PGEE936 
ADVANCED ELECTROMAGNETICS


INFORMATION 2021.01 

About
the course:
This is a 60h course on Electromagnetism
for graduate students either seeking the Master's or
PhD degree in Electrical Engineering. The course is
part of the Photonics curriculum of UFPE's Graduate
Program in Electrical Engineering (PPGEE). Relative to
a traditional undergraduate course on the subject,
PGEE936 employs a more indepth mathematical
formulation to solve electromagnetic problems. The
mathematical tools include the use of Dirac's delta
function for localized sources, solution of
Poisson's and 2nd order nonhomogeneous
differential equations by use of Green's functions in
3D space, use of special functions and concepts of
orthogonally for solving boundary value problems
either in electrostatics, magnetostatics or in
conducting media, as well as extensive use of vector
algebra. The course covers mostly static fields, and
use of the advanced mathematical tools for determining
those fields. The final part of the course is
dedicated to assembling Maxwell's equations for
dynamic fields and exploring the homogeneous and
nonhomogeneous forms of the wave equation. Plane
waves, attenuation and dispersion are treated in the
final part of the course. The topics that compose
PGEE936 form the basis for more advanced
applications of the Eletromagnetic Theory. The
followup course offered by PPGEEUFPE on this theme
is PGEE937 Fundamentals of Optics and Wave
Propagation. PGEE936 and PGEE937 together form the
foundations of Electromagnetics of static and dynamic
fields at the graduate level, in the Photonics
curriculum offered by PPGEEUFPE.
Six homework
assignements are given to students, and six examinations
are applied, based on the subjects treated in class and
related to the assignements.
1. Elements of vector algebra
TIMELINE 2021.01
OFFICIAL SCHEDULE OF CLASSES Wednesdays and Fridays; 1 PM  3 PM Start date: 03/31/2021 End date: 07/14/2021 Classes broadcast through PPGEE's youtube channel: http://youtube.com/ppgeeufpe Students that are or are not officially enrolled can request addition to the Facebook group @ https://www.facebook.com/groups/pgee936.202101 EXAMINATION DATES


CLASS NOTES 

CN#01 Introduction, vector algebra, basic
coordinate systems, transformations between coordinate
systems. CN#02 Integration in 3D space, differentiation in 3D space, gradient, divergent. CN#03 Divergent, curl, Green identities, Gauss, Stokes and Helmholtz theorems. CN#04 Introduction to Electrostatics. Fields of discrete and continuous charge distributions. Density function for a point charge. Dirac's delta functions in 3D space. Gauss's law. CN#05 Source distributions represented by Diracs delta functions. Potential energy. Maxwells equations for electrostatics in vacuum. Boundary conditions. CN#06 Electric dipole. Polarization, polarization charges. Determination of fields in material media using the polarization charge model. Constitutive relationship in dielectric media. Final form of Maxwell's equations for electrostatics. CN#07 Energy in dielectric media. Poisson's and Laplace's equations. Problem solving examples of Poisson's eq. for high symmetry problems. Integral solution for the potential function. Solution using Green's functions. Uniqueness theorem. Capacitance. Principle of virtual work. CN#08 Product solution in rectangular coordinates. Expansions in orthogonal functions. Solution of Laplace's eq. for twodimensional problems in cylindrical coordinates. Numerical solution of Laplace's equation. CN#09 Product solution in spherical coordinates. Legendre polynomials, associated Legendre polynomials. Spherical harmonics. Addition Theorem for Spherical Harmonics. CN#10 Product solution in cylindrical coordinates. Bessel functions. Orthogonality of Bessel Functions. Modified Bessel Functions. CN#11 Method of images for a planar interface. Green's function in the hemisphere. CN#12 Image method for spherical or cylindrical boundaries. Green's functions for spherical and cylindrical surfaces. CN#13 Boundary value problems and method of images involving more than one dielectric. CN#14 Electric current. Current density. Ohm's law. Charge conservation. Relaxation in conductive media. Energy exchange in conductive media. Boundary value problems in conductive media. CN#15 Magnetostatic force, magnetic flux density. Magnetic vector potential. Maxwell's eqs. for Magnetostatics in vacuum. CN#16 Field determination by use of the integral formulation. Vector potential and flux density of circular loop. Field of localized current distribution. Magnetic dipole. Magnetization. Magnetization current. Magnetic field vector. Maxwell's equations for Magnetostatics. Types of material media from a magnetic point of view. Magnetic permeability. CN#17 Magnetic scalar potential and boundary value problems in magnetic media CN#18 Faraday's law. Inductance and magnetic energy. CN#19 Displacement current. Maxwell's equations for timevarying fields, Poynting's theorem. CN#20 Homogeneous wave equation. General solution. Maxwell's equations for harmonic fields. CN#21 Inhomogeneous wave equation. Lorentz and Coulomb gauges. General solution of the inhomogeneous wave equation. CN#22 Poynting's theorem for harmonic fields. Plane wave in the harmonic regime. CN#23 Classical electron oscillator model. Generalized permittivity function. Poynting's theorem for LHI media (harmonic regime) CN#24 Plane wave propagation in LHI media. Attenuation and Dispersion. 

VIDEOCLASSES 



HOMEWORK 2021.01 

Homework 01  Homework
02  Homework 03  Homework 04  Homework 05  Homework
06  

MAIN
REFERENCES 

1. J. D. Jackson, "Classical Electrodynamics," 3rd. edition, Wiley 1998 2. Simon Ramo, John R. Whinnery and Thodore Van Duzer, " Fields and Waves in Communication Electronics", 3rd edition (1994). 3. G. B. Arfken, " Mathematical Methods for Physicists," 6th edition, Elsevier (2005). 4. Eduardo Fontana, "Eletromagnetismo  ebook  Parte I" (2011)  in portuguese (use google chrome to translate to english) 5. Eduardo Fontana, "Eletromagnetismo  ebook  Parte 2" (2013)  in portuguese(use google chrome to translate to english) 



ADDITIONAL
LINKS 



Online since March 5, 2021 Last Update: July 09, 2021 