Skip to main content Skip to navigation

PX3A3-10 Electrodynamics

Undergraduate Level 3
Module leader
David Leadley
Credit value
Module duration
10 weeks
Study location
University of Warwick main campus, Coventry
Introductory description

Einstein's 1905 paper on special relativity was called "On the electrodynamics of moving bodies". It derived the transformation of electric and magnetic fields when moving between inertial frames of reference. The module works through this transformation and looks at its implications. The module starts by covering the magnetic vector potential, A, which is defined so that the magnetic field B=curl A and which is a natural quantity to consider when looking at relativistic invariance.

The radiation (EM-waves) emitted by accelerating charges are described using retarded potentials, which are the time-dependent analogs of the usual electrostatic potential and the magnetic vector potential, and have the wave-like nature of light built in. The scattering of light by free electrons (Thomson scattering) and by bound electrons (Rayleigh scattering) will also be described. Understanding the bound electron problem led Rayleigh to his celebrated explanation of why the sky is blue and why sunlight appears redder at sunrise and sunset.

Module web page

Module aims

To introduce the magnetic vector potential and to show that electromagnetism is Lorentz invariant.

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

  1. Revision of special relativity. Revision of Maxwell's Equations in vacuum and in a
    macroscopic medium. Simple models of polarization. Displacement current; Potentials ϕ
    and A. Coulomb and Lorenz gauge. Laplace's and Poisson's equations and the solution of
    Maxwell's equations. Retarded potentials.
  2. Lorentz invariance of Maxwell’s equations. Four vectors. Covariant and contravariant
    representation. Minkowski’s metric tensor. Four vector formulation of Maxwell’s equation.
  3. Generation of EM waves and retarded potentials. The power radiated by accelerating
  4. The scattering of EM waves. Rayleigh scattering and Thompson scattering.
  5. Role of interaction of waves with electrical geometry. Waveguides and optical fibres.
Learning outcomes

By the end of the module, students should be able to:

  • Work with the vector potential and Lorentz invariant form of Maxwell's equations
  • Manipulate Maxwell’s equations and solve representative problems using 4-vectors
  • Describe physics of EM radiation and scattering and be able to describe the propagation of EM waves through free space and in waveguides
  • Solve Maxwell's equations to calculate the EM field from known source distributions
Indicative reading list

Classical Electrodynamics, JD Jackson
Electromagnetism, I.S. Grant and W.R. Phillips

View reading list on Talis Aspire

Subject specific skills

Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking

Transferable skills

Analytical, communication, problem-solving, self-study

Study time

Type Required
Lectures 20 sessions of 1 hour (20%)
Private study 80 hours (80%)
Total 100 hours
Private study description

Working through lecture notes, solving problems, wider reading, discussing with others taking the module, revising for exam, practising on past exam papers


No further costs have been identified for this module.

You do not need to pass all assessment components to pass the module.

Assessment group D
Weighting Study time
Coursework 15%
In-person Examination 85%

Answer 2 questions

  • Answerbook Green (8 page)
  • Students may use a calculator
Assessment group R
Weighting Study time
In-person Examination - Resit 100%

Answer 2 questions

  • Answerbook Pink (12 page)
  • Students may use a calculator
Feedback on assessment

Personal tutor, group feedback

Past exam papers for PX3A3


This module is Core for:

  • UPXA-FG31 Undergraduate Mathematics and Physics (MMathPhys)
    • Year 3 of FG31 Mathematics and Physics (MMathPhys)
    • Year 3 of FG31 Mathematics and Physics (MMathPhys)
  • Year 3 of UPXA-F303 Undergraduate Physics (MPhys)
  • Year 3 of UPXA-F3FA Undergraduate Physics with Astrophysics (MPhys)

This module is Option list A for:

  • UPXA-F300 Undergraduate Physics (BSc)
    • Year 3 of F300 Physics
    • Year 3 of F300 Physics
    • Year 3 of F300 Physics
  • Year 3 of UPXA-F303 Undergraduate Physics (MPhys)
  • UPXA-F3F5 Undergraduate Physics with Astrophysics (BSc)
    • Year 3 of F3F5 Physics with Astrophysics
    • Year 3 of F3F5 Physics with Astrophysics

This module is Option list B for:

  • UPXA-GF13 Undergraduate Mathematics and Physics (BSc)
    • Year 3 of GF13 Mathematics and Physics
    • Year 3 of GF13 Mathematics and Physics
  • Year 4 of UPXA-GF14 Undergraduate Mathematics and Physics (with Intercalated Year)