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MC424 Electromagnetic Theory
| Credits: 20 |
Convenor: Dr. J. Levesley |
Semester: 2 |
| Prerequisites: |
essential: MC123, MC121, MC224 |
desirable: MC223, MC225 |
| Assessment: |
Continual assessment/project: 40% |
Three hour exam: 60% |
| Lectures: |
24 |
Classes: |
12 |
| Tutorials: |
10 |
Private Study: |
80 |
| Labs: |
none |
Seminars: |
12 |
| Project: |
22 |
Other: |
none |
| Total: |
150 |
|
|
Explanation of Pre-requisites
Students must have a good understanding of simple dynamics, force, acceleration, and velocity. It is essential that students are competent at solving simple first order and second order differential equations. It is also very important that they can
reliably use the divergence theorem, Stokes' theorem, and compute line, surface and volume integrals. Vector identities will be used often.
It would be desirable that students understand gravitation. An understanding of special relativity will increase the number of projects a student may choose from.
Course Description
Electricity and magnetism govern our lives, from the boiling of the
kettle to the transmission of information around the globe. One of the
triumphs of 19th Century mathematics was to describe electromagnetic
phenomena using a deceptively simple set of differential equations,
Maxwell's Equations. These equations were used to predict
the existence of electromagnetic waves, a concept which pervades
physics. Such waves are responsible for tanning our skin, and
heating our microwave lunch. Electromagnetic
theory provides an excellent model for a number of natural phenomena, and
allows us to bend these phenomena to our own will.
The lectured material in this course will take the student through the development of some of the fundamental ideas in electromagnetic theory, culminating in the derivation of Maxwell's Equations. We then see how these
equations lead to the prediction of electromagnetic waves, and study a simple subclass of such waves, the plane waves.
The project work will build upon the lectured material, but will not be examinable. The project is intended to give the student the opportunity to do
some investigation into a question in electromagnetic theory which interests them.
Aims
This module is intended to give the student an appreciation of power of mathematics in modelling physical phenomena. It is hoped that the students will experience the evolutionary nature of mathematics, and feel some
of the excitement of discovery of new ideas. The students will also have an opportunity to apply some mathematical tools to produce useful answers
in real life situations.
Objectives
By the end of the course the students will
- know how to model simple circuits involving resistors, capacitors and inductors;
- how to derive Maxwell's Equations, and how to physically interpret these equations;
- be able to use Maxwell's Equations to derive the wave equation;
- have completed a project on a topic extending the lectured material.
Transferable Skills
In this course we will develop the ability
- to write mathematical English clearly and concisely;
- to orally present a technical topic to a specialist audience;
- to discuss a technical subject with other specialists;
- to work in a team;
- to do independent research.
Syllabus
Networks: resistors, capacitors, and inductors. Electrostatics: charge, the electric field, Gauss' Flux Theorem, electric potential, capacitance, energy stored in a capacitor, and energy stored in the electric field. Current density, charge conservation
Ohm's law, decay of charge, and energy dissipation in a conductor. Magnetic field: force on a moving charge, the law of Biot-Savart, magnetic field is divergence free, Ampère's Law, and the vector potential.
Electromagnetic induction: Faraday's Law, the dynamo, inductors, the energy stored in an inductor, and the energy stored in the magnetic field. Electric and magnetic media, and changes to Gauss' Flux Theorem and Ampère's Law. Maxwell's Equations and c
nstitutive relations. The wave equation and the plane wave solution. Polarisation, reflection and refraction.
Reading list
Background:
R. Dobbs,
Basic Electromagnetism,
Chapman and Hall, 1993.
C.A. Coulson and T.J.M. Boyd,
Basic Electricity,
Longman, 1979.
W.A. Rachinger,
Electricity and Magnetism, Diagnostic Tests,
Wiley and Sons, 1973.
Details of Assessment
The coursework for the continual assessment has three components:
fortnightly work based on example sheets worth 10%; a mini project
worth 5%, 1% of which will be for a short presentation; a
large project worth 25%, 5% of which will
be for a short presentation.
The written May/June examination consists of six questions, and candidates can get full marks for perfect answers to four questions. The examination is designed to test the students computational skills, as well as test their
understanding of the main concepts in the module. Project work will not be examined.
Next: MC430 Approximation Theory
Up: Year 4
Previous: Year 4
Roy L. Crole
10/22/1998