Physics 703 Fall 2003 and Physics 704 Spring 2004

Contact Information
Goals and Prerequisites
Course Content

Contact Information

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Goals

• 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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Course Content:

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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