Aims

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Classical mechanics of the 18th century has been largely superseded by the ideas of classical field theory.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 that 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; Differential operators; Line, surface and volume integrals; Conservative fields; Divergence theorem; Stokes’ theorem.
2. Electrostatics: Coulomb’s Law; Gauss’ Law for discrete charges; Electrostatic potential; Continuous charge distributions; Analogy with Newtonian gravitation.
3. Magnetostatics: Electric currents and Ohm’s law; Ampere’s law; Gauss’ law for magnetic fields; Magnetic vector potential; Biot-Savart Law.
4. Electromagnetism and waves: Lorentz force; Electromotive force; Faraday’s law; Conservation of charges; Maxwell’s equations; Electromagnetic waves; Plane wave solutions.
5. Introduction to magnetohydrodynamics: induction equation.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.

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.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments 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.