sections are included:

• Introductory Remarks

• Dielectrics and Dielectric Displacement

• The Behaviour of D at an Interface

• Examples

• Polarisation of a Sphere in an Electric Field E₀

• Energy of the Electric Field
  • The Energy Density Formula
  • Polarisation Energy

• Summary of Formulae of Electrostatics

The following sections are included:

• Introductory Remarks

• Continuity Equation and Stationary Current

• Ampère's Experiments and the Law of Biot and Savart

• Examples

• The Electromagnetic Vector Potential A

• Integral Form of Ampère's Law

• Further Examples

The following sections are included:

• Introductory Remarks

• Macroscopic Magnetisation

• Magnetic Properties of Matter

• Energy of the Magnetic Field

• Behaviour of B and H at Boundary Surfaces

• Current Circuits Compared with Flux Circuits

• Examples

• Summary of Formulae of Magnetostatics

The following sections are included:

• Preliminary Remarks

• Time-Dependent Fields and Faraday's Law of Induction

• Energy of the Magnetic Field

• The Generalised Ohm's Law

• E and B with Time-Dependent Potentials

• Displacement Current and Maxwell Equations

• Poynting Vector and Conservation of Energy
  • Application: The Conduction Wire
  • The Field Momentum Density

• Further Examples

The following sections are included:

• Introductory Remarks

• Inductances L_ij

• Examples

• The Vector Potential of a Long Solenoid

• Energy of a Self-Inductance

• Simple Current Circuits
  • Current Circuits with R and L
  • Circuits with L, C and R

• Self-Inductances: Conjugate Function Method

The following sections are included:

• Introductory Remarks

• Electromagnetic Waves in Vacuum

• Electromagnetic Waves in Media

• Frequency Dependence of ∈ and σ
  • The Generalised Dielectric Constant
  • Frequency Dependence of σ

• The (Normal) Skin Effect

The following sections are included:

• Introductory Remarks

• Maxwell's Equations for Moving Charges

• The Liénard–Wiechert Potentials of a Moving Point Charge

• The Fields E, B of a Moving Point Charge

• The Hertz Dipole
  • The Potentials
  • The Field Strengths

• Current Element Ids and Dipole Radiation
  • The Power of an Oscillating Dipole
  • Radiation Resistance

• Further Examples

The following sections are included:

• Introductory Remarks

• Continuity Conditions and Definition of the Surface Current

• Electromagnetic Waves in Media

• Kinematical Aspects of Reflection and Refraction: Snell's Law
  • Preliminary Remarks
  • Kinematical Aspects of Reflection and Refraction

• Dynamical Aspects of Reflection and Refraction: The Fresnel Formulae
  • The Conditions
  • Two Cases of Linear Polarisation
  • The Brewster Angle and the Case without Reflection
  • The General Case
  • Total Reflection

• Useful Formulation of the Fresnel Formulae

The following sections are included:

• Introductory Remarks

• Reflection and Absorption of Plane Waves by Metals

• The Theory of Drude

The following sections are included:

• Introductory Remarks

• Condition for Return of Waves

• Effect of Terrestrial Magnetic Field

The following sections are included:

• What are Wave Guides?

• Transverse Fields Derived from Longitudinal Fields

• Boundary Conditions

• Wave Guides and their TEM Fields
  • TEM Fields
  • The Coaxial Transmission Cable

• Fundamental Equations for the Coaxial Cable

• TM and TE Waves in Wave Guides
  • General Considerations
  • Wave Guides with Rectangular Cross Section
  • Wave Guides with Circular Cross Section

• Alternative Treatment using Scalar and Vector Potentials

• Wave Velocities

• Energy Transport in Wave Guides
  • The Complex Poynting Vector
  • Application of the Complex Poynting Vector
  • Attenuation of Wave Guides (σ ≠ 0)
  • Optimal Use of a Wave Guide

• Resonators (Closed Wave Guides)

• Examples

The following sections are included:

• Introductory Remarks

• Dispersion Relation: Normal and Anomalous Dispersion

• Absorption, Causality and Analyticity
  • Properties of A(ω)
  • Properties of ñ(ω)

• No Wave Packet with a Velocity > c

• Explanation of the Anomalous Dispersion

The following sections are included:

• Introductory Remarks

• Cause U and Effect E

• (U, E)-Linearity and Green's Functions

• Causality

• Causality and Analyticity

• Principal Value Integrals and Dispersion Relations

• Absorption: Special Cases

• Comments on Principal Values

• Subtracted Dispersion Relations

The following sections are included:

• Introductory Remarks

• The Special Theory of Relativity
  • Introduction
  • Einstein's Interpretation of Lorentz Transformations

• Minkowski Space

• The 10-Parametric Poincaré Group
  • Covariant and Contravariant Derivatives

• Construction of the Field Tensor F_μν

• Transformation from Rest Frame to Inertial Frame

• Covariant Form of Maxwell's Equations

• Covariantised Newton Equation of a Charged Particle

• Examples

The following sections are included:

• Introductory Remarks

• Euler–Lagrange Equation

• Symmetries and Energy-Momentum Tensor

• The Lagrangian of the Electromagnetic Field

• Gauge Invariance and Charge Conservation

• Lorentz Transformations and Associated Conservation Laws

• Masslessness of the Electromagnetic Field

• Transversality of the Electromagnetic Field

• The Spin of the Photon

• Examples

The following sections are included:

• Introductory Remarks

• Schrödinger Equation of a Charged Particle in an Electromagnetic Field
  • Hamiltonian of a Charge in an Electromagnetic Field
  • The Gauge Covariant Schrödinger Equation

• The Aharonov–Bohm Effect

The following sections are included:

• Introductory Remarks

• Quantisation of the n-Dimensional Harmonic Oscillator

• Hamiltonian of the Gauge Field

• Quantisation of the Electromagnetic Field

• One-dimensional Illustration of the Casimir Effect

• The Three-Dimensional Case

The following sections are included:

• Symmetrisation of the Maxwell Equations

• Quantisation of Electric Charge

• The Field of the Monopole

• Uniqueness of the Wave Function

• Regularisation of the Monopole Field

• Concluding Remarks

The following sections are included:

• Appendix A The Delta Distribution

• Appendix B Units and Physical Constants

• Appendix C Formulae

• Bibliography

• Index