Index of class resources
Handouts — homework problem
sets, homework solutions, other helpful handouts
General Class Information — class and
section times, instructor and TA information
EE 135 Electromagnetic Fields and Waves
Handouts
Messages
 Ch. 2 transmission line is the most demanding but interesting in
the course. We will learn wave transmission (physics),
equivalent circuit (EE), and solution
to a wave equation (mathematics). Please read
the text p.35p.66 (p.43p.66 is most critical)  Jan 10.
 Please write to
Yamada to request a permission code  Jan 11.
 It is expected that at least 80 % is confidently answered in the
diagnostic Math test for the "survival" in the course. If not,
refresh your Math as necessary:
complex functions, vector dot/cross products,
and differentiation chain rule, etc.  Jan 12.
 A general transmission line solution contains two constants  V0+ & V0. By the input
and load boundary conditions, they are determined. In a thrown baseball analysis,
we need two pieces of information, e.q., the initial position and velocity,
to determine all the motion uniquely  Jan 19.
 Ch. 3 is purely mathematical. Always work on examples for each formula.
Gradient in a polar coordinate, div & Gauss's theorem, curl (rot) & Stokes' theorem
are the keys  Jan 20.
 For the midterm exams, you can create one page of formulas for use during the exams.
You may
want to start preparing it in advance  Jan 21.
 Please read p.84p.90  Jan 23.
 Feel comfortable with the cylindrical and spherical coordinates, and del  Jan 31.
 Midterm #1 solution is posted  Feb 2.
 Lab #1 report due on Feb 7 (Tue) in class  Feb 2.
 Feel comfortable with div and curl (rot)  Feb 2.
 Feel the power of Gauss's law  Feb 9.
 Lab #2 session on 2/15 (111) & 16 (1012)  Feb 9.
 A half wavelength TL is invisible (Zin = ZL), but there is generally a
reflection. The reflectionless situation is related to impedance matching
(ZL = Z0) Feb 14.
 In the image charge problem, we must multiply a cosine component for the
electric field in the evaluation of the areal
charge density. I will comment on this on Thu  Feb 14.
 In the image charge method, we need to be careful in the potential evaluation
because the image charge will also move if we move the real charge. I will comment on this
on Thu  Feb 14.
 Please read Ch. 4 (review) and 5 (preview).  Feb 14.
 Please read Ch. 6.  Feb 22.
 Lab #3 session changed to 3/8 (111) & 9(1012)  Mar 1.
 Some raised many students will have schedule conflict for midterm #2
on 3/7 (Tue). If
this is the case, I will consider 3/9 (Th). Talk to
you in class tomorrow, 3/2.  Mar 1.
 Midterm #2 is scheduled on 3/9 (Thu).  Mar 2.
 Extra credit project (optional)
 due 3/20. Type up to two pages. Anything you
considered about the EM related things  for example, different solution
for a textbook problem, your thought about the breakdown of Kirchhoff
voltage law in the timevarying B field
or a report of recent news/discovery in the field, etc.
Covered topics by now
 E & M field.
 Wave as a function of t and x.
 Phasor technique and application to circuits.
 Transmissionline equivalent circuit  role of L & C.
 V & I wave equations, their solution with phasor, & reflection coefficient.
 Determination of "constants" in wave equation under the short/opencircuit & matched
conditions.
 Reflection coefficient "Gamma" in terms of Z0 & ZL.
 Characteristic impedance "Z0".
 Input impedance "Zin(z)" giving an equivalent impedance for the TL and ZL.
 Standing wave ratio "S" in terms of "Gamma".
 Power in transmission line.
 Bounce diagram.
 Vector dot/cross product, coordinate systems (Cartesian, cylindrical, & spherical),
"del".
 Gauss's law.
 Stokes's law.
 E field by highly symmetric charge distributions  rod, sphere, and plane.
 Dielectricconductor boundary condition.
 Dielectricdielectric boundary condition.
 RC = epsilon/sigma.
 Image method.
 Electric field vs. magnetic field.
 Lorentz force.
 Magnetic force for current conductor.
 BiotSavart law.
 Ampere's law.
 Gauss's law for magnetism.
 Force between two current conductors.
 The meaning of the ground in electrostatics.

Homework reminder & solution
Midterm exam #1
 Scheduled on 2/2 (Thu), in the same room in the same time slot.
