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.
An expanded version of these notes has appeared as a textbook.
“Still those papers lay before me, Problems made express to bore me, When a silent change came o’er me, In my hard uneasy chair. Fire and fog, and candle faded, Spectral forms the room invaded, Little creatures, that paraded On the problems lying there.”
James Clerk Maxwell as a Cambridge undergraduate; Ode to the maths examples sheets
Div, Grad and Curl
Introduction and Electrostatics
Introduction; Charge, Current and Conservation; Forces and Fields; Maxwell Equations; Gauss' Law; Coulomb Law; Electrostatic Potential; Electrostatic Energy; Conductors.
Magnetostatics
Ampere's Law; The Vector Potential; Magnetic Monopoles; Gauge Transformations; Biot-Savart Law; Magnetic Dipoles; Magnetic Forces; What is a Magnet?
Electrodynamics
Faraday's Law of Induction; Inductance; Magnetostatic Energy; Resistance; Displacement Current; Light; Polarisation; Poynting Vector.
Electromagnetism and Relativity
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.
Electromagnetic Radiation
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.
Electromagnetism in Matter
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.
“He could not lecture. He seemed to have no planned course...I grew weary of seeing his demonstrator standing, with thumbs in his waistcoat pockets, almost behind the professor as the latter struggled to boil water.”
Student evaluation (by Karl Pearson, no less) of a later version of Maxwell at Cambridge
“Never repeat a phrase. Never go back and ammend. If at a loss for a word, not to ch-ch-ch or eh-eh-eh, but to stop and wait for it. Never doubt a correction given to me by another.”
Faraday's advice to himself on lecturing.