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Unformatted text preview: ECE 329 Introduction to Electromagnetic Fields Fall 08 University of Illinois Oelze, Kim, Waldrop, Kudeki Exam 2 Thursday, Oct 23, 2008 — 7:008:15 PM ETWL war» 1' Section: H 8 AM 9 PM 12 Noon 1 PM ( Please clearly PRINT your name in CAPITAL LETTERS and circle your section in the above boxes. This is a closed book exam and calculators are not allowed. You are allowed one formula. sheet of 8.5 by
ll inch dimensions — both sides of the sheet may be used. Please show all your work and make sure to
include your reasoning for each answer. All answers should include units wherever appropriate. Problem 1 (25 points) Problem 2 (25 points) Problem 3 (25 points) ( Problem 4 (25 points) TOTAL (100 pointsfﬂ‘ 1. Consider a. transverse electromagnetic wave ﬁeld propagating in vacuum in +y direction. The
ﬁeld varies co—sinusoidally in time with an angular frequency of w = 271' X 108 rad/s. The wave
polarization is righthand circular. a) (5 pts) What is the corresponding wavenurnber ﬂ? ' _ .— W I; _. .. _ 00 C; ”‘7 ﬂ“ W ’ Zvﬁlbgqh’tﬂ: 277‘ (”j
C/ bx(0%“/J 3 b) (10 pts) What is the expression for ﬁeld phasor E if the wave electric ﬁeld Re{Eejwt} = 255 V/m
at t— — 0 and (Ir, y,z)= (0 0 ,0)? We», 7; a 29 on (wt{3%) 4% 940012195) / o l)
CHAS 35 a Kc {04.4 WWIe r
M “ﬂair/4:04 V {gig/n H’s {IVKCVU c) (5 pts) Given that the electric ﬁeld Re{Eej‘”t} = 2:27 V/m at t = O and (1,11, 2) = (0, 0,0), what
is the corresponding magnetic intensity vector H at the. same time and location? Hint: this
part can be answered independent of part (b) d) (5 pts) Determine the timeaveraged power transported by the wave per unit area. (in +y direc— tion). a) ' E:2(Q+J% a”? 15L A “ Hrgeérfxﬂi 2i , /\ n A ﬁg ‘N
: ; ”Am; +2 3 7' ' //
4i” (283% \% “Io wz/
2 2. The gap between a pair of parallel inﬁnite copper plates extends from 2 = O to z = W > O and is
originally occupied by vacuum (60, no). The plates carry equal and oppositely signed surface charge
densities and as a consequence we have a constant electric ﬁeld E = 32 V / In in vacuum in the gap region, L
Cm mg:
i ’— 2 1‘ L: > 3% “(Tag / Fig/W / / a) (6 pts) What are the corresponding displacement vector D and polarization vector P in the gap
region? N b) (4 pts) What is the surface charge density p3 of the copper plate at z = O?
gal/ma D W (3?" %<0/ c) (9 pts) What would be the new values of E, D, and P in the gap region if the gap were ﬁlled with
a nonconducting fluid of permittivity e = 8150 without changing the surface charge densities of
the copper plates? ’ "* /\
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Pr> cg. a» 72% d) (6 pts) What would be the new equilibrium values of E, D, and P in the gap region if some
amount of salt were dissolved in the ﬂuid in the gap (see part c) to raise its conductivity to
a = 4 S/ in (conductivity of sea. water)? State the values of E, D, and P after a steadystate
equilibrium is reached and brieﬂy explain your answer.
g = f), P 90 {M alum/m». 9mm in A ant/Law‘s?
: ‘mﬁ/i’ aha—1e; mm M him/“ea“?
A i \ 99. (h a , 1,4,1 «4:5 rod/bomb” C m/ 3 M 3W l/v ML! W M m ”away ﬁes mime m (We 3. For a uniform plane wave propagating in an imperfect dielectric the magnetic ﬁeld intensity in phasor notation (without the time dependent portion cm) is given as
r K Lr e
1:1: 4e“(0 0001+j0. 2)ng A.
Since the medium is nearly perfect, all the wave parameters 7], 16, Up, and A expressed in terms of
,u, e w and f are identical to those for a perfect dielectric except that the attenuation constant 04 is not 0 buW If the ielative pei meability yr— — [to “—.and the speed of light In the _...medium*a 4 and 108 m/s. respectively, determine. (a) the fi equency of the wave in Hertz; (b) the wavelenmhej u ave; (c) the dielectric constant of the medium. ((1) the conductivity of
the medium; (e) the location z where the peak amplitude of the magnetic ﬁeld intensity is 1/6 of the
value at z = 0; (f) the electric ﬁeld phasor 133(2). All the answers should have the correct units
and directions where applicable. Use the fact that the speed of light and intrinsic impedance in free
space are 3 x 108 m/s and 1207r 9, respectively. No partial points will be given. 0t: 0.00M LEV/w L; ‘QW m 7N.“ :?km N » ”’7
lNli’k ”VF/J ii: :quo:%ﬁlwﬁ $416027ﬂ/ 4. A dielectric material is sandwiched between a perfect dielectric (60, 1.10) and a. conductor as shown in
the ﬁgure below. Perfect. Dielectlic (Region 1) Medium 2 (Region 2) Assuming that charge density [)3 on the surface of the COIldlllctOl 15 460 C/ m and the fields in medium
1 are uniform detelmine the following when ﬁelds E2: %2 V/m, H2—  3m + 4y A/m in medium 2
and H3— — 0 in medium 3: lav ,[1 /\ /\ A
b) (5pts)Js(z=0)= Ex (3/): +415): 3 ‘7 ~+X é:
// __ /\
c) (5 pts)E1= 527, _ (52,)12 : g V C’Z— Arm»; D51):
€5,— ' “g” 2 4% Weca/«R no W06.
9 C/Lgowrcruf % = l d) <5 pts) H1 =32,
: $24,491; 1‘: / (z/gﬁkm W 99x9»; “Wu? Wilﬂ
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