Physics 703 Fall 2003 and Physics 704 Spring 2004
Contact Information
Goals and Prerequisites
Course Content
Lectures : MWF 11:15 AM - 12:05 PM, PSC 203
Lecturer: Prof. Fred Myhrer
email: myhrer@physics.sc.edu
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The goals of the course, PHYS 703, and the second semester course, PHYS
704, are:
- The students will be able to solve the Laplace equation for
electrostatic
problems in two- and three- dimensions using Green's function methods.
- The students will be able to solve problems in electro- and magneto-
statics
using special functions and their series expansions.
- The students will be able to use mathematical handbooks of special
functions or corresponding mathematical software which are necessary tools
for solving electromagnetic boundary condition problems for different
simple geometries.
- The students will be able to use Fourier analysis as a method of
solving electrostatic equations and problems with electromagnetic waves
(PHYS 704 mainly).
- The students will be able to solve guided-wave propagation, electromagnetic
radiation and scattering problems (PHYS 704).
Prerequisites
Students are expected to have passed a course in
electromagnetic theory at the undergraduate
level, PHYS 504 or equivalent, with at least a grade of B
before enrolling in these two courses.
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Text:
J.D. Jackson, "Electromagnetic Theory" John Wiley and Sons, New York
(1998) Third Edition.
The first semester of the electromagnetic theory course, PHYS 703,
will emphasize the three first chapters of the text, which focus on
electrostatics.
These chapters introduce the advanced mathematical tools necessary in order
to tackle most practical problems in engineering designs of, for example
magnets, microwave cavities and wave guides. These mathematical methods
are very useful in order to verify the correctness of standard computer generated
solutions of various designs. The mathematical tools developed in this
course are fundamental for describing many familiar electromagnetic phenomena.
These three chapters introduce the use of Green's functions and Fourier
series to solve the electrostatic Laplace and the Poisson second order
differential
equations in two- and three- dimensions for various simple geometries.
Topics covered includes:
- The Green's theorem and the Green's function and the general
solution to the electrostatic Laplace and Poisson equations is derived.
- The mirror image method in electrostatics is discussed and specific
expressions for Green's function are derived.
- Series solutions to the Laplace equation are derived for with
various electrostatic boundary conditions in two and three dimensions for
Cartesian-, cylindrical- and spherical- coordinates.
- Expansions of the electrostatic potential in terms of orthogonal
functions are introduced using Legendre polynomials, spherical harmonics,
hypergeometric function (solution to Laplace in a metallic cone) and Bessel
functions.
- The Green's function as a mode sum.
- The electromagnetic retarded Green's functions for electromagnetic
waves.
The remainder of the semester is used to solve problems in dielectrics
and magnetostatics using the multipole expansion, special functions and
the derived Green's functions.
The second semester course, PHYS 704, concentrates on describing
electromagnetic wave phenomena using Green's functions and Fourier analysis
techniques. Topics covered includes:
- Reflection and transmission of plane electromagnetic waves from
dielectric boundaries and conductors. Electromagnetic waves through thin
dielectric and metallic planes.
- Frequency dispersions at low and high frequencies and absorption
of electromagnetic waves.
- Resonant cavities, rectangular and cylindrical and other waveguides.
Energy loss in wave guides. TE-, TM- and TEM modes presented.
- Electromagnetic radiation fields, cyclotron-, bremsstrahlung- and
multipole- radiation.
- Theory of scattering of electromagnetic waves. Polarization of waves.
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This page maintained by "Fred Myhrer"