Spring 2016 AGRON / E E / MTEOR 518
Problem Set 1: Due Tuesday, January 19, 2016.
Assigned January 13, 2016.
Please note that this assignment is two pages long! Be sure to look at the last page!
The complete questions for problems 3, 4, 5, and 6 come from “Fundamentals of Applied
Electromagnetics” (Ulaby, 1997 version) and have been scanned to pdf and linked on the
course website with the material from the first class period.
1. Review “Style Conventions” and Tables 1 through 4 in “Guide for Metric Practice.”
Write out the unit mK in full (i.e. how it would be written without using abbreviations). Write two correct forms of the abbreviation for the units “watts per steradian.”
2. (1.3 in Ulaby’s “Fundamentals of Applied Electromagnetics,” 1997 version). The height
of an ocean wave is described by the function
y(x, t) = 1.5 sin (0.5t − 0.6x) m.
(1)
Determine the phase velocity (up ) and the wavelength (λ), and then sketch (or graph
with MATLAB) y(x, t) at t = 2 s over the range from x = 0 to x = 2λ.
3. (1.8 in Ulaby). The voltage of an electromagnetic wave traveling on a transmission
line is give by... Don’t forget to include the units of α.
4. (1.9 in Ulaby).
are given by... Complex number: z = x+jy,
√
√ Complex numbers z1 and z2√
+
where j = −1. Equation (1.41) is |z| = x2 + y 2 and Equation (1.43) is |z| = + zz ∗
where ∗ denotes complex conjugate.
5. (3.2 in Ulaby). Given A = x̂2 − ŷ3 + ẑ and...
6. (3.3 in Ulaby). Given vectors A = x̂ + ŷ2 − ẑ3, ...
7. Use “Electric Field Hockey” on the PhET website (http://phet.colorado.edu/) to
recall the effect of electric fields. Play and experiment. Then make the puck positive.
Place a positive charge to the left of the puck, and another positive charge behind the
goal. Experiment so that you can position the charges to make a goal, and to not make
a goal, by only sliding the charge to the left of the puck left or right. Does changing
the mass of the puck make a difference? Explain why or why not.
1
8. Use “Microwaves” on the PhET website to discover why water is so electrically interesting.
(a) Pick “One Molecule” and adjust the frequency so it is just above zero. Select
“Full field.”
i. Which side of a water molecule (the oxygen or hydrogen side) is negative?
Explain how you can tell.
ii. Why does the water molecule continue to move after the electric field reverses
direction?
(b) Now pick “Many Molecules.” If you want to reach the maximum temperature
possible, which is more important: amplitude or frequency? Or are they equally
important? Explain how you determined your answer by briefly describing the
experiments you conducted. Be sure to use “Reset” each time you begin a new
experiment. After clicking on “Reset” you must click on the “Microwave on/off”
button.
9. A short tutorial for MATLAB written by one of my former professors is available on
the course webpage in either PDF or HTML. Read and do the examples in MATLAB.
Please read up to (and including) Section 3.2, Scripts and Functions. Then read
Section 5, Advanced Graphics. Finally read Section 7, Efficiency in MATLAB. Recreate
Figures 1 through 5 and 7 and paste these into a word processor so that they occupy
one or two sheets, print them out, and include in your homework.
10. Read “Iowa: America’s most biologically altered state” on the course website. This
article was published in the Ames Tribune.
(a) How many square meters is an acre? How many acres in a square kilometer?
(b) The author says:
We are all stockholders in the corporation of creation and evolution. As
the author Henry David Thoreau said, “In wildness is the preservation
of the world.”
What do you think the author is saying?
(c) What are the “two sides with different realities” that the author mentions?
(d) How can remote sensing be used to monitor the ecology of Iowa? Give at least
two examples.
(e) Does your research (or research that you may be interested in conducting in the
future) address issues related to ecology? Why or why not?
2