On successful completion of this module, students will be able to:
Describe how to find the Fourier transform of a Green function and hence evaluate it for the equation of d'Alembert.
Use the retarded Green function to solve the Maxwell equations for electromagnetic fields.
Describe electromagnetic radiation, including plane-wave and spherical vector waves.
Explain the concepts of electromagnetic potential and that of retarded time for charges undergoing acceleration.
Analyse simple radiating systems, in which the electric dipole, magnetic dipole or electric quadrupole dominate.
Show how the orthogonality and magnitude of electric and magnetic radiative fields may be established.
Use expressions for the fields to evaluate the differential power radiated in a particular direction, and hence find the total power.
Determine the motion of a radiating charged particle in the electric field of another charged particle or in a constant magnetic field.
The purpose of module MA3432 is to outline the properties of Classical Electrodynamics as an example of a massless vector field and to indicate important features in the theory of radiation, including the intensity and directions of radiation from accelerated particles with charge. Applications determining the motion of charged particles in particular electric and magnetic fields are considered, emphasis being placed upon the role of radiation in finding the dynamics of the particles. The module forms an element of the undergraduate programme in theoretical physics being built upon prerequisite first and second year courses in classical dynamics and mathematics and leading to courses in the fourth and final year including quantum field theory. The module content will include;
Cartan formalism for Maxwell equations.
Solving Maxwell's equations; Green functions for Laplacian, d'Alembertian.
EM waves, polarization & stokes parameters.
Liénard-Wiechert potential; velocity, acceleration fields for moving charge.
Radiation theory; velocity and acceleration fields in three dimensions.
Non-relativistic Larmor formula and relativistic Liénard
Linear & circular accelerated motion; radiation inconstant magnetic field.
Angular districution of relativistic radiation; electric & magnetic elements.
Radiation during collisions, Bremsstrahlung.
Introduction to radiation damping; scattering and absorbtion of radiation.
Envoi: quantum chromodynamics and the unified electroweak interaction.
Classical Electrodynamics, J. David Jackson, John Wiley (3rd edition) 1998
Introduction to Electrodynamics, David J. Griffiths, Prentice-Hall, 1999
Electrodynamics courses at Stanford University: EM fields & EM radiation
MA3431 Classical Field Theory
This module will be examined jointly
in a 2-hour examination in Trinity term. Assignments will contribute 15% to the final annual grade. Supplementals if required will consist of 100% exam.