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2005/06 Undergraduate Module Catalogue

MATH3433 Electromagnetism

15 creditsClass Size: 100

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2005/06

Pre-requisites

MATH2360 or MATH2420 or equivalent.

This module is approved as an Elective

Objectives

To develop a mathematical description of electromagnetic phenomena. On completion of this module, students should be able to a) write down Maxwell?s equations for the electromagnetic field; b) solve simple problems in electrostatics and magnetostatics; c) obtain the wave equation and construct solutions representing plane electromagnetic waves;

Syllabus

Electromagnetic theory is concerned with electric and magnetic fields produced by electric charges and currents. Such fields are widespread in nature and occur on all scales from those within radio and computer circuits and up to the magnetic fields which pervade the sun, stars and galaxies. The behaviour of these fields is described by a set of four partial differential equations, known as Maxwell?s equations, which express the divergence and curl of electric and magnetic fields in terms of the sources producing them. A major triumph of the theory has been Maxwell?s demonstration that these partial differential equations possess solutions in the form of waves travelling at the speed of light. He was thus led to predict the existence of radio waves some 20 years before they were detected experimentally, and from this discovery has grown the modern telecommunications industry. As well as being a subject of immense practical application, electromagnetic theory is a cornerstone of modern theoretical physics and has close links with the theory of relativity. The topics covered are: 1. Basic experimental results for electric and magnetic fields and their expression in integral form and as differential equations. 2. Electrostatics, building from Coulomb?s law. Gauss?s law. The idea of electrostatic potential. Solving certain electrostatic problems using Gauss?s law. The electric dipole. Conductors and capacitors. Electrostatic energy. 3. Magnetostatics. Amphre?s law. The solenoidal condition on the magnetic field. The idea of a vector potential. The Bio-Savart law; calculation of the magnetic field due to a current loop. Magnetic materials. Ohm?s law. 4. Faraday?s experiments and Faraday?s law. Generators and motors. 5. Displacement current. Maxwell?s equations and boundary conditions. Derivation of the wave equation. Electromagnetic waves in free space. Reflection and transmission of waves at dieletric interfaces. Electromagnetic waves in electrical conductors. Waveguides.

Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Lectures: 26 hours. 7 examples classes.

Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

One 3 hour examination at end of semester (100%).

Reading list

The reading list is available from the Library website

Last updated: 13/05/2005

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