Electrodynamics: Dance of Fields

Electrodynamics in 22 chapters — from “Coulomb’s Law and the Electrostatic Field” to “Radiation from Arbitrary Charge Motion: Liénard-Wiechert Fields and Beyond”.

Chapters

  1. Coulomb’s Law and the Electrostatic Field
    • Charge as a conserved quantity: the empirical facts
    • Coulomb’s law and the superposition principle
    • The electric field: from calculational convenience to physical object
    • Gauss’s law in integral form
    • Visualizing field lines and flux
    • Summary and forward view
    • Problems
    • Selected solutions
  2. Electrostatic Potential and Energy
    • The curl-free nature of electrostatic fields
    • Potential of point charges and continuous distributions
    • Equipotentials and the geometry of potential
    • Electrostatic energy: from pairs to fields
    • The uniqueness theorem and boundary-value problems
    • Summary and forward view
    • Problems
    • Selected solutions
  3. Solving Laplace and Poisson: Method of Images and Separation
    • The method of images: exploiting symmetry and uniqueness
    • Images in spheres and cylinders
    • Separation of variables in Cartesian coordinates
    • Spherical harmonics and multipole expansions
    • Summary and forward view
    • Problems
    • Selected solutions
  4. Conductors, Capacitance, and Dielectrics
    • Electrostatic boundary conditions at conductor surfaces
    • Capacitance: definition, calculation, and energy storage
    • Polarization and the bound charge density
    • The displacement field D and Gauss’s law in matter
    • Linear dielectrics and the permittivity
    • Summary and forward view
    • Problems
    • Selected solutions
  5. Currents, Ampère's Law, and the Magnetostatic Field
    • Current density and the continuity equation
    • The Biot–Savart law
    • Ampère's law
    • The vector potential
    • Magnetic field lines, flux, and the absence of magnetic charge
    • Summary and forward view
    • Problems
    • Selected solutions
  6. Magnetic Forces and the Lorentz Force Law
    • The Lorentz force
    • Motion in uniform fields: the cyclotron and the drift
    • Force and torque on current loops
    • Magnetic energy and inductance
    • Summary and forward view
    • Problems
    • Selected solutions
  7. Magnetic Materials: Ferromagnetism and the H Field
    • Magnetisation and bound currents
    • The auxiliary field H and Ampère's law in matter
    • Linear magnetic materials: permeability μ
    • Ferromagnetism, hysteresis, and permanent magnets
    • Summary and forward view
    • Problems
    • Selected solutions
  8. Faraday's Law and Electromagnetic Induction
    • Faraday's experiments and the flux rule
    • From flux rule to the differential law
    • Lenz's law and the minus sign
    • Motional EMF and the two-mechanisms puzzle
    • Mutual inductance and the transformer
    • Summary and forward view
    • Problems
    • Selected solutions
  9. Maxwell's Displacement Current and the Complete Equations
    • The crack in Ampère's law
    • Maxwell's fix
    • The Maxwell equations
    • Potentials and gauge freedom
    • A glimpse of waves
    • Summary and forward view
    • Problems
    • Selected solutions
  10. Conservation Laws: Energy, Momentum, and the Stress Tensor
    • Poynting's theorem: energy flow in the fields
    • Visualising energy flow: the Poynting vector in circuits and radiation
    • Momentum density and the Maxwell stress tensor
    • Radiation pressure and the Abraham-Minkowski controversy
    • Summary and forward view
    • Problems
    • Selected solutions
  11. Plane Waves in Vacuum: The Simplest Radiative Solution
    • The wave equation and the plane-wave ansatz
    • Transversality: E, B, and k form a right-handed triad
    • Polarization: linear, circular, elliptical
    • Energy and momentum in a plane wave
    • Summary and forward view
    • Problems
    • Selected solutions
  12. Waves in Matter: Dispersion, Absorption, and the Refractive Index
    • Maxwell's equations in a linear medium, and what the constitutive relations conceal
    • Plane waves in a medium: complex permittivity, complex wave number, complex index
    • Where dispersion comes from: the Lorentz oscillator
    • Normal and anomalous dispersion, transparency windows, and conductors
    • Phase, group and signal velocity, and the Kramers–Kronig relations
    • Energy and momentum in a dispersive medium
    • Stokes parameters: what matter does to polarization
    • Summary and forward view
    • Problems
    • Selected solutions
  13. Reflection and Refraction: Fresnel Equations and Brewster's Angle
    • Boundary conditions at a dielectric interface
    • Snell's law and the geometry of refraction
    • Fresnel equations for s and p polarisation
    • Brewster's angle and total internal reflection
    • Summary and forward view
    • Problems
    • Selected solutions
  14. Guided Waves and Resonant Cavities
    • Boundary conditions at a perfect conductor
    • TE and TM modes in a rectangular waveguide
    • Dispersion in waveguides: ω(k) and group velocity
    • Resonant cavities: standing waves and the quality factor
    • Summary and forward view
    • Problems
    • Selected solutions
  15. Retarded Potentials and the Inhomogeneous Wave Equation
    • The inhomogeneous wave equations for φ and A
    • Green's function and retarded potentials
    • The Liénard-Wiechert potentials for a moving point charge
    • Near, intermediate, and far zones
    • Summary and forward view
    • Problems
    • Selected solutions
  16. Electric Dipole Radiation: The Simplest Radiator
    • The oscillating dipole and its retarded potential
    • Radiation fields: the 1/r transverse wave
    • Angular distribution and the sin2θ pattern
    • Total radiated power: the Larmor formula
    • Summary and forward view
    • Problems
    • Selected solutions
  17. Magnetic Dipole and Electric Quadrupole Radiation
    • The magnetic dipole: an oscillating current loop
    • Power radiated by a magnetic dipole
    • Electric quadrupole radiation: the next multipole
    • The multipole hierarchy and selection rules
    • Summary and forward view
    • Problems
    • Selected solutions
  18. Antennas and Arrays: Engineering Radiation Patterns
    • The half-wave dipole antenna
    • Antenna arrays and interference
    • Phased arrays and beam steering
    • Reciprocity: antennas as transmitters and receivers
    • Summary and forward view
    • Problems
    • Selected solutions
  19. Special Relativity: Spacetime, Lorentz Transformations, and Four-Vectors
    • Einstein's 1905 postulates and the Lorentz transformation
    • Spacetime diagrams and the invariant interval
    • Four-vectors: position, velocity, momentum, and current
    • Tensors and the metric: raising and lowering indices
    • Summary and forward view
    • Problems
    • Selected solutions
  20. The Electromagnetic Field Tensor and Covariant Maxwell Equations
    • Constructing Fμν from E and B
    • Lorentz transformation of fields: E and B mix
    • The covariant Maxwell equations
    • Invariants: E · B and E2−c2B2
    • Summary and forward view
    • Problems
    • Selected solutions
  21. Relativistic Particle Dynamics in Electromagnetic Fields
    • The Lorentz force in covariant form
    • Motion in constant uniform fields
    • Radiation from accelerated charges: the Larmor formula generalized
    • Synchrotron radiation: the ultra-relativistic regime
    • Summary and forward view
    • Problems
    • Selected solutions
  22. Radiation from Arbitrary Charge Motion: Liénard-Wiechert Fields and Beyond
    • The Liénard-Wiechert fields: exact E and B
    • The velocity fields: the Coulomb field boosted
    • The acceleration fields: the radiation term
    • Beaming and the radiation reaction force
    • Coda: the classical electron radius and the limits of classical theory
    • Summary and forward view
    • Problems
    • Selected solutions