PHY3051 Electromagnetism II 2019-20
Dr J. Bertolotti
Delivery Weeks: T1:01-11
Level: 6 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 60 students (approx)


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 early part of the module provides a brief recap and reinforces the difficult material treated at the end of PHY2021. The Maxwell equations are stated and manipulated to obtain the wave equation, and the form of the solutions discussed. The dielectric and magnetic properties of solids are then introduced, with emphasis on the frequency dependence of their real and imaginary components, and the consequences for wave propagation. Wave propagation at interfaces between dissimilar materials is considered, leading to derivation of Fresnel reflection and transmission coefficients. The need to guide electromagnetic waves of different frequency is discussed, and guiding by transmission lines, waveguides and optical fibers is introduced. Finally the electromagnetic fields generated by charges moving with uniform or oscillatory velocity are discussed. A number of interesting physical phenomena are considered that are important in a wide variety of areas and in many key technologies. This is a core subject for Physics programmes and is supported by Stage 3 tutorials and problems classes.

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 and constitutive equations
    2. The equation of continuity
    3. Scalar and vector potentials
    4. Gauge invariance, the Coulomb and Lorentz gauges
    5. Electromagnetic plane waves in an insulating isotropic medium
    6. Polarization, momentum and energy, the Poynting vector
  2. Electromagnetic materials
    1. Classical description of atomic polarisability, dispersion
    2. Dielectrics, paraelectrics and ferroelectrics: general concepts
    3. Metals and the skin effect
    4. Classical model of atomic diamagnetism
    5. Diamagnetism, paramagnetism and ferromagnetics: general concepts
    6. Langevin (classical) theory of paramagnetism and electron paramagnetism
    7. M–B loops, and demagnetisation factors
    8. Gyrotropic media
    9. Metamaterials
  3. Electromagnetic waves at boundaries and guiding waves
    1. Distributed impedance: the Telegrapher's equations
    2. Coaxial cables and planar waveguides
    3. Fresnel's equations and their optical consequences
    4. Dielectric waveguides
    5. Metallic waveguides
  4. Fields Produced by Moving Charges
    1. Radiation from an oscillating dipole
    2. Radiation from a set of moving charges
    3. Scattering
    4. Lienard-Weichert potentials
    5. Fields of a uniformly moving point charge

Learning and Teaching

Learning Activities and Teaching Methods

Description Study time KIS type
20×1-hour lectures 20 hours SLT
2×1-hour problems/revision classes 2 hours SLT
3×1-hour tutorials 3 hours SLT
5×6-hour self-study packages 30 hours GIS
4×4-hour problem sets 16 hours GIS
Reading, private study and revision 79 hours GIS


Weight Form Size When ILOS assessed Feedback
0% Guided self-study 5×6-hour packages Fortnightly 1-10 Discussion in tutorials
0% 4 × Problems sets 4 hours per set Fortnightly 1-10 Solutions discussed in problems classes.
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 25 hrs
GIS - guided independent study 125 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 MPhys only
Distance learning YES (see PHY3054)
Keywords Physics; Maxwell's equations; Electromagnetic fields; Waves; Radiation; Properties of matter.
Created 01-Oct-10
Revised 23-Jul-16