ECEN 3400

Electromagnetic Fields and Waves

Lecture: 12:00-12:50 M W F, ECEE 1B32

Help/Recitation/Lab Demo Sessions: T 9:30-11:00am, ECEE 1B32; TH 3:30-5:00pm, ECEE 265 (optional but you may earn up to 5 extra points)

Page last updated 10 February 2017

Page created by and curtesy of Prof. Kuester

Latest Announcements

  March 17 2017: Homework 7 is assigned. Due 3-24
Assignments and other dated items on this page are generally correct for about one week from today. Items more than one week in the future and undated material are subject to change without notice. Any deviations from this policy will be listed as announcements to the left or below. Please check this page regularly for updates.

Remember that all questions about the grading of homework problems should be directed first to the GTP Assistant who graded that homework.

Instructor: Prof. Dejan S Filipovic

Office Phone



Office Hours

(303) 735-6319

ECOT 243

  Monday 3.30-4.30pm, Friday 2-3pm, or by appointment

Graduate Teaching Practicum Assistants




Office Hour

Conrad Andrews

ECEE 285

Thursday, 12-1pm
Michael Grayson ECEE 285
Thursday, 1-2pm





Office Hour

Alexander Anderson

ECEE 285

Wednesday 9-10am, Thursday, 11am-12pm
Ben Van Court ECEE 1B08
M/T: 3-6pm, W/F: 4-6pm

Main Headings on this Page

Course Information     Course Calendar    Lecture and Reading Schedule    Exam Dates   Old Announcements

Supplementary Textbook (Popović, and B. Popović)
Introductory Electromagnetics: Practice, Problems and Labs 
(Rev. 04-12-2012)

Sample Exams 
    Free Technical Software

Course Information


In this course, you will be introduced to the behavior of electromagnetic fields, and will see some of the ways in which they are used in electrical engineering. The text is Electromagnetics, by B. Notaroš. A scanned copy of the supplementary text, Introductory Electromagnetics, by Z. Popović, and B. Popović is freely available in PDF format for download (be sure to check the errata file for a list of all known corrections to the text). The additional volume Introductory Electromagnetics: Practice, Problems and Labs by Z. Popović, and B. Popović contains full or partial solutions to some of the problems, and may also be downloaded. This file has incorporated all known corrections up to the present time.

The following books are put on reserve at the Engineering Library:

Additionally, the following Internet resources may be of interest:

CU Engineering Fellows ( may offer review and study sessions for this course if interest is expressed.


Your grade for the course will be determined as follows (the value of your weakest hour or final exam will be reduced by 5%):



2 Hour Exams

25% each

Final Exam


Additional Credit

To pass the course your cummulative score must be above 60%. Specifically, your grade will be assigned according to the following score table:

Cummulative Score Final Grade
93-100 A
90-92.9 A-
85-89.9 B+
80-84.9 B
75-79.9 B-
70-74.9 C+
65-69.9 C
60-64.9 C-
50-59.9 D
<50 F

I expect that you will abide by all University expectations of academic integrity. Please read the information on this, as well as on disabilities, religious observances and standards of behavior.

Class preparation

Please read the assigned section of the book prior to each lecture. Use office hours to clear all possible questionmarks you may have.


Homework assignments are due every Friday in the lecture unless indicated to the contrary on the calendar below. Late homework is not accepted. You can turn homework in early by sliding them under my door. If you have questions about the grading of your homework, please contact the grader (see the top of the page) by email or during his office hour to resolve your question. Only if the issue cannot be resolved between you and the grader should you bring the question to me.


Occasionally you may need to compute or plot something which is a little more complex than a handheld calculator is convenient for. In such a case, you may use any appropriate software, so long as your results are clear. Matlab, Mathematica and MathCad are all fine for this purpose; even Excel works well. Several freeware programs are listed below which can be used if you don't want to pay for software specifically for this course.


There will be two in-class (50 minute) hour exams. The exams are closed-book and closed-notes, and are combination of theoretical questions and problems. No extra notes and no calculators for the theoretical part (30min); however, for the problem solving part (20min) you will be allowed to bring one 8-˝" by 11" sheet of notes and a calculator. The study questions and problems will be sent a week before the test. The final exam is 2.50 hours and is also a combination of theoretical questions and problems. The first part (theory) is closed notes; for the second part (problems) you may bring two 8-˝" by 11" sheet(s) of notes and a calculator. The schedule of exams is listed in the calendar. Currently planned dates are March 3 and April 14, 2017, but these are subject to minor changes if circumstances warrant. The final exam (2-˝ hours long) will be held the week of May 8th. The final exam will be cumulative, but with emphasis on the final third of the course. Thus, half of the questions on the final exam will be on chapters 1-7 of the text, and the other half will be on the material from chapters 8-12.

