MAS3805 : Classical Fields

Semester 2 Credit Value: 10
ECTS Credits: 5.0


To introduce the fundamental concepts and governing equations of classical field theory, with special emphasis on electrodynamics.

Module summary
Classical mechanics of the 18th century has been largely superseded by the ideas of classical field theory. Everything in the physical world, from fundamental particles, to magnetism, light and gravity, is described in terms of a field permeating space and time. The basic ideas of field theory are common to all these applications: moving sources disturb the field, disturbances propagate as waves, and the field reacts back on the sources. The exemplar of field theory is the theory of electric and magnetic fields which forms the core of this module. You will see the power of mathematics in explaining phenomena from electromagnetism and gravity.

Outline Of Syllabus

1. Introduction and revision: Scalar and vector fields; Div, grad, curl and the Laplacian;
Conservative and Solenoidal fields-Poincare Lemma;
Laplace’s equation, Poisson’s equation and the Wave equation.
2. Electrostatics: Coulomb’s Law; Gauss’ Law for discrete charges; Electrostatic potential; Continuous charge distributions.
3. Magnetostatics: Magnetic forces; Electric currents and Ohm’s law; Biot-Savart Law;
Ampere’s law;
Magnetic vector potential.
4. Electromagnetism and waves: Lorentz force law; Displacement currents and electromagnetic induction; Maxwell’s equations;
Wave equations;
Plane wave solutions; Permittivity and dispersive waves.
5. Sources: Multivariable Fourier transforms;
Wave equation with sources;
Retarded potentials;
Simple examples with radiating sources.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Scheduled Learning And Teaching ActivitiesDrop-in/surgery120:102:00Office hours
Guided Independent StudyIndependent study125:0025:00Studying, practising, and gaining understanding of course material
Guided Independent StudyIndependent study33:009:00Review of coursework assignments and course test
Guided Independent StudyIndependent study26:0012:00Preparation for coursework assignments
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Description Length Semester When Set Percentage Comment
Written Examination1202A90N/A
Written Examination402M5Class test
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Coursework assignments
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The written exercises are expected to consist of two assignments of equal weight: the exact nature of assessment will be explained at the start of the module. The coursework assignments and the (in class) coursework test allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists