||Prof. J. Bertolotti
||15 NICATS / 7.5 ECTS
||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.
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;
- self-evaluate, check and correct solutions to problems.
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©nard-Wiechert potentials.
- Larmor formula
- Polarization of dielectric materials. Multipole expansion.
- Electric susceptibility and the displacement field.
- Clausius-Mossotti 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 non-conductive 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.
- 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
|2×1-hour problems/revision classes
|5×6-hour self-study packages
|4×4-hour problem sets
|Reading, private study and revision
||Discussion in tutorials
||4 × Problems sets
||4 hours per set
||Solutions discussed in problems classes.
||2 hours 30 minutes
||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).
Garg A. (2012), Classical Electromagnetism in a Nutshell, Princeton University Press, ISBN 978-0-691-13018-7 (UL: 537 GAR)
Kittel C. (2005), Introduction to Solid State Physics (8th edition), Wiley, ISBN 978-0-471-41526-8 (UL: 530.41 KIT)
Reitz J.R., Milford F.J. and Christy R.W. (1993), Foundations of Electromagnetic Theory (4th edition), Addison-Wesley, ISBN 0-201-52624-7 (UL: 530.141 REI)
Prior Knowledge Requirements
||Electromagnetism I (PHY2021)
Re-assessment is not available except when required by referral or deferral.
|Original form of assessment
||Form of re-assessment
||Time scale for re-assessment
||Written examination (100%)
||August/September assessment period
Notes: See Physics Assessment Conventions.
KIS Data Summary
|Learning activities and teaching methods|
|SLT - scheduled learning & teaching activities
|GIS - guided independent study
|PLS - placement/study abroad
|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
||YES (see PHY3054)
||Physics; Maxwell's equations; Electromagnetic fields; Waves; Radiation; Properties of matter.