If you have 3 or 4 final exams on the same day, you need to see the instructor(s) of the course(s) that have their final exams in the third (and possibly fourth) time slots of that day in a timely manner, to make arrangements to take those exams on a different day in accordance with University rules. The official deadline for doing so will be posted.

Sample Exams

Samples of some previous exams (problems) from recent years will be posted below. Note that some of these were written for use with the book by Popović and Popović, so the notations may differ from those used in the present text by Notaroš.

Sample Exam 1-1 Sample Exam 1-2 Sample Exam 2-1 Sample Exam 2-2

Sample Final Exam 1 Sample Final Exam 2

Syllabus and Schedules

The calendar below gives a day by day list of lecture topics, reading and homework assignments. It is student's responsibility to check this page for all assignments, and to be prepared appropriately.


Refer to lecture and reading assignment schedule for lecture topics and homework assignments. HW = Homework due that day.
Problems numbered x.x are taken from the text (Notaroš); problems numbered Px.x are taken from the supplementary text (
Popović and Popović).
Homework assignments will not be changed when there is less than one week until they are due; otherwise they may be changed as needed. If you like to do homework well ahead of time, be warned of this and check before turning in your assignment that you have done the correct problems.




Lecture 1

Lecture 2

HW: 1.2, 1.6
Grader: Carlos Mulero 

Lecture 3

Lecture 4

Lecture 5

HW: 1.10, 1.21, 1.29, 1.30
Lecture 6


Lecture 7

Lecture 8

HW: 1.34, 1.44,  1.58, 1.60

Lecture 9

Lecture 10

Lecture 11

HW: 1.77, 1.80, 1.87, 1.89

Lecture 12

Lecture 13

Lecture 14

HW: 1.47, 2.4, 2.8, 2.18

Lecture 15

Lecture 16

Lecture 17


Lecture 18


Lecture 19


Hour Exam #1

Covers material through Lecture 16

Lecture 20

Lecture 21

Lecture 22

HW: 3.7, 3.26, 4.2, 4.10

Lecture 23

Lecture 24

Lecture 25

HW: 4.24, 5.10, 6.12, 6.16

Lecture 26

Lecture 27

Lecture 28




Lecture 29

Lecture 30

Lecture 31


Lecture 32

Lecture 33


Hour Exam #2

Covers material through Lecture 26

Lecture 34

Lecture 35

Lecture 36


Lecture 37

Lecture 38

Lecture 39



Lecture 40

Lecture 41

Lecture 42


Lecture and Reading Schedule

Lecture No.


Reading Assignment [from text (BN) or Supplementary Textbook (PP)]





Coulomb's Force Laws

BN, sections 1.1; PP, Chapters 1 and 2


Electric Fields

BN, sections 1.2-1.4; PP, sects. 3.1-3.3


Computing E fields from charge distributions

BN, section 1.5


Field lines; The electrostatic potential

BN, sections 1.6-1.8


E from the potential

BN, sections 1.9-1.10


More examples on potential; Introduction to Gauss' Law

BN, section 1.12


Using Gauss' Law

BN section 1.13


Gauss' Law Examples; Conductors

BN sections 1.16-1.17; PP section 6.2


Conductors in Electrostatic Field; Electrostatic Shielding

BN section 1.18


Electrostatic Images

BN section 1.21



BN sections 1.11, 2.1-2.2 and 2.17



BN sections 2.3-2.4


Generalized Gauss' law; Boundary conditions

BN sections 2.5-2.9


Capacitance, Electrostatic Coupling

BN sections 2.12-2.14


Electrostatic Energy

BN section 2.15-2.16


Steady Current in Conductors

BN sections 3.1-3.4


Resistors and Electrodes

BN sections 3.5-3.6, 3.8, 3.11 and 3.13


Amper's Law; The Magnetic Field; Biot-Savart Law

BN sections 4.1-4.3


Ampere's Law BN section 4.4


More Ampere's Law; Gauss's Law for B BN sections 4.5 and 4.8


Magnetization and Ampere's Law BN sections 5.1 and 5.3-5.4


Magnetic Material Properties BN sections 4.11, 5.2 and 5.5


Electromagnetic Induction; Faraday's Law BN sections 6.1-6.7; PP, section 14.2


Mutual and Self Inductance BN sections 7.1-7.3


Magnetic Field Energy; Magnetic Applications

BN sections 7.4-7.5
27 Displacement Current; Integral and Differential Forms of Maxwell's Equations BN sections 8.1-8.4
28 Time-Harmonic (Phasor) Form of Maxwell's Equations BN sections 8.6-8.8
29 Linearly Polarized Plane Waves BN sections 9.1-9.4
30 Skin Effect BN sections 9.10-9.11; PP, chapter 20
31 Poynting's theorem BN sections 8.11-8.12
32 Introduction to Transmission Lines; Waves on a Uniform TL BN sections 12.1-12.3


Reflection of Waves on a TL

BN sections 12.4-12.5


Reflection of Plane Waves (Normal Incidence) BN sections 10.1-10.2


Impedance of Loaded TLs BN section 12.6
36 TL Examples and VSWR


More TLs

BN sections 12.13-12.14


More TLs



More TLs



More TLs



More TLs

EM Wave Applications PP sections 25.2 and 25.3

Some Free Programs of Interest


A "student version" of a program which can numerically solve (among other things) electrostatic and magnetostatic field problems. This version is limited as to problem size, but is free.