 Ch. 13: wave, phasor, transmission line (except for Smith Chart), & vector analysis
(before div and curl).
 One sheet of formulas (both sides) allowed in the exam.
 No textbooks, no notes, & no calculators.
 Read all the problems at the beginning. First problems are not necessarily the easiest.
 Incomplete answers may be given partial credit if the logic is solid.
Just give it a try if you know something.
 Long problems contain a lot of hints. Do not be scared.
 The gravitation example is to show the trend of the exam. All the problems are
of course related to Ch. 13.
 Many problems are related to the HW sets, but they
are cooked so that they will be in fact simpler.
They look different, but are simpler scientifically. The HW problems heavily
overlapping with the lecture
are of course what you want to focus on in preparation.
 If more time is spent on certain topics than the others in the lecture, they must be important.
You may want to review them carefully.
 Good luck.
 solution p1
solution p2
 Those who do not feel comfortable with Q5 need to review vector
analysis techniques seriously. We will use them
extensively in the following chapters and they will be the basic
components in the midterm #2 and final.
Midterm exam #2
 Scheduled on 9th of March (Thu).
 Ch.46: electrostatics, magnetostatics, & Maxwell's eqs.
 Special emphasis on Ch.4 & Ch.5.
 Vector analysis (grad, div, curl) included.
 One sheet of formulas (both sides) allowed in the exam.
 No textbooks, no notes, & no calculators.
 Five main questions with many subquestions. Do not be late for
the starting time 8 am.
 Coulomb's law.
 Gauss's law.
 Capacitance evaluation.
 Image charge technique.
 Potential calculation.
 Lorentz force.
 BiotSavart law.
 Ampere's law.
 Faraday's law.
 High symmetry cases are important. This is why you want to be familiar
with the cylindrical and pherical coordinates. Be familiar with the textbook
notations. r = sqrt(x*x+y*y) and R = sqrt(x*x+y*y+z*z).
 solution
 Typo: in the solution above, 3(c), "16" in the denominator must be "2".
 Average 51, 10's  80's. People scoring less than 40 in midterm #2 or
the total less than 90 in midterms # 1 & #2 want to prepare seriously
for the final.
Final exam
 If you want to prepare for the final 3/20, then ...
 Two pages of formula sheets.
 Study midterms #1 & #2 carefully. Solvable nice high symmetry systems are
limited: they are wires, circles,
cylinders, spheres, & parallel plates, and we have covered almost all of them in
midterm #2. This means the same physical systems will be
highly likely considered in the final exam (but questions will be of
course different, or at least look different).
 Understand the concept (meaning of wave solutions) in Ch. 7.
 There are eight questions. They are about 35 % from midterm #1 area, 55 % from midterm #2 area,
and 10 % from Ch. 7.
 Concentrate on major topics.
 It is much better to know 5 things perfectly rather than to know 10 things 50 %.
 If you do not know the exact answer, but know the functional form of the answer, e.g.,
such that the field is proportional
to 1/r, then write it for partial credit.
 solution p1
solution p2
solution p3
Class notes
Laboratory
 Lab courses scheduled on Wed 111 (changed) and Thu 1012 at BE 161. For the final
assignment of people and schedule, see below. If not show up, no credit.
 Please print the lab manual/report and bring it to the lab.
 final lab schedule as of 1/24
 lab #1 manual/report : the report due on 2/7 (Tue).
 lab #2 manual/report : the session on 2/15 (111),
16 (1012) and the report
due on 3/2 (Thu) in class .
 lab #3 manual/report : the session on 3/8 (111), 9 (1012) and
the report due on 3/16 (Thu) in class.
General Class Information
 Lecture times:
 Tue & Thu, 89:45, E2 192
 Associated Lab:
 BE 161
 Instructor:
 Name: Toshishige Yamada (
tyamada@mail.arc.nasa.gov)
 Phone: 4591912
 Office: BE 129
 Instructor Office Hours:
 Tue & Thu, 1011:45
 Teaching Assistant:
 Name: Mona Zebarjadi (
mona@soe.ucsc.edu)
 Phone: 4591292
 Office: BE 230
 TA Office Hours:
 Fri, 122
 Textbook:
 F. T. Ulaby, Fundamentals of Applied Electromagnetism, 2004 Media ed.,
(Prentice, Upper Saddle River, 2004).
