PX28415 Statistical Mechanics, Electromagnetic Theory and Optics
Introductory description
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 discussed in the other half of this module.
In the second half of the module, we develop 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...).
Module aims
The module should study Maxwell's equations and their solutions and introduce statistical mechanics and its central role in physics.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
I. Electromagnetic Theory and Optics: Ampere's law, Faraday/Lenz's law, Gauss's law in differential form. Need for the displacement current. Statement of Maxwell's equations. Maxwell equations in vacuum and in matter. Magnetisation and polarization of materials. Relation of E and P, B and M. Solutions to Maxwell equations in vacuum. Electromagnetic waves, Poynting vector, intrinsic impedance, polarisation. Boundary conditions. Interfaces between dielectrics, separation into perpendicular and parallel components. Refractive index. Ohm's law. Interface with a metal, skin effect.
Optics: reflection and refraction. Wavefronts at plane and spherical surfaces. Lenses. Basics of optical instruments, resolution.
II. Statistical Mechanics: Systems and states: microstates. Fundamental assumptions of stat. mech. Equilibrium State. Definition of entropy for closed system in equilibrium. Maximization of entropy of a closed system in equilibrium. Fluctuations and Large Systems. Boltzmann distribution and Lagrange multipliers: Partition function, Z. Evaluation of Z for a spinhalf system in a magnetic field and harmonic oscillator and system with degeneracy. Relationship of Z to thermodynamic quantities E, S and F=ETS. Minimization of F in equilibrium for systems at fixed T and V. Microscopic basis for thermodynamics and relation to statistical mechanics. Classical Thermodynamics of Gases: Thermal equilibrium, quasistatic and reversible changes. Statistical Mechanics of Classical Gases. Thermodynamic potentials G and H. The ideal gas law, the Gibbs paradox. GrandCanonical ensembles: system not closed (possibility of particle exchange between systems). BoseEinstein and Fermi Dirac distribution functions. Density of states. Chemical potential. Fermi energy. Relevance of FermiDirac and BoseEinstein to matter. Phonons: Einstein model, Debye model and dispersive phonons, role of elastic modulus, phonon heat capacity, thermal expansion.
Learning outcomes
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 planewave 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 FermiDirac and BoseEinstein distributions)
 Discuss the structure of statistical mechanics and explain its relation to classical thermodynamics
Indicative reading list
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).
View reading list on Talis Aspire
Subject specific skills
Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking.
Transferable skills
Analytical, communication, problemsolving, selfstudy
Study time
Type  Required 

Lectures  40 sessions of 1 hour (27%) 
Other activity  20 hours (13%) 
Private study  90 hours (60%) 
Total  150 hours 
Private study description
Working through lecture notes, solving problems, wider reading, discussing with others taking the module, revising for exam, practising on past exam papers
Other activity description
14 problem classes
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D
Weighting  Study time  

Coursework  15%  
Assessed work as specified by department 

Statistical Mechanics, Electromagnetic Theory and Optics  85%  
Answer 4 questions

Assessment group R
Weighting  Study time  

Inperson Examination  Resit  100%  
Answer 4 questions

Feedback on assessment
Personal tutor, group feedback
Courses
This module is Core for:

UPXAGF13 Undergraduate Mathematics and Physics (BSc)
 Year 2 of GF13 Mathematics and Physics
 Year 2 of GF13 Mathematics and Physics

UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
 Year 2 of FG31 Mathematics and Physics (MMathPhys)
 Year 2 of FG31 Mathematics and Physics (MMathPhys)

UPXAF300 Undergraduate Physics (BSc)
 Year 2 of F300 Physics
 Year 2 of F300 Physics
 Year 2 of F300 Physics

UPXAF303 Undergraduate Physics (MPhys)
 Year 2 of F300 Physics
 Year 2 of F303 Physics (MPhys)
 Year 2 of UPXAF3N1 Undergraduate Physics and Business Studies

UPXAF3F5 Undergraduate Physics with Astrophysics (BSc)
 Year 2 of F3F5 Physics with Astrophysics
 Year 2 of F3F5 Physics with Astrophysics
 Year 2 of UPXAF3FA Undergraduate Physics with Astrophysics (MPhys)
 Year 2 of UPXAF3N2 Undergraduate Physics with Business Studies
This module is Option list B for:
 Year 2 of UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)

UMAAG100 Undergraduate Mathematics (BSc)
 Year 2 of G100 Mathematics
 Year 2 of G100 Mathematics
 Year 2 of G100 Mathematics

UMAAG103 Undergraduate Mathematics (MMath)
 Year 2 of G100 Mathematics
 Year 2 of G103 Mathematics (MMath)
 Year 2 of G103 Mathematics (MMath)
 Year 2 of UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 2 of UMAAG1NC Undergraduate Mathematics and Business Studies
 Year 2 of UMAAGL11 Undergraduate Mathematics and Economics
 Year 2 of UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)
 Year 2 of UMAAG101 Undergraduate Mathematics with Intercalated Year