MMath&Phys Mathematics and Physics / Course details

Electrodynamics (M)

For recommneded theory units following this module please see PHYS40202, PHYS40481, PHYS40771 and  PHYS40682.

To cover theoretical aspects of electromagnetic fields and radiation.

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; Lorentz transformations applied to radiated power; synchrotron radiation and; 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. Some optional sessions will provide extra problem solving opportunities and cover a few interesting “extra-curricular” topics.

Recommended texts:

Griffiths, D.J., Introduction to Electrodynamics, (Cambridge University Press, 4th edition, 2017) 
Heald, M.A. & Marion, J.B., Classical Electromagnetic Radiation, (Academic Press, 
3rd Edition, 1995) 

Supplementary reading:

Jackson, J.D., Classical Electrodynamics, (John Wiley & Sons, 3rd edition, 1999) 
Feynman, R.P., The Feynman Lectures on Physics, Vol II (Addison Wesley, 1964) 

  Zangwill, A., Modern Electrodynamics (Cambridge University Press, 2013) 

 Rybicki, G.B. & Lightman, A.P., Radiative Processes in Astrophysics (John Wiley & Sons, 1979) 
Schwartz, M., Principles of Electrodynamics, (Dover Publications, 1972)