# Classical Electrodynamics

Course
2017-2018

Electric and Magnetic Fields

## Description

The course covers Maxwell’s theory of electromagnetic field, wave theory of light, and propagation of electromagnetic waves in media.

The course exploits vector calculus, theory of linear differential equations and elements of asymptotic analysis to derive a number of foundational results in the theory of electromagnetism.

The course is divided into four major components

1. Maxwell's equations: derivation, solution strategies, conservation laws.
2. Electromagnetic waves.
4. Electromagnetic fields in material media.

The course will be delivered in traditional style, combining power-point enhanced lectures with weekly home assignments.

The detailed list of topics includes

• Maxwell's four equations in the integral and differential form

• Continuity equation and local conservation laws

• Energy conservation law and Poynting's theorem

• Maxwell's stress tensor

• Properties of Maxwell's homogeneous equations.

• Solving Maxwell's homogeneous equations. The Fourier method.

• Electromagnetic waves in vacuum.

• Properties of Maxwell's equations with sources.

• The vector and scalar potentials.

• Gauge symmetry.

• The retarded potentials.

• The Lienard-Wiechert formula.

• Maxwell's equations in good conductors.

• The skin effect.

• Theory of reflection.

• Waveguides.

• Electric field in dielectric media. Dielectric polarisation. Bound charge.

• Electric susceptibility, dielectric constant, electric displacement.

• Magnetic field in magnetically polarisable media. Magnetisation. Bound current.

• Magnetic susceptibility, types of magnetic response. Permeability.

• Material interfaces and boundary conditions.

• Electromagnetic waves in material media.

• Refraction of electromagnetic waves.

## Course objectives

The course will provide students with working knowledge of Maxwell's equations
and interaction of electromagnetic fields with matter.

At the end of the course the student will be able to

• Construct solutions to homogeneous Maxwell's equations in vacuum,

• Calculate the energy flux and the stresses carried by the E-M field,

• Calculate the E-M field created by an arbitrary moving charge,

• Calculate the dipole radiation power,

• Derive equations for the E-M field in conductors and linear dielectric media,

• State and solve elementary boundary problems for E-M field,

• Analyise refraction/reflection of E-M waves in simple geometries,

The course will also help the student advance their hands-on knowledge of vector algebra,
vector calculus, linear algebra and differential equations.

Rooster

## Mode of instruction

Seminar and Lecturers

## Assessment method

Written examination with short questions

## Blackboard

Blackboard will be used for the provision of lecture notes, distribution of home assignment worksheets, and announcements.