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 in-depth 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 non-homogeneous 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 non-homogeneous 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 follow-up course offered by PPGEE-UFPE 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 PPGEE-UFPE.
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
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:
Students that are or are not officially enrolled can request addition to the Facebook
group @ https://www.facebook.com/groups/pgee936.202101
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 two-dimensional 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 time-varying 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.
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 - e-book - Parte I" (2011) - in portuguese (use google chrome to translate to english)
5. Eduardo Fontana, "Eletromagnetismo - e-book - Parte 2" (2013) - in portuguese(use google chrome to translate to english)
Online since March 5, 2021
Last Update: July 09, 2021