BSc Physics with Theoretical Physics

Electromagnetism

Pre-requisites:

• Mathematics 2 PHYS10372 OR Introduction to Vector Calculus MATH11411
• Electricity & Magnetism PHYS10342

To introduce Maxwell's equations and use them to derive properties of electromagnetic waves; to introduce simple models for the interaction of electromagnetic fields with matter.

On completion successful students will be able to:

1. Derive Maxwell's equation set from the empirical laws of electromagnetism.

2. Use the fundamental laws of electromagnetism to solve simple problems of electrostatics, magnetostatics and electromagnetic induction in a vacuum;

3. Modify Maxwell's laws to apply in the presence of materials and solve problems involving them;

4. Derive the electromagnetic boundary conditions which apply at the interface between two simple media, and to use them to solve problems involving two or more materials.

5. Explain the properties of plane electromagnetic waves in a vacuum and in simple media and to be able to derive these properties from Maxwell's equations

1. Mathematical Preliminaries

Revision of Vector Calculus; Dirac δ-function and point particles; Laplace’s & Poisson’s equations and their uniqueness theorem.

(2 lectures)

2. Maxwells equations in a vacuum

Continuity equation; Integral forms of Maxwell’s equations; Differential forms of Maxwell’s equations; Potential formulation; Electrostatics and magnetostatics as the time independent limit; Calculation of field configurations; Electric and magnetic dipoles; Connections between electromagnetism and special relativity.

(7 lectures)

3. Electromagnetic effects in simple materials

Conductors: mechanisms for conduction; the method of images and the motion of particles near a conductor. Dielectrics: capacitance, relative permittivity; polarization & electric susceptibility; mechanism for polarization; electrostatics in a dielectric; Interfaces between dielectrics. Magnetism: inductance & permeability; magnetization & magnetic susceptibility; diamagnetism and paramagnetism; magnetostatics.  Ferromagnetism: ideal ferromagnets; hysteresis.

(8 lectures)

4.  Electromagnetic waves

Maxwell’s equations in free space; Plane waves; Wave solutions for E & B fields; Poynting vector, irradiance & radiation pressure; Polarization of EM waves; Reflection of EM waves at a perfect conductor; EM waves in the presences of a current; EM waves in a dielectric.

(5 lectures)

10% Tutorial Work/attendance 

Feedback will be offered by tutors on students’ written solutions to weekly example sheets, and model answers will be issued.

Grant, I.S. & Phillips, W.R. Electromagnetism (2nd ed.) (Wiley)

Griffiths, D.J. Introduction to Electrodynamics (4^th ed.) (Cambridge Uni. Press)

Useful references

Bleaney, B.I. & Bleaney B. Electricity & Magnetism (3^rd ed.) (Oxford Uni. Press)

Duffin, W.J. Electricity and Magnetism (4^th ed.) (Duffin, previous eds. McGraw-Hill)

Jackson, J.D. Classical Electrodynamics (3^rd ed.) (Wiley)

Tuition fees for home students commencing their studies in September 2027 will be £10,050 per annum. Tuition fees for international students will be £40,300 per annum.

For general information please see the undergraduate finance pages.

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

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