PX384 Electrodynamics

Weighting: 7.5 CATS

The module starts by revising the magnetic vector potential, A, which is defined so that the magnetic field B=curl A. We will see that this is the natural quantity to consider when exploring how electric and magnetic fields transform under Lorentz transformations (special relativity).

The radiation (EM-waves) emitted by accelerating charges will be described using retarded potentials (these 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:
At the end of the module, you should:

• Be familiar with the vector potential and Lorentz invariant form of Maxwell's equations
• Be able to manipulate Maxwell’s equations and solve representative problems using 4-vectors
• Understand the physics of EM radiation and scattering and be able to describe the propagation of EM waves through free space
• Know how Maxwell's equations can be solved 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 (examples, exercises on-line). Minkovsky’s metric tensor (exercises on-line). Four vector formulation of Maxwell’s equation (examples, exercises on-line).
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.

Commitment: 15 Lectures

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

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