Lecturer: David Leadley

Weighting: 10 CATS

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.

Aims:

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

Objectives:

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

Syllabus:

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
   charges.
4. The scattering of EM waves. Rayleigh scattering and Thompson scattering.
5. Role of interaction of waves with electrical geometry. Waveguides and optical fibres.

Commitment: 20 Lectures

Assessment: 1.5 hour examination (85%), coursework (15%)

Recommended Text: IS Grant and WR Phillips, Electromagnetism, Wiley