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# PHY2206 Electromagnetic Fields 1995-1999

Code: PHY2206 (given 1995-1999)
Title: Electromagnetic Fields
InstructorsDr C.D.H. Williams
HE credits: 10
ECTS credits: 5
Availability: unrestricted
Level: 2
Prerequisites: none
Corequisites: none
Background Assumed: Electricity and Magnetism (PHY1004) and Mathematics II (PHY1016)
Duration: Semester II
Directed Study: 22 lectures
Private Study: 78 hours
Supports Programme Aims: 1, 2, 4 and 7
Supports Programme Objectives: 1, 2 and 5

Assessment Methods
Two 30-minute tests (40%), Problems Classes (10%) and one 90-minute examination (50%)

Rationale
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 PHY1004 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 (PHY4420 or PHY3126).

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 field obey.

Teaching and Learning Methods
Lectures, handouts, self-study 'drill problems', tutorials and problems classes.

Transferable Skills
Application of vector analysis to physical problems.

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

Module Text
Reitz J.R., Milford F.J. and Christy R.W., Foundations of Electromagnetic Theory (4th edition), Addison-Wesley (University library: 530.141 REI)

Not applicable

Syllabus Plan and Content
Note: References to specific sections in the module text are given in square brackets. There are links to pdf versions of handouts.

1. Introduction
1. Brief history of electromagnetism
2. Gradient of a scalar field [1-3]
3. Vector properties of the 'Del' operator [1-7]
4. Divergence of a vector field [1-5]
5. Curl of a vector field and Stokes's theorem [1-5]
6. Curvilinear coordinate systems [1-7]
7. Vector analysis summary sheet

2. Fields
1. The force between two charged particles
2. Interpretation of divergence; the continuity equation [7-2]
3. Flux and the divergence theorem [2-6]
4. Charge distribution and Gauss's law [2-7]
5. Electrostatic potentials [2-4]

3. Electrostatic Fields in Matter
1. Simple electric dipole [2-8]
2. Multipole distributions [2-9]
3. Polarisation P and displacement D in dielectric media [4-4]
4. Surface and volume polarization [4-2]
5. Dielectric tensors and constants [4-5]
6. Clausius-Mossotti equation [5-1]
7. Microscopic models of dielectric media
1. Polar molecules (Langevin-Debye equation) [5-3]
2. Non-polar molecules [5-2]
3. Ferroelectrics and electrets [5-4]
8. Conductors and electric fields in conducting media [7-3]
9. Boundary conditions for electric fields [4-7]
10. Energy density of the electrostatic field

4. Electrostatic Systems
1. Laplaces's equation as a special case of Poisson's equation [3-1]
2. General properties of solutions to Laplaces's equation [3-2]
3. Analytic solutions to Laplace's equation in special cases
4. Solutions to one-dimensional problems [3-3]
5. Solutions to two-dimensional problems [3-8]
6. Solutions to three-dimensional problems
7. Numerical solution of Laplace's equation [3-12]
8. Electrostatic images [3-9]
9. Poisson's equation [3-13]

5. Magnetostatic Fields in Matter
1. Definition and properties of B [8-4]
2. Ampère's law [8-5]
3. Magnetic vector potential A [8-6]
4. Properties of a small current-loop [8-7]
5. Microscopic models of magnetic materials
1. Diagmagnetism [10-2]
2. Paramagnetism [10-3]
3. Ferromagnetism [10-4]
6. Surface- and volume-current distributions [9-1]
7. Magnetic-field intensity H [9-4]
8. Boundary conditions for macroscopic magnetic fields [9-7]
9. Energy density of magnetic field [12-2]

6. Electromagnetic Systems
1. Steady currents in the presence of magnetic materials [9-9]
2. Forces in magnetic fields [12-3]
3. Electromagnetic induction for stationary magnetic media [11-1]
5. Measurement of susceptibilities [11-1]

7. Conclusions
1. Summary
2. Analogous equations in other areas of physics

Feedback to Students
This is a core module and so is supported by tutorials and problems classes. A comprehensive set of self-testing 'Drill Problems', with hints and answers 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.

Feedback from Students
Feedback from students on the module is gathered via the standard student representation mechanisms.