University of Illinois at Urbana-Champaign
The Grainger College of Engineering
Electrical & Computer Engineering

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Back To: Rao's Faculty Bio

Fundamentals of Electromagnetics for Teaching and Learning:

A Two-Week Intensive Course for Faculty in Electrical-, Electronics-, Communication-, and Computer- Related Engineering Departments in Engineering Colleges in India

by

Nannapaneni Narayana Rao
Edward C. Jordan Professor Emeritus of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign, USA
Distinguished Amrita Professor of Engineering
Amrita Vishwa Vidyapeetham, India

Program for Hyderabad Area and Andhra Pradesh Faculty
Sponsored by IEEE, IETE, and Vasavi College of Engineering
IETE Conference Hall, Osmania University Campus
Hyderabad, Andhra Pradesh
June 3 – June 11, 2009

Yhderabad Program Picture 1    Hyderabad Program Picture 2

Workshop for Master Trainer Faculty Sponsored by IUCEE
(Indo-US Coalition for Engineering Education)
Infosys Campus, Mysore, Karnataka
June 22 – July 3, 2009

Mysore Program Picture 1    Mysore Program Picture 2

About the Course

equations

Electromagnetics (EM) is known to be a subject dreaded by students to learn and by teachers to teach.  This course is intended for faculty from different colleges throughout India, ranging from younger faculty with minimal number of years of teaching the subject to master trainers who have taught the subject for some larger number of  years, and who in turn are expected to train other faculty, following their participation in this course.  The goal of the course is to instill the ability to overcome the dread and develop confidence and comfort in teaching and learning EM.

The pedagogical approach to be employed is one of minimizing the time spent on mathematical derivations and focusing on in-depth discussion of concepts, and on problem-solving, as time permits.  The topical coverage is designed to impart the elements of engineering electromagnetics that (a) constitute the foundation for preparing an electrical-related engineering major to take follow-on courses in electromagnetics, and (b) represents the essentials of electromagnetics for a computer-related engineering major taking this course only.

It is hoped that, as a result of this Course, you will find the teaching and learning of electromagnetics to be comfortable and even enjoyable, as implied by the picture that follows, taken at the Centennial celebration of the EE Department of the University of Washington in 2006!

N.N. Rao

Textbooks for the Course

“Elements of Engineering Electromagnetics, Sixth Edition,” by Nannapaneni Narayana Rao, Low-Priced Indian Edition, Pearson Education, 2006; hereafter referred to as EEE.

“Fundamentals of Electromagnetics for Engineering,” by Nannapaneni Narayana Rao, Low-Priced Indian Edition, Pearson Education, 2009 (Published in August 2008); hereafter referred to as FEME.

See below pictures of presentation of the two books to Srimati Daggubati Purandeswari, Honorable Minister of State for Human Resources Development, Government of India, at her residence in Hyderabad on July 19, 2009.

Book presentation 1    Book presentation 2

Before continuing on, please read the following items, and also about the text books at http://faculty.ece.illinois.edu/rao/EMFware/index.html:

Making the learning of Maxwell’s equations painless
Why study electromagnetics?
The deductive approach of teaching EM, the approach that worked at Illinois
Deductive versus inductive approach

Introductory Presentation, Part 1 (PPT, 86 slides; 21.79MB)
Introductory Presentation, Part 2 (PPT, 74 slides; 5.27MB)

Note: Since the time of the above Introductory Presentations in June 2009, Andreas C. Cangellaris, Mac E. Van Valkenburg Professor of Electrical and Computer Engineering, became the Head of the Department. See below his picture, taken from Introductory Presentation, Part 1.

Andreas Cangellaris

Also, read his contribution in the "Why Study Electromagnetics?" section of "Elements of Engineering Electromagnetics, Sixth Edition," Low-Priced Indian Edition, a copy of which he is holding in the picture.

Course Outline

The notation within parentheses for each topic denotes the following:

EEE 1.1, etc., refer to the section(s) in EEE.
FEME 1.1, etc., refer to the section(s) in FEME.
S1.1, etc., refer to problems from “Problem Solving in Electromagnetics,” presently under preparation, to serve as a supplement to the textbooks. The statements for these are included in the PowerPoint (PPT) presentations.  The solutions to some of these problems will be discussed during the Course, as time permits.

