Lecturer: Paul Goddard and Nicholas d'Ambrumenil

Weighting: 15 CATS

Any macroscopic object we meet contains a large number of particles, each of which moves according to the laws of mechanics (which can be classical or quantum). Yet we can often ignore the details of this microscopic motion and use a few average quantities such as temperature and pressure to describe and predict the behaviour of the object. Why we can do this, when we can do this and how to do it are the domain of statistical mechanics and are discussed in one half of the module.

The other half of the module develops the ideas of first year electricity and magnetism into Maxwell's theory of electromagnetism. Establishing a complete theory of electromagnetism has proved to be one the greatest achievements of physics. It was the principal motivation for Einstein to develop special relativity, it has served as the model for subsequent theories of the forces of nature and it has been the basis for all of electronics (radios, telephones, computers, the lot...).

Aims:

The module should study Maxwell's equations and their solutions and introduce statistical mechanics and its central role in physics.

Objectives:

By the end of the module you should:

• understand Maxwell's equations and quantities like the Poynting vector and refractive index
• be able to manipulate these equations in integral or differential form and derive the appropriate boundary conditions at boundaries between linear isotropic materials
• be familiar with plane-wave solutions to these equations in free space, dielectrics and ohmic conductors
• have an understanding of geometrical optics, polarisation of light, the behaviour of light in lenses and prisms, and the properties of different light sources (including lasers)

Syllabus:

By the end of the module, students should be able to:

• Write down and manipulate Maxwell's equations in integral or differential form and derive the boundary conditions at boundaries between linear isotropic materials
• Derive the plane-wave solutions to Maxwell's equations in free space, dielectrics and ohmic conductors
• Describe the interaction of light with optical materials and explain the basics of geometrical optics
• Explain the ergodic hypothesis and define thermal equilibrium for various ensembles
• Define the partition function and calculate thermodynamic averages from it (this includes the Fermi-Dirac and Bose-Einstein distributions)
• Discuss the structure of statistical mechanics and explain its relation to classical thermodynamics

Commitment: about 40 Lectures + problems classes

Assessment: 2 hour examination(85%) + assessed work (15%)

Recommended Text: Young and Freedman, University Physics 11th Edition
IS Grant and WR Phillips, Electromagnetism
E Hecht, Optics
Concepts in Thermal Physics by S. J. Blundell and K. M. Blundell (OUP, 2010). Further reading: Statistical mechanics: a survival guide by A. M. Glazer and J. S. Wark (OUP, 2001); Statistical Physics by A. M. Guenault (Springer, 2007).