Electrodynamics - Table of contents

This is a table of contents for my notes on electrodynamics. The posts are arranged in an order that might be found in a textbook.

Electrostatics

• Coulomb's law and the electric field
• Gauss's law in electrostatics
• Gauss's law in electrostatics - examples
• Curl and Stokes's theorem
• Curl and potential in electrostatics
• Electric potential
• Electric potential - examples
• Potential of two charged wires
• Linear charge distributions
• Surface charges
• Work and energy - continuous charge
• Work and energy - point charges
• Conductors
• Electrostatic pressure
• Capacitance
• Electrostatic boundary conditions
• Green's reciprocity theorem

Method of images

• Method of images
• Method of images - point charge and sphere
• Method of images - two conducting planes
• Method of images - moving charge and plane
• Method of images - point charge and two planes
• Two charged wires and a cylinder
• Method of images - sphere in uniform field

Laplace's equation

• Laplace and Poisson equations - uniqueness of solutions
• Laplace's equation - separation of variables
• Laplace's equation - average values of solutions
• Laplace's equation - Fourier series
• Laplace's equation - rectangular pipe
• Thompson-Lampard theorem
• Laplace's equation - Fourier series in three dimensions
• Laplace's equation in spherical coordinates
• Laplace's equation in spherical coordinates - examples
• Laplace's equation in spherical coordinates - surface charge
• Laplace's equation in cylindrical coordinates
• Laplace's equation - infinite pipe
• Laplace's equation - cylindrical shell

Dipoles and the multipole expansion

• Electric dipole
• Multipole expansion in electrostatics
• Dipoles in the multipole expansion
• Dipole-dipole interactions (torques)
• Dipole force and energy
• Quadrupole moment

Dielectrics and polarization

• Polarizability of hydrogen
• Polarizability - spherical charge distribution
• Point charge and neutral atom
• Polarized objects in electrostatics
• Bound charges in a dielectric
• Field of a polarized sphere
• Field of a polarized cylinder
• Electric displacement
• Electric displacement - boundary conditions
• Electric field within a cavity inside a dielectric
• Dielectric constant
• Uniqueness of potential in dielectrics

Magnetic fields in vacuum

• Magnetostatics - the Lorentz force law
• Electron charge to mass ratio
• Currents in magnetic fields
• Volume current density and dipole moment
• Biot-Savart law
• Magnetic field of a solenoid
• Solenoid with arbitrary cross-section
• Ampère's law for steady currents
• Ampère's law - surface of integration and the steady current assumption
• Divergence of magnetic field - magnetic monopoles
• Magnetic vector potential
• Magnetic field of rotating sphere of charge
• Magnetostatic boundary conditions
• Magnetic dipole
• Magnetic dipole moment of a current loop
• Currents and relativity
• Magnetic field - uniqueness conditions
• Gyromagnetic ratio
• Torque on a magnetic dipole
• Torque on a magnetic moment - general current distribution
• Force on a magnetic dipole

Magnetic fields in matter

• Magnetization - bound currents
• Auxiliary magnetic field H
• Magnetostatic boundary conditions for H
• Magnetic permeability
• Electron speed in a copper wire
• Diamagnetism

Electrodynamics

• Ohm's law, conductivity and resistivity
• Ohm's law in the microscopic realm
• Electromotive force
• Motional emf
• Magnetic flux
• Faraday's law
• Faraday's law and the Biot-Savart law
• Faraday's law, Ampère's law and the quasistatic approximation
• Lenz's law
• Mutual inductance
• Self-inductance
• LC circuit - the oscillator
• Energy in a magnetic field
• Maxwell's correction to Ampère's law - displacement current
• Maxwell's equations
• Maxwell's equations with varying charge but constant current
• Maxwell's equations in matter
• Maxwell's equations in matter - boundary conditions
• Transformers

Energy and momentum in electromagnetism

• Poynting vector
• Poynting's theorem and conservation of energy
• Maxwell stress tensor (non-relativistic)
• Momentum in electromagnetic fields
• Angular momentum in electromagnetic fields
• Energy in a magnetic field
• Energy flow in time-dependent fields
• Electromagnetic Lagrangian
• Euler-Lagrange equations for a free particle in an electromagnetic field
• Momentum and energy for a free particle in an electromagnetic field
• Hamiltonian for the electromagnetic force
• Equations of motion for a charged point particle

Electromagnetic waves

• Wave equation - derivation and examples
• Wave equation - wave speed and standing waves
• Wave equation - sinusoidal waves and complex notation
• Wave equation - solution by separation of variables
• Waves - boundary conditions
• Electromagnetic waves in vacuum
• Electromagnetic waves - energy, momentum and light pressure
• Spherical electromagnetic wave
• Electromagnetic waves in matter - reflection and transmission coefficients
• Electromagnetic waves in matter - normal reflection and transmission
• Three laws of geometrical optics
• Fresnel equations for perpendicular polarization
• Decay time for free charge in a conductor
• Skin depth of electromagnetic waves in conductors
• Skin depth of water and metals
• Electromagnetic waves in conductors - phases and amplitudes
• Electromagnetic waves in conductors - energy density and intensity
• Reflection at a conducting surface - the physics of mirrors
• Phase velocity and group velocity in a wave packet
• Frequency dependence of electric permittivity
• Refraction and dispersion coefficients
• Resonances in a dispersive medium
• Wave guides - derivation of the wave equation
• Rectangular wave guides - transverse electric waves

Potentials and gauge transformations

• Maxwell's equations in terms of potentials
• Potentials for a point charge
• Potentials for an electromagnetic wave
• Gauge transformations in electrodynamics
• Coulomb and Lorenz gauges
• Lorenz gauge is always possible
• Lagrangian for classical electromagnetism

Retarded potentials

• Retarded potentials
• Retarded potentials in an infinite straight wire
• Retarded potential of a wire loop
• Jefimenko's equation for time-dependent electric field
• Jefimenko's equation for time-dependent magnetic field
• Liénard-Wiechert potentials for a moving point charge
• Liénard-Wiechert potentials for a charge moving with constant velocity
• Point charge in hyperbolic motion - visible and invisible points
• Liénard-Wiechert potential for a charge moving on a hyperbolic trajectory
• Fields of a moving point charge

Radiation from accelerating charges

• Electric dipole time-varying potentials - Lorenz gauge condition
• Fields and radiated power from an oscillating electric dipole
• Radiation resistance
• Radiation from a rotating dipole
• Fields of an oscillating magnetic dipole
• Electric dipole radiation from an arbitrary source
• Electric quadrupole radiation
• Radiation from a current loop with time-varying current
• Radiation from a point charge - the Larmor formula
• Radiative decay of the Bohr hydrogen atom
• Liénard's generalization of the Larmor formula for an accelerating charge
• Synchrotron radiation
• Radiation reaction - the Abraham-Lorentz force
• Abraham-Lorentz formula - physical basis
• Radiation reaction - a few examples
• Radiation reaction - energy conservation with a constant external force
• Radiation reaction with a delta-function external force
• Physical basis of the radiation reaction force
• Power radiated by radiation reaction force
• Radiation damping
• Radiation from a charge on a spring
• Radiation from a radio station