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EE 135 - Winter 2006

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



  • 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.35-p.66 (p.43-p.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 mid-term 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.84-p.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 (11-1) & 16 (10-12) - 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 (11-1) & 9(10-12) - 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 time-varying 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.
  • Transmission-line 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/open-circuit & 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.
  • Dielectric-conductor boundary condition.
  • Dielectric-dielectric boundary condition.
  • RC = epsilon/sigma.
  • Image method.
  • Electric field vs. magnetic field.
  • Lorentz force.
  • Magnetic force for current conductor.
  • Biot-Savart 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. 1-3: 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. 1-3.
  • 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.4-6: 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.
  • Biot-Savart 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


  • Lab courses scheduled on Wed 11-1 (changed) and Thu 10-12 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 (11-1), 16 (10-12) and the report due on 3/2 (Thu) in class .
  • lab #3 manual/report : the session on 3/8 (11-1), 9 (10-12) and the report due on 3/16 (Thu) in class.

General Class Information

Lecture times:
Tue & Thu, 8-9:45, E2 192
Associated Lab:
BE 161
Name: Toshishige Yamada ( tyamada@mail.arc.nasa.gov)
Phone: 459-1912
Office: BE 129
Instructor Office Hours:
Tue & Thu, 10-11:45
Teaching Assistant:
Name: Mona Zebarjadi ( mona@soe.ucsc.edu)
Phone: 459-1292
Office: BE 230
TA Office Hours:
Fri, 12-2
F. T. Ulaby, Fundamentals of Applied Electromagnetism, 2004 Media ed., (Prentice, Upper Saddle River, 2004).

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