1.1 A 2-kHz sound wave traveling in the x-direction in air was observed to have a
differential pressure p(x,t) = 10 N/m2 at x = 0 and t = 50 s. If the reference phase
of p(x,t) is 36 , find a complete expression for p(x,t). The velocity of sound in air is

8.2 A plane wave traveling in medium 1 with r1 = 2.25 is normally incident upon
medium 2 with r2 = 4. Both media are made of nonmagnetic, non-conducting
materials. If the electric field of the incident wave is given by
Ei = y 8 cos(6 109 t 30 x)
(V/m).
(a

Table 2-1: Transmission-line manners R'. L'. G. and C ' fnr three types of lines.
Ml: 1-1: Fundamental SI units.
tn-Wire Mild-Plate Unit
'I
E -_R* 9,.
ml to
I
E In [(0/4) + (/(n/dil l I L Him
I u,-
110 .10 2 SIM
WW") In [(D/d) + (RD/d)! ~

2-D Array of a Liquid Crystal Display
1. WAVES & PHASORS
7e Applied EM by Ulaby and Ravaioli
Examples of EM Applications
Fundamental Forces of Nature
Gravitational Force
Force exerted on mass 2 by mass 1
Gravitational field induced by mass 1
Charge: Elect

EECS 230 Exam 2-Section 2
Name: 6; 2;, 19 a UMID
Problem 1: 10 Points
A circular loop of radius a=5cm is in the x-y plane. If the loop
carries current I=40A in the -direction and is in the
presence of a magnetic field B=Bo 2, describe the force
acting on

9. RADIATION & ANTENNAS
Applied EM by Ulaby, Michielssen and Ravaioli
Examples of Antennas
Antenna Properties
1. An antenna is a transducer that
converts a guided wave propagating on a
transmission line into an electromagnetic
wave propagating in an unbou

8. WAVE REFLECTION & TRANSMISSION
7e Applied EM by Ulaby and Ravaioli
Signal Refraction at Boundaries
Radiation by antenna (Chapter 9)
Wave propagation in lossless medium (Chapter 7)
Wave refraction across a
boundary (this chapter)
Wave propagation in los

3. VECTOR ANALYSIS
7e Applied EM by Ulaby and Ravaioli
Laws of Vector Algebra
Properties of Vector Operations
Equality of Two Vectors
Commutative property
Mod 3.1
Position & Distance Vectors
Position Vector: From origin to point P
Distance Vector: Between

5.4 The rectangular loop shown in Fig. P5.4 consists of 20 closely wrapped turns
and is hinged along the z-axis. The plane of the loop makes an angle of 30 with the
y-axis, and the current in the windings is 0.5 A. What is the magnitude of the torque
exer

3.44 Each of the following vector fields is displayed in Fig. P3.44 in the form of a
vector representation. Determine A analytically and then compare the result with
your expectations on the basis of the displayed pattern.
(f) A = x xy2 , for 10 x, y 10
F

2. TRANSMISSION LINES
7e Applied EM by Ulaby and Ravaioli
Transmission Lines
A transmission line connects a generator to a load
Transmission lines include:
Two parallel wires
Coaxial cable
Microstrip line
Optical fiber
Waveguide
etc.
Transmission Li

5. MAGNETOSTATICS
7e Applied EM by Ulaby and Ravaioli
Electric vs Magnetic Comparison
Electric & Magnetic Forces
Magnetic force
Electromagnetic (Lorentz)
force
Magnetic Force on a Current Element
Differential force dFm on a differential current I dl:
Torq

EECS 230 Sample Exam II
1.
(8 points) Explain the difference between convection and conduction current.
2.
(7 points) Explain how a maglev train works.
3. (30 points) A cylinder-shaped carbon resistor is 8 cm in length and its circular cross section
has a

GRADIENT, DIVE
3V 3V
3V
VV _
=ax+ 8)! +3 I
BGEN
, CE.
., A? y
CURL.
u 7
LAPLACIAN OPE'
m1 , '
rim? .- 1" H;-
:
.V 3 z
e ;\ ' V. Pivot axis
3 .
3A, gl+m
v. _
A: 8x + ay Oz
7: i a
a 3 3 8A. 3A ,. 8A BA A 3A
v _ _ _'

