David Tong: Electromagnetism

David Tong: Lectures on Electromagnetism

These lecture notes provide a comprehensive introduction to Electromagnetism, aimed at undergraduates. Individual chapters and problem sheets are available below. The full set of lecture notes come in around 230 pages and can be downloaded here. Please do email me if you find any typos or corrections.

PostScript      PDF


  • Div, Grad and Curl:   PDF

  • 1. Introduction and Electrostatics:   PDF
    Introduction; Charge, Current and Conservation; Forces and Fields; Maxwell Equations; Gauss' Law; Coulomb Law; Electrostatic Potential; Electrostatic Energy; Conductors.
  • 2. Magnetostatics:   PDF
    Ampere's Law; The Vector Potential; Magnetic Monopoles; Gauge Transformations; Biot-Savart Law; Magnetic Dipoles; Magnetic Forces; What is a Magnet?
  • 3. Electrodynamics:   PDF
    Faraday's Law of Induction; Inductance; Magnetostatic Energy; Resistance; Displacement Current; Light; Polarisation; Poynting Vector.
  • 4. Electromagnetism and Relativity:   PDF
    Review of Special Relativity; Indices; Continuity Equation; Magnetism and Relativity; Maxwell Equations in Covariant Form; Gauge Transformations in Covariant Form; Lorentz Force Law; Relativistic Motion of Particles in Background Fields. The action for relativistic particles. The Maxwell Action. The Energy Momentum Tensor and Angular Momentum.
  • 5. Electromagnetic Radiation:   PDF
    Retarded Potentials; Green's functions for Helmholtz and Wave Equations; Dipole Radiation; Larmor Formula; Pulsars; Thomson Scattering and Rayleigh Scattering; Lienard-Wierchert Potentials; Bremsstrahlung, Cyclotron and Synchrotron Radiation.
  • 6. Electromagnetism in Matter:   PDF
    Polarisation; Electric Displacement; Bound Currents; Macroscopic Maxwell Equations; Reflection, Refraction and the Fresnel Equations; Dispersion; Atomic Polarisability; Kramers-Kronig Relation; Drude Model for Conductors; Plasma Oscillations; Screening, Debye-Huckel Model, Thomas Fermi Theory, Lindhard Theory and Friedel Oscillations.

Problem Sheets

  • Problem Sheet 1:   Postscript    PDF    Electric Fields

  • Problem Sheet 2:   Postscript    PDF    Magnetic Fields

  • Problem Sheet 3:   Postscript    PDF    Electromagnetic Waves and Relativity

Electromagnetism on the Web

Some Classic Resources