PHY3051 
Electromagnetism II 
202425 

Prof. J. Bertolotti 


Delivery Weeks: 
T1:0111 

Level: 
6 (NQF) 

Credits: 
15 NICATS / 7.5 ECTS 

Enrolment: 
60 students (approx) 

Description
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:

Module Specific Skills and Knowledge:
 describe all the fundamental aspects of electromagnetism;
 explain and solve problems involving the magnetic properties of materials;
 explain and solve problems involving the dielectric properties of materials;
 explain many aspects of the interaction of electromagnetic
radiation with matter;
 calculate the effect of such interactions using
appropriate vector mathematics;
 calculate the fields of moving charges;
 solve problems requiring application of Maxwell's equations to a
variety of situations as outlined in the syllabus below;

Discipline Specific Skills and Knowledge:
 use vector analysis to solve problems in science and engineering;

Personal and Key Transferable / Employment Skills and Knowledge:
 develop and present a coherent solution to a problem;
 selfevaluate, check and correct solutions to problems.
Syllabus Plan

Maxwell's Equations and Electromagnetic Waves
 Maxwell's equations for the electromagnetic field.
 Scalar and vector potentials.
 The equation of continuity.
 The wave equation and wave solutions to Maxwell equations.
 Linear, circular and elliptical polarization states of a wave.
 Energy of a wave and the Poynting theorem.
 The electromagnetic stress tensor and the momentum of an electromagnetic field.
 Gauge invariance and Gauge fixing. The Weyl, Lorenz and Coulomb gauges.
 Covariance of Maxwell equations and Lorentz transforms
 Field generated by a moving charge. The LiÃ©nardWiechert potentials.
 Larmor formula

Electromagnetic materials
 Polarization of dielectric materials. Multipole expansion.
 Electric susceptibility and the displacement field.
 ClausiusMossotti relation.
 Boundary conditions for the electric and the displacement fields.
 Magnetic dipoles and magnetization.
 Magnetic susceptibility and the magnetic field.
 Boundary conditions for the magnetic induction and the magnetic fields.
 Larmor precession.
 Paramagnetism and Curie law.
 Ferromagnetism, spontaneous magnetization, and magnetic hysteresis.

Electromagnetism at boundaries and guiding of waves
 Waves in nonconductive materials.
 Waves in conductive materials and the skin effect.
 Dispersive media and the group velocity.
 Fresnel coefficients and their consequences (Snell's law, Brewster angle, total internal reflection).
 Reflection and transmission from a conductive material.
 Transmission lines and impedance.
 The telegrapher's equation.
 The rectangular waveguide. TE and TM modes of a waveguide.
 Optical fibres.

Wave propagation
 Metals as plasmas, and the plasma frequency.
 Plasma oscillations and plasmons.
 Surface plasma polaritons.
 Anisotropic media and the susceptibility tensor.
 Biaxial and uniaxial media. Waveplates.
 Double refraction.
 Nonlinear media and the nonlinear polarization.
 Nonlinear susceptibility.
 Phase matching.
 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 
20×1hour lectures 
20 hours

SLT 
2×1hour problems/revision classes 
2 hours

SLT 
3×1hour tutorials

3 hours

SLT 
5×6hour selfstudy packages 
30 hours

GIS 
4×4hour problem sets 
16 hours

GIS 
Reading, private study and revision 
79 hours

GIS 
Assessment
Weight 
Form 
Size 
When 
ILOS assessed 
Feedback 
0% 
Guided selfstudy 
5×6hour packages 
Fortnightly 
110 
Discussion in tutorials

0% 
4 × Problems sets 
4 hours per set 
Fortnightly 
110 
Solutions discussed in problems classes. 
100% 
Final Examination 
2 hours 30 minutes 
January 
110 
Mark via MyExeter, collective feedback via ELE and solutions. 
Resources
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:

Garg A. (2012), Classical Electromagnetism in a Nutshell, Princeton University Press, ISBN 9780691130187

Kittel C. (2005), Introduction to Solid State Physics (8^{th} edition), Wiley, ISBN 9780471415268

Reitz J.R., Milford F.J. and Christy R.W. (1993), Foundations of Electromagnetic Theory (4^{th} edition), AddisonWesley, ISBN 0201526247
ELE:
Further Information
Prior Knowledge Requirements
Prerequisite Modules 
Electromagnetism I (PHY2021) 
Corequisite Modules 
none 
Reassessment
Reassessment is not available except when required by referral or deferral.
Original form of assessment 
Form of reassessment 
ILOs reassessed 
Time scale for reassessment 
Whole module 
Written examination (100%) 
110 
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% 

Miscellaneous
IoP Accreditation Checklist 
 EM04 Maxwell's equations and plane electromagnetic wave solution; Poynting vector
 SS07 Magnetic properties of matter
 EM06 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 
01Oct10 
Revised 
06Aug20 