# MMath&Phys Mathematics and Physics

Year of entry: 2023

## Course unit details:Electromagnetism

Unit code PHYS20141 10 Level 2 Semester 1 No

Electromagnetism

### Pre/co-requisites

Unit title Unit code Requirement type Description
Mathematics 1 PHYS10071 Pre-Requisite Compulsory
Electricity & Magnetism PHYS10342 Pre-Requisite Compulsory
Mathematics 2 PHYS10372 Pre-Requisite Compulsory

### Aims

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.

### Learning outcomes

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

### Syllabus

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)

### Assessment methods

Method Weight
Other 10%
Written exam 90%

10% Tutorial Work/attendance

### Feedback methods

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 (4th ed.) (Cambridge Uni. Press)

Useful references

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

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

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

### Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 22
Tutorials 4
Independent study hours
Independent study 72.5

### Teaching staff

Staff member Role
Mark Hughes Unit coordinator