In addition, within the PPT presentations, there are a number of examples.  The notation for these is as follows:

D1.2, etc., refer to the drill problems in EEE, included in the PPT presentation.
P1.5, etc., refer to the chapter-end problems in EEE included in the PPT presentation.
E1.1, etc., are other examples in the PPT presentation.

Module 1:  Vectors and Fields (PPT, 141 Slides; 4.45MB)
1.1 Vector algebra (EEE 1.1; FEME 1.1; S1.1)
1.2 Cartesian coordinate system (EEE 1.2; FEME 1.2; S1.2)
1.3 Cylindrical and spherical coordinate systems (EEE 1.3; FEME App. A; S1.3; S1.4)
1.4 Scalar and vector fields (EEE 1.4; FEME 1.3; S1.5)
1.5 Sinusoidally time-varying fields (EEE 3.6; FEME 1.4; S1.6)
1.6 The electric field (EEE 1.5; FEME 1.5; S1.7; S1.8)
1.7 The magnetic field (EEE 1.6; FEME 1.6; S1.9; S1.10))
1.8 Lorentz force equation (EEE 1.7; FEME 1.6; S1.11)

Module 2:  Maxwell’s Equations in Integral Form (PPT, 96 Slides; 4.88MB)
2.1 The line integral (EEE 2.1; FEME 2.1; S2.1; S2.2)
2.2 The surface integral (EEE 2.2; FEME 2.2; S2.3)
2.3 Faraday’s law (EEE 2.3; FEME 2.3; S2.4; S2.5)
2.4 Ampere’s circuital law (EEE 2.4; FEME 2.4; S2.6; S2.7)
2.5 Gauss’ laws (EEE 2.5; FEME 2.5, 2.6; S2.8; S2.9)
2.6 The law of conservation of charge (EEE 2.6; FEME 2.5; S2.10)
2.7 Application to static fields (EEE 2.7; S2.11; S2.12)

Module 3: Maxwell’s Equations in Differential Form (PPT, 69 Slides; 3.42MB)
3.1 Faraday’s law and Ampere’s circuital Law (EEE 3.1; FEME 3.1, 3.2; S3.1; S3.2; S3.3)
3.2 Gauss’ laws and the continuity equation (EEE 3.2; FEME 3.4, 3.5, 3.6; S3.4; S3.5; S3.6)
3.3 Curl and divergence (EEE 3.3; FEME 3.3, 3.6, App. B; S3.7; S3.8; S3.9)

Module 4:  Wave Propagation in Free Space (PPT, 85 Slides; 5.01MB)
4.1 Uniform plane Waves in time domain (EEE 3.4; FEME 4.1, 4.2, 4.4, 4.5; S4.1; S4.2; S4.3)
4.2 Sinusoidally time-varying uniform plane waves (EEE 3.5; FEME 4.1, 4.2, 4.4, 4.5; S4.4; S4.5; S4.6)
4.3 Polarization (EEE 3.6; FEME 1.4, 4.5; S4.7; S4.8)
4.4 Power Flow and energy storage (EEE 3.7; FEME 4.6; S4.9; S4.10; S4.11)

Module 5: Materials and Wave Propagation in Material Media (PPT, 134 Slides; 7.18MB)
5.1 Conductors and dielectrics (EEE 4.1, 4.2; FEME 5.1; S5.1; S5.2; S5.3)
5.2 Magnetic materials (EEE 4.3; FEME 5.2; S5.4)
5.3 Wave equation and solution (EEE 4.4; FEME 5.3; S5.5; S5.6; S5.7)
5.4 Uniform waves in dielectrics and conductors (EEE 4.5; FEME 5.4; S5.8; S5.9)
5.5 Boundary conditions (EEE 4.6; FEME 5.5; S5.10; S5.11; S5.12)
5.6 Reflection and transmission of uniform plane waves (EEE 4.7; FEME 5.6; S5.13; S5.14)

Module 6: Statics, Quasistatics, and Transmission Lines (PPT, 138 Slides, 7.04MB)
6.1 Gradient and electric potential (EEE 5.1, 5.2; FEME 6.1; S6.1; S6.2; S6.3)
6.2 Poisson’s and Laplace’s equations (EEE 5.3; FEME 6.2; S6.4; S6.5)
6.3 Static fields and circuit elements (EEE 5.4; FEME 6.3; S6.6)
6.4 Low-frequency behavior via quasistatics (EEE 5.5; FEME 6.4; S6.7)
6.5 Condition for the validity of the quasistatic approximation (EEE 5.5; FEME 6.5, 7.1; S6.8)
6.6 The distributed circuit concept and the transmission line (EEE 6.1, 11.5; FEME 6.5, 6.6; S6.9; S6.10)

