PGEE936 - Advanced Electromagnetics - PPGEE

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 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.

Evaluation Method:

Six homework assignements are given to students, and six examinations are applied, based on the subjects treated in class and related to the assignements.

Course Programme:

1. Elements of vector algebra
2. Electrostatics
3. Boundary value problems in electrostatics
4. Electrical conduction
6. Magnetostatics
7. Faraday's law, displacement current and Maxwell's equations for dynamic fields
8. Electromagnetic oscillations, plane waves, attenuation and dispersion

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

EXAMINATION	1	2	3	4	5	6
DATE	04/16/2021	05/05/2021	05/21/2021	06/09/2021	06/25/2021	07/14/2021

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 Dirac’s delta functions. Potential energy. Maxwell’s 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.

VIDEOCLASSES

VC1-03/31/2021	VC2 - 04/02/2021	VC3 - 04/07/2021	VC4-04/09/2021
VC5 - 04/14/2021	VC6 - 04/21/2021	VC7 - 04/23/2021	VC8 - 04/28/2021
VC9 - 04/30/2021	VC10 - 05/07/2021	VC11 - 05/12/2021	VC12 - 05/14/2021
VC13 - 05/19/2021	VC14 - 05/26/2021	VC15 - 05/28/2021	VC16 - 06/02/2021
VC17 - 06/04/2021	VC18 - 06/11/2021	VC19 - 06/16/2021	VC20 - 06/18/2021
VC21 - 06/23/2021	VC22 - 06/30/2021	VC23 - 07/02/2021	VC24 - 07/07/2021