7. PLANE WAVE PROPAGATION
7e Applied EM by Ulaby and Ravaioli
Guided EM Waves
Unbounded EM Waves
Maxwells Equations
For sinusoidal time variations:
Complex Permittivity
Wave Equations
Wave Equations cont.
Lossless Media
If the medium is nonconducting ( =

7.19 In a medium characterized by r = 9, r = 1, and = 0.1 S/m, determine the
phase angle by which the magnetic field leads the electric field at 100 MHz.
Solution: The phase angle by which the magnetic field leads the electric field is
where is the phase

6.2 The loop in Fig. P6.2 is in the xy plane and B = z B0 sin t with B0 positive.
What is the direction of I ( or ) at:
(a) t = 0
(b) t = /4
(c) t = /2
z
R
y
Vemf
I
x
Figure P6.2 Loop of Problem 6.2.
Solution: I = Vemf /R. Since the single-turn loop is no

6.19 At t = 0, charge density v0 was introduced into the interior of a material with
a relative permittivity r = 9. If at t = 1 s the charge density has dissipated down to
103 v0 , what is the conductivity of the material?
Solution: We start by using Eq.

4.51 Figure P4.51 shows three planar dielectric slabs of equal thickness but with
different dielectric constants. If E0 in air makes an angle of 45 with respect to the
z-axis, find the angle of E in each of the other layers.
z
E0
45
0 (air)
1 = 30
2 = 50

2.19 A 50- lossless transmission line is terminated in a load with impedance ZL =
(30 j50) . The wavelength is 8 cm. Find:
(a) the reflection coefficient at the load,
(b) the standing-wave ratio on the line,
(c) the position of the voltage maximum nearest

7.2 Write general expressions for the electric and magnetic fields of a 1-GHz
sinusoidal plane wave traveling in the +y-direction in a lossless nonmagnetic medium
with relative permittivity r = 9. The electric field is polarized along the x-direction,
its

10. SATELLITE COMMUNICATION & RADAR SENSORS
Applied EM by Ulaby, Michielssen and Ravaioli
Geosynchronous Satellites
To remain in sync with Earths rotation,
a satellite has to be at an orbital
altitude of 35,786 km above the
Earths equator.
Three geosynchr

2.1 A transmission line of length l connects a load to a sinusoidal voltage source
with an oscillation frequency f . Assuming the velocity of wave propagation on the
line is c, for which of the following situations is it reasonable to ignore the presence

EECS 230 Midterm 2
27 November, 2012
Name: UMID
Section 1 Section 2
Problem 1: 25 points
(a) Provide a precise statement of Lenzes law.
Leaf/5 law fronts: lm He dinghy bf Hue cal/yen;
in a conJuahn 9.70 i: MA m 2% 12ng indmal
In); HY (MM/m 0y)?! tie Gluh

6. MAXWELLS EQUATIONS IN TIME-VARYING FIELDS
7e Applied EM by Ulaby and Ravaioli
Maxwells Equations
In this chapter, we will examine Faradays and Ampres laws
Faradays Law
Electromotive force (voltage) induced by
time-varying magnetic flux:
Three types of

4. ELECTROSTATICS
7e Applied EM by Ulaby and Ravaioli
Maxwells Equations
God said:
And there was light!
Charge Distributions
Volume charge density:
Total Charge in a Volume
Surface and Line Charge Densities
Example 1
Current Density
For a surface with any

5.21 Current I flows along the positive z-direction in the inner conductor of a
long coaxial cable and returns through the outer conductor. The inner conductor has
radius a, and the inner and outer radii of the outer conductor are b and c, respectively.
(

EECS 230 Exam 2-Section 1
Name: 22 22. 23 m4 UMID
Problem 1:10 points
An electron moving in the +2 direction is in the presence of a
magnetic eld B=Bo 3. What is the direction of the magnetic
force acting on the electron?
E:gx:-)M3,X8092 QEMBp
Problem 2:

3.5 Given vectors A = x + y 2 z 3, B = x 2 y 4, and C = y 2 z 4, find
(a) A and a ,
(b) the component of B along C,
(c) AC ,
(d) A C,
C),
(e) A (B
C),
(f) A (B
(g) x B, and
(h) (A y ) z .
Solution:
(a) From Eq. (3.4),
A=
and, from Eq. (3.5),
q
12 + 22 +