Module 7: Transmission Line Analysis in Time Domain (PPT, 133 Slides, 5.97MB)
7.1 Line terminated by a resistive load (EEE 6.2; FEME 7.4; S7.1; S7.2; S7.3; S7.4)
7.2 Transmission-line discontinuity (EEE 6.3; S7.5; S7.6; S7.7)
7.3 Lines with reactive terminations and discontinuities (EEE 6.4; S7.8; S7.9)
7.4 Lines with initial conditions (EEE 6.5; FEME 7.5; S7.10; S7.11; S7.12)
7.5 Lines with nonlinear elements (EEE 6.6; FEME 7.6; S7.13)

Instructional Objectives

By the end of Module 1, you should be able to do the following:

1.  Perform vector algebraic operations in Cartesian, cylindrical, and spherical coordinates

2. Find the unit normal vector and the differential surface at a point on a surface

3. Find the equation for the direction lines associated with a vector field

4. Identify the polarization of a sinusoidally time-varying vector field

5. Calculate the electric field due to a charge distribution by applying superposition in conjunction with the electric field due to a point charge

6. Calculate the magnetic field due to a current distribution by applying superposition in conjunction with the magnetic field due to a current element

7.  Apply Lorentz force equation to find the electric and magnetic fields, for a specified set of forces on a charged particle moving in the field region

By the end of Module 2, you should be able to do the following:

8.  Evaluate line and surface integrals

9.  Apply Faraday's law in integral form to find the electromotive force induced around a closed loop, fixed or revolving, for a given magnetic field distribution

10. Make use of the uniqueness of the magnetomotive force around a closed path to find the displacement current emanating from a closed surface for a given current distribution

11. Apply Gauss’ law for the electric field in integral form to find the displacement flux emanating from a closed surface bounding the volume for a specified charge distribution within the volume

12. Apply Gauss’ law for the magnetic field in integral form to simplify the problem of finding the magnetic flux crossing a surface

13. Apply Gauss' law for the electric field in integral form, Ampere's circuital law in integral form, the law of conservation of charge, and symmetry considerations, to find the line integral of the magnetic field intensity around a closed path, given an arrangement of point charges connected by wires carrying currents

14. Apply Gauss’ law for the electric field in integral form to find the electric fields for symmetrical charge distributions

15. Apply Ampere’s circuital law in integral form, without the displacement current term, to find the magnetic fields for symmetrical current distributions

By the end of Module 3, you should be able to do the following:

16. Obtain the simplified forms of Faraday’s law and Ampere’s circuital law in differential forms for any special cases of electric and magnetic fields, respectively, or the particular differential equation that satisfies both laws for a special case of electric or magnetic field

17. Determine if a given time-varying electric/magnetic field satisfies Maxwell’s curl equations, and if so find the corresponding magnetic/electric field, and any required condition, if the field is incompletely specified

18. Find the magnetic field due to one-dimensional static current distribution using Maxwell’s curl equation for the magnetic field

19. Find the electric field due to one-dimensional static charge distribution using Maxwell’s divergence equation for the electric field

20. Establish the physical realizability of a static electric field by using Maxwell’s curl equation for the static case, and of a magnetic field by using the Maxwell’s divergence equation for the magnetic field

21. Investigate qualitatively the curl and divergence of a vector field by using the curl meter and divergence meter concepts, respectively

22. Apply Stokes’ and divergence theorems in carrying out vector calculus manipulations

By the end of Module 4, you should be able to do the following:

23. Write the expression for a traveling wave function for a set of specified characteristics of the wave

24. Obtain the electric and magnetic fields due to an infinite plane current sheet of an arbitrarily time-varying uniform current density, at a location away from it as a function of time, and at an instant of time as a function of distance, in free space

25. Find the parameters, frequency, wavelength, direction of propagation of the wave, and the associated magnetic (or electric) field, for a specified sinusoidal uniform plane wave electric (or magnetic) field in free space

26. Write expressions for the electric and magnetic fields of a uniform plane wave propagating away from an infinite plane sheet of a specified sinusoidal current density, in free space

