Einstein's 1905 paper was called "On the electrodynamics of moving bodies". It derived the transformation of electric and magnetic fields when moving between inertial frames of reference. This 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.
To introduce the magnetic vector potential and to show that electromagnetism is Lorentz invariant.
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.
- 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.
- Lorentz invariance of Maxwell’s equations. Four vectors. Covariant and contravariant
representation. Minkowski’s metric tensor. Four vector formulation of Maxwell’s equation.
- Generation of EM waves and retarded potentials. The power radiated by accelerating
- The scattering of EM waves. Rayleigh scattering and Thompson scattering.
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
- 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
Subject specific skills
Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking
Analytical, communication, problem-solving, self-study
|Lectures||15 sessions of 1 hour (20%)|
|Private study||60 hours (80%)|
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 D1
|2 hour online examination (Summer)||85%|
Answer 2 questions out of 3
Feedback on assessment
Personal tutor, group feedback
This module is Core for:
- Year 3 of UPXA-FG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
- Year 3 of UPXA-FG31 Undergraduate Mathematics and Physics (MMathPhys)
- Year 3 of UPXA-F304 Undergraduate Physics (BSc MPhys)
- Year 3 of UPXA-F303 Undergraduate Physics (MPhys)
This module is Option list A for:
- Year 3 of UMAA-G100 Undergraduate Mathematics (BSc)
- Year 4 of UMAA-G101 Undergraduate Mathematics with Intercalated Year
- Year 3 of UPXA-F300 Undergraduate Physics (BSc)
- Year 4 of UPXA-F301 Undergraduate Physics (with Intercalated Year)
This module is Option list B for:
UMAA-G105 Undergraduate Master of Mathematics (with Intercalated Year)
- Year 3 of G105 Mathematics (MMath) with Intercalated Year
- Year 5 of G105 Mathematics (MMath) with Intercalated Year
UMAA-G103 Undergraduate Mathematics (MMath)
- Year 3 of G103 Mathematics (MMath)
- Year 4 of G103 Mathematics (MMath)
UMAA-G106 Undergraduate Mathematics (MMath) with Study in Europe
- Year 3 of G106 Mathematics (MMath) with Study in Europe
- Year 4 of G106 Mathematics (MMath) with Study in Europe
- Year 3 of UPXA-GF13 Undergraduate Mathematics and Physics (BSc)
- Year 4 of UPXA-GF14 Undergraduate Mathematics and Physics (with Intercalated Year)