PX3847.5 Electrodynamics
Introductory description
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 (EMwaves) emitted by accelerating charges are described using retarded potentials, which are the timedependent analogs of the usual electrostatic potential and the magnetic vector potential, and have the wavelike 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 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.
 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
charges.  The scattering of EM waves. Rayleigh scattering and Thompson scattering.
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 4vectors
 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
View reading list on Talis Aspire
Subject specific skills
Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking
Transferable skills
Analytical, communication, problemsolving, selfstudy
Study time
Type  Required 

Lectures  15 sessions of 1 hour (20%) 
Private study  60 hours (80%) 
Total  75 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
Costs
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
Weighting  Study time  

Coursework  15%  
2 hour online examination (Summer)  85%  
Answer 2 questions out of 3

Feedback on assessment
Personal tutor, group feedback
Courses
This module is Core for:
 Year 3 of UPXAFG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
 Year 3 of UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
 Year 3 of UPXAF304 Undergraduate Physics (BSc MPhys)
 Year 3 of UPXAF303 Undergraduate Physics (MPhys)
This module is Option list A for:
 Year 3 of UMAAG100 Undergraduate Mathematics (BSc)
 Year 4 of UMAAG101 Undergraduate Mathematics with Intercalated Year
 Year 3 of UPXAF300 Undergraduate Physics (BSc)
 Year 4 of UPXAF301 Undergraduate Physics (with Intercalated Year)
This module is Option list B for:

UMAAG105 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

UMAAG103 Undergraduate Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 4 of G103 Mathematics (MMath)

UMAAG106 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 UPXAGF13 Undergraduate Mathematics and Physics (BSc)
 Year 4 of UPXAGF14 Undergraduate Mathematics and Physics (with Intercalated Year)