27. Obtain the expressions for the fields due to an array of infinite plane sheets of specified spacings and sinusoidal current densities, in free space

28. Write the expressions for the fields of a uniform plane wave in free space, having a specified set of characteristics, including polarization

29. Express linear polarization and circular polarization as superpositions of clockwise and counterclockwise circular polarizations 

30. Find the power flow and the electric and magnetic stored energies associated with electric and magnetic fields

By the end of Module 5, you should be able to do the following:

31. Find the charge densities on the surfaces of infinite plane conducting slabs (with zero or nonzero net surface charge densities) placed parallel to infinite plane sheets of charge

32. Find the displacement flux density, electric field intensity, and the polarization vector in a dielectric material in the presence of a specified charge distribution, for simple cases involving symmetry

33. Find the magnetic field intensity, magnetic flux density, and the magnetization vector in a magnetic material in the presence of a specified current distribution, for simple cases involving symmetry

34. Determine if the polarization of a specified electric/magnetic field in an anisotropic dielectric/magnetic material of a given permittivity/permeability matrix represents a characteristic polarization corresponding to the material

35. Write expressions for the electric and magnetic fields of a uniform plane wave propagating away from an infinite plane sheet of a specified sinusoidal current density, in a material medium

36. Find the material parameters from the propagation parameters of a sinusoidal uniform plane wave in a material medium

37. Find the power flow, power dissipation, and the electric and magnetic stored energies associated with electric and magnetic fields in a material medium

38. Determine whether a lossy material with a given set of material parameters is an imperfect dielectric or good conductor for a specified frequency

39. Find the charge and current densities on a perfect conductor surface by applying the boundary conditions for the electric and magnetic fields on the surface

40. Find the electric and magnetic fields at points on one side of a dielectric-dielectric interface, given the electric and magnetic fields at points on the other side of the interface

41. Find the reflected and transmitted wave fields for a given field of a uniform plane wave incident normally on a plane interface between two material media  

By the end of Module 6, you should be able to do the following:

42. Understand the geometrical significance of the gradient operation

43. Find the static electric potential due to a specified charge distribution by applying superposition in conjunction with the potential due to a point charge, and further find the electric field from the potential

44. Obtain the solution for the potential between two conductors held at specified potentials, for one-dimensional cases (and the region between which is filled with a dielectric of uniform or nonuniform permittivity, or with multiple dielectrics) by using the Laplace’s equation in one dimension, and further find the capacitance per unit area (Cartesian) or per unit length (cylindrical) or capacitance (spherical) of the arrangement

45. Perform static field analysis of arrangements consisting of two parallel plane conductors for electrostatic, magnetostatic, and electromagnetostatic fields

46. Perform quasistatic field analysis of arrangements consisting of two parallel plane conductors for electroquasistatic and magnetoquasistatic fields

47. Understand the condition for the validity of the quasistatic approximation and the input behavior of a physical structure for frequencies beyond the quasistatic approximation

48. Understand the development of the transmission-line (distributed equivalent circuit) from the field solutions for a given physical structure and obtain the transmission-line parameters for a line of arbitrary cross section by using the field mapping technique

By the end of Module 7, you should be able to do the following:

49. Find the voltage and current variations at a location on a lossless transmission line as functions of time and at an instant of time as functions of distance, and the steady state values of the line voltage and current, for a line terminated by a resistive load and excited by turning on a constant voltage source, by using the bounce-diagram technique

50. Design a lossless transmission line system by determining its parameters from information specified concerning the voltage and/or current variations on the line

51. Design a system of three lines in cascade for achieving a specified unit impulse response

52. Compute the reflected power for a wave incident on a junction of multiple lossless transmission lines from one of the lines and the values of power transmitted into each of the other lines, where the junction may consist of lines connected in series, parallel, or series-parallel, and include resistive elements

53.  Find the solutions for voltage and current along a transmission-line system excited by a constant voltage source and having reactive elements as terminations/discontinuities

54. Find the voltage and current variations at a location on a lossless transmission-line system as functions of time and at an instant of time as functions of distance, for specified nonzero initial voltage and/or current distributions along the system

55. Analyze a transmission line terminated by a nonlinear element by using the load line technique

56. Understand the effect of time delay in interconnections between logic gates

By the end of the course, you should be able to smile at Maxwell’s equations!

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University of Illinois at Urbana-Champaign
The Grainger College of Engineering
Electrical & Computer Engineering

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