MPhys Physics with Astrophysics / Course details

Electrodynamics (M)

To cover theoretical aspects of electromagnetic fields and radiation.

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates

On completion successful students will be able to

1. use scalar and vector potentials and explain the concept of gauge invariance;
2. demonstrate the compatibility of electrodynamics and special relativity;
3. use Lorentz covariant formalism (scarlars, 4-vectors and tenors) in the context of electrodynamics and special relativity;
4. solve Poisson's equation and the inhomogenous wave equation;
5. distinguish between radiation fields and other electromagnetic fields;
6. calculate the radiated power produced by accelerating charges.
    

1.     Electromagnetic Field Equations (7 lectures)

Maxwell's equations and wave solutions. Definition of scalar and vector potentials. Electro- and magnetostatics and Poisson’s equation; multipole expansions. Electrodynamics in Lorentz Gauge; the inhomogeneous wave equation and the retarded time.

2.     Electromagnetism and Relativity (7 lectures)

Covariant and contravariant formalism of Lorentz transformations; Scalars, four vectors and tensors; relativistic dynamics. Consistency of Maxwell's equations and relativity. Electromagnetic field tensor and electrodynamics in covariant form.

3.     Accelerating Charges (6 lectures)

Lienard-Wiechert potentials; Power radiated from an arbitrarily moving charge. Larmor’s power formula; synchrotron radiation; bremsstrahlung.

4.     Harmonically Varying Sources (2 lectures)

Multipole radiation: electric (Hertzian) and magnetic dipole radiation; slow-down of pulsars. Rayleigh and Thomson scattering.

Feedback will be offered by examples class tutors based on examples sheets, and model answers will be issued. A few optional sessions will provide extra problem solving opportunities and cover a few interesting “extra-curricular” topics.

Recommended texts:
Heald, M.A. & Marion, J.B. Classical Electromagnetic Radiation, (Academic Press,
London 1995)
Griffiths, D.J., Introduction to Electrodynamics (Benjamin Cummings; 3rd edition (December 30, 1998)

Supplementary reading:
Jackson, J.D., Classical Electrodynamics, (John Wiley & Sons, 3rd edition 1999)
Schwartz, M., Principles of Electrodynamics, (Dover Publications, 1972)
Feynman, The Feynman Lectures on Physics, Vol II (Addison Wesley, 1964)