PHY3054 Electromagnetism II (IS) 2022-23
Prof. J. Bertolotti
Delivery Weeks: T1:01-11
Level: 6 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 4 students (approx)


This module is an Independent Study version of PHY3051. It is taken by students remote from Exeter, e.g. at Stage 3 of F304, who are therefore unable to attend traditional lectures and tutorials.

This is the second electromagnetism module taken by Physics students. It builds on PHY2021 (Electromagnetism I) and covers fundamental physics that students are capable of directly observing. The dielectric and magnetic properties of solids are introduced and a range of interesting phenomena are covered including the scattering of light the propagation of electromagnetic waves, etc., are important in a wide variety of areas and in many key technologies. The early part of the module is primarily a recap and a reinforcing of the difficult material treated at the end of PHY2021.

Module Aims

The module aims to develop students' understanding of Maxwell's equations and their applications including some advanced topics. Specifically, students will get to the point where they can handle the fundamentals of fields due to moving charges and also to begin to explore the interaction of electromagnetic radiation with matter.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

Syllabus Plan

  1. Maxwell's Equations and Electromagnetic Waves
    1. Maxwell's equations for the electromagnetic field.
    2. Scalar and vector potentials.
    3. The equation of continuity.
    4. The wave equation and wave solutions to Maxwell equations.
    5. Linear, circular and elliptical polarization states of a wave.
    6. Energy of a wave and the Poynting theorem.
    7. The electromagnetic stress tensor and the momentum of an electromagnetic field.
    8. Gauge invariance and Gauge fixing. The Weyl, Lorenz and Coulomb gauges.
    9. Covariance of Maxwell equations and Lorentz transforms
    10. Field generated by a moving charge. The Liénard-Wiechert potentials.
    11. Larmor formula
  2. Electromagnetic materials
    1. Polarization of dielectric materials. Multipole expansion.
    2. Electric susceptibility and the displacement field.
    3. Clausius-Mossotti relation.
    4. Boundary conditions for the electric and the displacement fields.
    5. Magnetic dipoles and magnetization.
    6. Magnetic susceptibility and the magnetic field.
    7. Boundary conditions for the magnetic induction and the magnetic fields.
    8. Larmor precession.
    9. Paramagnetism and Curie law.
    10. Ferromagnetism, spontaneous magnetization, and magnetic hysteresis.
  3. Electromagnetism at boundaries and guiding of waves
    1. Waves in non-conductive materials.
    2. Waves in conductive materials and the skin effect.
    3. Dispersive media and the group velocity.
    4. Fresnel coefficients and their consequences (Snell's law, Brewster angle, total internal reflection).
    5. Reflection and transmission from a conductive material.
    6. Transmission lines and impedance.
    7. The telegrapher's equation.
    8. The rectangular waveguide. TE and TM modes of a waveguide.
    9. Optical fibres.
  4. Wave propagation
    1. Metals as plasmas, and the plasma frequency.
    2. Plasma oscillations and plasmons.
    3. Surface plasma polaritons.
    4. Anisotropic media and the susceptibility tensor.
    5. Biaxial and uniaxial media. Waveplates.
    6. Double refraction.
    7. Nonlinear media and the nonlinear polarization.
    8. Nonlinear susceptibility.
    9. Phase matching.
    10. Wave diffraction. The Fresnel (paraxial) approximation and the Fraunhofer (far field) approximation.

Learning and Teaching

Learning Activities and Teaching Methods

Description Study time KIS type
5×6-hour self-study packages 30 hours GIS
4×4-hour problem sets 16 hours GIS
Reading, private study and revision 104 hours GIS


Weight Form Size When ILOS assessed Feedback
0% Guided self-study 5×6-hour packages Fortnightly 1-10 Self-evaluation
0% 4 × Problems sets (marked by module convener) 4 hours per set Fortnightly 1-10 Written
100% Final Examination 2 hours 30 minutes January 1-10 Mark via MyExeter, collective feedback via ELE and solutions.


The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

Supplementary texts:


Further Information

Prior Knowledge Requirements

Pre-requisite Modules Electromagnetism I (PHY2021)
Co-requisite Modules none


Re-assessment is not available except when required by referral or deferral.

Original form of assessment Form of re-assessment ILOs re-assessed Time scale for re-assessment
Whole module Written examination (100%) 1-10 August/September assessment period

Notes: See Physics Assessment Conventions.

KIS Data Summary

Learning activities and teaching methods
SLT - scheduled learning & teaching activities 0 hrs
GIS - guided independent study 150 hrs
PLS - placement/study abroad 0 hrs
Total 150 hrs
Summative assessment
Coursework 0%
Written exams 100%
Practical exams 0%
Total 100%


IoP Accreditation Checklist
  • EM-04 Maxwell's equations and plane electromagnetic wave solution; Poynting vector
  • SS-07 Magnetic properties of matter
  • EM-06 Polarisation of waves and behaviour at plane interfaces
Availability Programme F304 (Physics with Professional Experience) only
Distance learning YES (see PHY3051)
Keywords Physics; Maxwell's equations; Electromagnetic fields; Waves; Radiation; Properties of matter.
Created 01-Oct-10
Revised 06-Aug-20