PHSI425 Advanced Electromagnetism

This course completes the standard framework of classical electromagnetism.

Electrodynamics formulated in terms of scalar and vector potentials, mechanical conservation laws for electromagnetism and an introduction to the theory of electromagnetic radiation.

Prerequisites:
PHSI 332

This paper consists of 15 lectures and 6 tutorials. There are 3 assignments.

Assesment:
Final Exam 70%, Assignments 30%

Important information about assessment for PHSI425

Course Coordinator:
Dr Terry Scott

After completing this paper students are expected to have achieved the following major learning objectives:

• Be able to recast the electric and magnetic fields in terms of scalar and vector potentials and to recast Maxwell’s equations in terms of these potentials.
• Understand the concept of an electromagnetic gauge, in particular to understand the use and importance of the Coulomb and Lorentz gauges. To be able to perform simple gauge transformations.
• Understand the conservation of energy and linear momentum in the interaction between electromagnetic fields and matter. To be able to use the Poynting vector to find the energy density, linear momentum density, and angular momentum density of a system of electromagnetic fields, charges, and currents.
• Understand the concept of retarded time and retarded scalar and vector potentials. To be able to show that these potentials satisfy the appropriate Laplace equations.
• Understand the Lienard-Wiechert potentials as special cases of retarded potentials. To understand the physical significance of these potentials and be able to use them to analyse simple configurations of charges and currents.
• Understand the production of electromagnetic radiation by accelerating charges.
• To be able to derive and analyse the fields radiated by oscillating electric and magnetic dipoles.

Topics:

• Review: Theory of vector fields and the Helmholtz theorem.
• Electrostatic multipole expansion.
• Magnetic vector potential.
• Magnetostatic multipole expansion
• Energy conservation in electromagnetic interactions, Poynting’s theorem, the Poyting vector.
• Conservation of linear momentum, the Maxwell stress tensor. Conservation of angular momentum.
• Maxwell’s equations in terms of the scalar and vector potentials. Gauge transformations. The Coulomb and Lorentz gauges.
• Retarded potentials.
• The Lienard-Wiechert potentials.
• Electric and magnetic fields from Lienard-Wechert potentials.
• Dipole radiation.
• Radiation from an arbitrary source.
• Power radiated by a point charge.
• Radiation reaction.

Resources:
Textbook: Griffiths, D.J. Introduction to Electrodynamics, Fourth edition