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Prospectus

Classical Electrodynamics

Course
2021-2022

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 in which you are required to apply your mathematical skills and physics understanding to a variety of situations and systems.

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

After completion of this course you will be able to: – apply the theory of electromagnetism through Maxwell’s equations, using the tools of vector calculus. – explain the unifying connections between seemingly different phenomena in nature such as electromagnetic induction and optics. – describe the basic properties of wave propagation, diffraction and interference.
You will also have enhanced your general problem-solving and mathematical skills.

Timetable

Schedule
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Assessment method

Written Examination with short questions