FEMM - Finite Element Method Magnetics

Freeware. From the reference manual: "FEMM is a suite of programs for solving low frequency electromagnetic problems on two-dimensional planar and axisymmetric domains. The program currently addresses linear/nonlinear magnetostatic problems, linear/nonlinear time harmonic magnetic problems, and linear electrostatic problems." FEMM is a Windows program, useful for getting numerical solutions of fields and parameters such as inductance and capacitance, among many possible applications.


Windows Freeware. From the website: "Create your graphs for scientific publication with XL-Plot. It reads ascii files and it outputs a vector drawing. XL-Plot is for Windows 95,98, 2000 and XP. The primary purpose of XL-Plot is to create a figure for scientific publication rapidly. It contains a few basic statistical functions, such as Students t-test and linear correlation of two sets of data (two columns in a spreadsheet). XL-Plot has a number of built-in functions that can be fitted to the data in columns on a spreadsheet or to a curve in a graph. The user can easily add fitting functions of his own design.Additional options are Fourier Transformation, (de-)convolution and Matrix inversion." It is a modest piece of software that does a surprising number of tasks well.


Another freeware plotting program for Windows, concentrating on the display of functions. This one can do 3D (surface) plots. It has some animation capabilities as well.


A freeware numerical mathematics program similar in many ways to Matlab. It is available for Windows, Linux, Unix and OS/2 (this latter is no longer maintained). May be worth a look, though I haven't really used it myself.


A free mathematical software package for various Unix flavors and for Windows, somewhat more advanced in capabilities than Euler. It aims to do many of the same things as Matlab. From its website: "Scilab is a scientific software package for numerical computations in a user-friendly environment. It features:


If you qualify for accommodations because of a disability, please submit to your professor a letter from Disability Services by September 30 so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities. Contact Disability Services at 303-492-8671 or by e-mail at If you have a temporary medical condition or injury, see Temporary Medical Conditions: Injuries, Surgeries, and Illnesses guidelines under Quick Links at Disability Services website and discuss your needs with your professor.

Religious observances

Campus policy regarding religious observances requires that faculty make every effort to deal reasonably and fairly with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required attendance.  In this class, I request you inform me in writing by September 30 if there are any dates when accomodations need to be made.
See full details at 

In-class behavior

Students and faculty each have responsibility for maintaining an appropriate learning environment. Those who fail to adhere to such behavioral standards may be subject to discipline. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, color, culture, religion, creed, politics, veteran's status, sexual orientation, gender, gender identity and gender expression, age, disability, and nationalities.  Class rosters are provided to the instructor with the student's legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records.  Cell phones MUST be turned off (or placed in 100% silent mode) before the class start. Students whose cell phones ring during the lecture will be asked to leave the lecture. See policies at   and at

Honor code

All students of the University of Colorado at Boulder are responsible for knowing and adhering to the academic integrity policy of this institution. Violations of this policy may include: cheating, plagiarism, aid of academic dishonesty, fabrication, lying, bribery, and threatening behavior.  All incidents of academic misconduct shall be reported to the Honor Code Council (; 303-735-2273). Students who are found to be in violation of the academic integrity policy will be subject to both academic sanctions from the faculty member and non-academic sanctions (including but not limited to university probation, suspension, or expulsion). Other information on the Honor Code can be found at  and at

Discrimination and Sexual Harassment  

The University of Colorado Boulder (CU-Boulder) is committed to maintaining a positive learning, working, and living environment. The University of Colorado does not discriminate on the basis of race, color, national origin, sex, age, disability, creed, religion, sexual orientation, or veteran status in admission and access to, and treatment and employment in, its educational programs and activities. (Regent Law, Article 10, amended 11/8/2001).  CU-Boulder will not tolerate acts of discrimination or harassment based upon Protected Classes or related retaliation against or by any employee or student. For purposes of this CU-Boulder policy, "Protected Classes" refers to race, color, national origin, sex, pregnancy,  age, disability, creed, religion, sexual orientation, gender identity, gender expression,  or veteran status.  Individuals who believe they have been discriminated against should contact the Office of Discrimination and Harassment (ODH) at 303-492-2127 or the Office of Student Conduct (OSC) at 303-492-5550.  Information about the ODH, the above referenced policies, and the campus resources available to assist individuals regarding discrimination or harassment can be obtained at 

Old Announcements