Problem 8.18 For some types of glass, the index of refraction varies with
wavelength. A prism made of a material with
n = 1.71
(0 in m),
where 0 is the wavelength in vacuum, was used to disperse white light as shown in
Fig. P8.18. The white light
ECE 381 Homework Set 2
Spring 2008, Will post Feb. 1, Dvorak
1 Ulaby Problem 1.8
2 Ulaby Problem 1. 12
3 Ulaby Problem 1.15
4 Ulaby Problem 1.18
5 Ulaby Problem 1.22
6 Ulaby Problem 1.23
7 Ulaby Problem 1.24
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Problem 7.19 Ignoring reection at the airsoil boundary, if the amplitude of a
3-GHz incident wave is 10 V/m at the surface of a wet soil medium, at what depth will
it be down to 1 mV/m? Wet soil is characterized by r = 1, r = 9, and = 5 104
Problem 7.4 The electric eld of a plane wave propagating in a nonmagnetic
material is given by
E = [y 3 sin( 107t 0.2 x)
+ z 4 cos( 107t 0.2 x)] (V/m)
(a) The wavelength.
(b) r .
(a) Since k = 0.2 ,
= 10 m.
Problem 6.11 The loop shown in P6.11 moves away from a wire carrying a current
I1 = 10 A at a constant velocity u = y7.5 (m/s). If R = 10 and the direction of I2 is
as dened in the gure, nd I2 as a function of y0 , the distance between the wire and
Problem 5.19 Three long, parallel wires are arranged as shown in Fig. P5.19.
Determine the force per unit length acting on the wire carrying I3 .
I1 = 10 A
I3 = 10 A
I2 = 10 A
Figure P5.19: Three parallel wires of Problem 5.19.
Solution: Since I1
Problem 4.48 With reference to Fig. 4-19, nd E1 if E2 = x3 y2 + z2 (V/m),
1 = 20 ,
2 = 180 , and the boundary has a surface charge density
s = 3.54 1011 (C/m2 ). What angle does E2 make with the z-axis?
Solution: We know that E1t = E2t for any 2 media. H
Problem 4.24 Charge Q1 is uniformly distributed over a thin spherical shell of
radius a, and charge Q2 is uniformly distributed over a second spherical shell of
radius b, with b > a. Apply Gausss law to nd E in the regions R < a, a < R < b,
and R > b.
Problem 2.27 At an operating frequency of 300 MHz, a lossless 50- air-spaced
transmission line 2.5 m in length is terminated with an impedance ZL = (40 + j20) .
Find the input impedance.
Solution: Given a lossless transmission line, Z0 = 50 , f = 300 MHz,
Problem 2.20 A 300- lossless air transmission line is connected to a complex
load composed of a resistor in series with an inductor, as shown in Fig. P2.20. At
5 MHz, determine: (a) , (b) S, (c) location of voltage maximum nearest to the load,
and (d) loc
Problem 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
Problem 1.4 A wave traveling along a string is given by
y(x, t ) = 2 sin(4 t + 10 x) (cm),
where x is the distance along the string in meters and y is the vertical displacement.
Determine: (a) the direction of wave travel, (b) the reference phase 0 , (c)
UNIVERSITY OF ARIZONA
Department of Electrical and Computer Engineering
ECE 381 Section 1 Fall 2011 Ziolkowski
Hour Exam 2 ' October 24, 2011
You can ACE this exam Think
No guessing allowedl! Remember that partial credit will be given