PHY2006 Fundamental Electromagnetism II

2010-2011

Code: PHY2006
Level: 2
Title: Fundamental Electromagnetism II
Instructors: Prof. G.P. Srivastava
CATS Credit Value: 10
ECTS Credit Value: 5
Pre-requisites: N/A
Co-requisites: N/A
Duration: L1-L11
Availability: unrestricted
Background Assumed: Fundamental Electromagnetism I (PHY1104) and Mathematics for Physicists (PHY1116)
Directed Study Time: 22 lectures
Private Study Time: 66 hours
Assessment Tasks Time: 12 hours

Aims

The electromagnetic force holds atoms, molecules and materials together and plays a vital role in our understanding of almost all existing and potential technological developments. The laws of Electromagnetism as enunciated by James Clerk Maxwell enable physicists to comprehend and exploit an enormous range of phenomena. The first-year module PHY1104 dealt with the electric and magnetic field vectors E and B in free space. This module extends the range of problems which can be solved, to ones involving matter, and also develops the student's ability to apply vector analysis. Maxwell's equations in differential form will be developed systematically, starting from the force between two charged particles, thereby building a firm foundation for the study of advanced material in subsequent electromagnetism modules (PHY3143).

Intended Learning Outcomes

Students will be able to:

• state Maxwell's equations and explain how they can be related to the force between two particles,
• give a semiclassical description of the microscopic origin and interpretation of macroscopic fields (D and H) in matter,
• apply vector analysis to the solution of problems in electromagnetism,
• use vector analysis to apply Maxwell's equation's and solve standard problems,
• define the fields commonly used in electromagnetism, and state the laws these fields obey.

Transferable Skills

Application of vector analysis to physical problems.

Learning / Teaching Methods

Lectures, handouts, tutorials and problems classes.

Assignments

Students are expected to work through the set of self-study problems and prepare for problems classes.

Assessment

Problems-class assignments (10%), 30-minute mid-term test in Week L6 (20%) and one 90-minute examination (70%).

Syllabus Plan and Content

1. Introduction
   1. Brief history of electromagnetism
   2. Gradient of a scalar field
   3. Vector properties of the 'Del' operator
   4. Divergence of a vector field
   5. Curl of a vector field and Stokes's theorem
   6. Curvilinear coordinate systems
2. Fields
   1. The force between two charged particles
   2. Interpretation of divergence; the continuity equation
   3. Flux and the divergence theorem
   4. Charge distribution and Gauss's law
   5. Electrostatic potentials
3. Electrostatic Fields in Matter
   1. Simple electric dipole
   2. Multipole distributions
   3. Polarisation P and displacement D in dielectric media
   4. Surface and volume polarization
   5. Clausius-Mossotti equation
   6. Microscopic models of dielectric media
      1. Polar molecules (Langevin-Debye equation)
      2. Non-polar molecules
      3. Ferroelectrics and electrets
   7. Boundary conditions for electric fields
   8. Energy density of the electrostatic field
4. Electrostatic Systems
   1. Laplaces's and Poisson's equations
   2. General properties of solutions to Laplaces's equation
   3. Analytic solutions to Laplace's equation in special cases
   4. Solutions to single-variable problems
   5. SSolutions to two-variable problems
   6. Electrostatic images
5. Magnetostatic Fields in Matter
   1. Definition and properties of B
   2. Ampère's law
   3. Magnetic vector potential A
   4. Faraday-Lenz law
   5. Magnetic materials
      1. Diamagnetism
      2. Paramagnetism
      3. Ferromagnetism
   6. Magnetic-field intensity H
   7. Boundary conditions for macroscopic magnetic fields
   8. Energy density of magnetic field
   9. Electromagnetic properties of superconductors
6. Electromagnetic Systems
   1. Steady currents in the presence of magnetic materials
   2. Forces in magnetic fields
   3. Electromagnetic induction for stationary magnetic media
   4. Faraday's law
   5. Measurement of susceptibilities
7. Conclusions
   1. Maxwell's equations
   2. Energy density of an electromagnetic field
   3. The Poynting vector
   4. Summary

Core Text

Griffiths D.J. (1999), Introduction to Electrodynamics (3^rd edition), Prentice Hall, ISBN 0-13-805326-X (UL: 537 GRI)

Supplementary Text(s)

Good R.H. (1999), Classical Electromagnetism, Saunders College Publishing, ISBN 0-03-022353-9 (UL: 537 GOO)
Lorrain P., Corson D.R. and Lorrain F. (1987), Electromagnetic Fields and Waves (3^rd edition), Freeman, ISBN 0-716-71869-3 (UL: 530.141 LOR)
Reitz J.R., Milford F.J. and Christy R.W. (1993), Foundations of Electromagnetic Theory (4^th edition), Addison-Wesley, ISBN 0-201-52624-7 (UL: 530.141 REI)

Formative Mechanisms

This is a core module and so is supported by tutorials and problems classes. Homework sheets are provided for students to monitor their own progress. Students needing advice should initially raise the matter with their tutor and, if the problem is not resolved, contact the lecturer.

Evaluation Mechanisms

The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.