Introduction Intended audience Major sources Preface Outline of course Vectors Introduction Vector algebra Vector areas The scalar product The vector product Rotation The scalar triple product The vector triple product Vector calculus Line integrals Vector line integrals Surface integrals Vector surface integrals Volume integrals Gradient Divergence The Laplacian Curl Summary Time-independent Maxwell equations Introduction Coulomb's law The electric scalar potential Gauss' law Poisson's equation Ampère's experiments The Lorentz force Ampère's law Magnetic monopoles? Ampère's circuital law Helmholtz's theorem The magnetic vector potential The Biot-Savart law Electrostatics and magnetostatics Time-dependent Maxwell's equations Introduction Faraday's law Electric scalar potential? Gauge transformations The displacement current Potential formulation Electromagnetic waves Green's functions Retarded potentials Advanced potentials? Retarded fields Summary Electrostatics Introduction Electrostatic energy Ohm's law Conductors Boundary conditions on the electric field Capacitors Poisson's equation The uniqueness theorem One-dimensional solution of Poisson's equation The method of images Complex analysis Separation of variables Dielectric and magnetic media Introduction Polarization Boundary conditions for and Boundary value problems with dielectrics Energy density within a dielectric medium Magnetization Magnetic susceptibility and permeability Ferromagnetism Boundary conditions for and Boundary value problems with ferromagnets Magnetic energy Magnetic induction Introduction Inductance Self-inductance Mutual inductance Magnetic energy Alternating current circuits Transmission lines Electromagnetic energy and momentum Introduction Energy conservation Electromagnetic momentum Momentum conservation Electromagnetic radiation Introduction The Hertzian dipole Electric dipole radiation Thompson scattering Rayleigh scattering Propagation in a dielectric medium Dielectric constant of a gaseous medium Dielectric constant of a plasma Faraday rotation Propagation in a conductor Dielectric constant of a collisional plasma Reflection at a dielectric boundary Wave-guides Relativity and electromagnetism Introduction The relativity principle The Lorentz transformation Transformation of velocities Tensors The physical significance of tensors Space-time Proper time 4-velocity and 4-acceleration The current density 4-vector The potential 4-vector Gauge invariance Retarded potentials Tensors and pseudo-tensors The electromagnetic field tensor The dual electromagnetic field tensor Transformation of fields Potential due to a moving charge Fields due to a moving charge Relativistic particle dynamics The force on a moving charge The electromagnetic energy tensor Accelerated charges The Larmor formula Radiation losses Angular distribution of radiation Synchrotron radiation

• Introduction
  • Intended audience
  • Major sources
  • Preface
  • Outline of course
• Vectors
  • Introduction
  • Vector algebra
  • Vector areas
  • The scalar product
  • The vector product
  • Rotation
  • The scalar triple product
  • The vector triple product
  • Vector calculus
  • Line integrals
  • Vector line integrals
  • Surface integrals
  • Vector surface integrals
  • Volume integrals
  • Gradient
  • Divergence
  • The Laplacian
  • Curl
  • Summary
• Time-independent Maxwell equations
  • Introduction
  • Coulomb's law
  • The electric scalar potential
  • Gauss' law
  • Poisson's equation
  • Ampère's experiments
  • The Lorentz force
  • Ampère's law
  • Magnetic monopoles?
  • Ampère's circuital law
  • Helmholtz's theorem
  • The magnetic vector potential
  • The Biot-Savart law
  • Electrostatics and magnetostatics
• Time-dependent Maxwell's equations
  • Introduction
  • Faraday's law
  • Electric scalar potential?
  • Gauge transformations
  • The displacement current
  • Potential formulation
  • Electromagnetic waves
  • Green's functions
  • Retarded potentials
  • Advanced potentials?
  • Retarded fields
  • Summary
• Electrostatics
  • Introduction
  • Electrostatic energy
  • Ohm's law
  • Conductors
  • Boundary conditions on the electric field
  • Capacitors
  • Poisson's equation
  • The uniqueness theorem
  • One-dimensional solution of Poisson's equation
  • The method of images
  • Complex analysis
  • Separation of variables
• Dielectric and magnetic media
  • Introduction
  • Polarization
  • Boundary conditions for  and 
  • Boundary value problems with dielectrics
  • Energy density within a dielectric medium
  • Magnetization
  • Magnetic susceptibility and permeability
  • Ferromagnetism
  • Boundary conditions for  and 
  • Boundary value problems with ferromagnets
  • Magnetic energy
• Magnetic induction
  • Introduction
  • Inductance
  • Self-inductance
  • Mutual inductance
  • Magnetic energy
  • Alternating current circuits
  • Transmission lines
• Electromagnetic energy and momentum
  • Introduction
  • Energy conservation
  • Electromagnetic momentum
  • Momentum conservation
• Electromagnetic radiation
  • Introduction
  • The Hertzian dipole
  • Electric dipole radiation
  • Thompson scattering
  • Rayleigh scattering
  • Propagation in a dielectric medium
  • Dielectric constant of a gaseous medium
  • Dielectric constant of a plasma
  • Faraday rotation
  • Propagation in a conductor
  • Dielectric constant of a collisional plasma
  • Reflection at a dielectric boundary
  • Wave-guides
• Relativity and electromagnetism
  • Introduction
  • The relativity principle
  • The Lorentz transformation
  • Transformation of velocities
  • Tensors
  • The physical significance of tensors
  • Space-time
  • Proper time
  • 4-velocity and 4-acceleration
  • The current density 4-vector
  • The potential 4-vector
  • Gauge invariance
  • Retarded potentials
  • Tensors and pseudo-tensors
  • The electromagnetic field tensor
  • The dual electromagnetic field tensor
  • Transformation of fields
  • Potential due to a moving charge
  • Fields due to a moving charge
  • Relativistic particle dynamics
  • The force on a moving charge
  • The electromagnetic energy tensor
  • Accelerated charges
  • The Larmor formula
  • Radiation losses
  • Angular distribution of radiation
  • Synchrotron radiation