I realize that, no matter how careful I have endeavored to be,
occasional errors may still exist. I should be grateful if
you would be kind enough to notify me a3 you discover them
either in the book or in this manual.
Sincerely,
David K. Cheng
Electrical and Computer Engineering
Department
Syracuse University
Syracuse, NY
(For the use of instructors only.)
13210
-roduced by Addison-Wesley from camera-ready copy supplied by the
lhor.
I'yright 0 1983 by ·AddiRon-Wealey Publishing Company. Inc.
I rights reserved. No part of this publication may be reproduced.
Ired in a retrieval sY8tem~ran.mitlted, in any form or by any
Ins, electronic, mechanical, photocopying, recording, or otherwise,
lhout the prior written permi8sion of the publisher. Printed in
. United States of America. Published simultaneously in Canada.
N 0-201.10129.1
FGHIJ·AL-89818
..
A note to instructors using FIELD AND WAVE ELECTROHAGNETICS.
Dear Colleague:
As teachers of introductory electromagnetics, we are all aware
of two facts: that most students consider the subject matter
difficult and that there are numerous books on the market
dealing with this subject. It is understandable that s~udents
find electromagnetics difficult. First of all, the subject
matter is buil t upon abstract models that demand a good mathematical background. Second, before the course on electromagnetics, students who have studied circuit theory normally
encounter functions of only one independent variable, namely,
time' whereas 1n electromagnetics they are suddenly required to
deal'with functions of four variables (space and time). This is
a big transition, and visualization problems associated with
solid geometry add to the difficulty. Finally, students are
often confused about the way the subject matter Is developed,
even after they have completed the course, mainly because most
books do not provide a unified and comprehensible approach.
As I point out in the Preface of the book, the inductive approach of beginning with the various experimental laws tends to
be fragmented and lacks cohesiveness, whereas the practice of
writing the four general Maxwell's equations at the outset
without discussing their necessity and sufficiency presents a
major stumbling block for learning. Students are often puzzled
about the structure of the electromagnetic model. I sincerely
believe that the gradual axiomatic approach based on Helmholtz's
theorem used in this book provides unity in the gradational
development of the electromagnetic model from the very simple
model for electrostatics. Although a rigorous mathematical
proof of Helmholtz's theorem is relatively involved (not included in the book), the physical concept of specifying both the
flow source and the vortex (circulation) source in order to
define a vector field is Quite simple.
Many review ~Destlons are provided at the end of each chapter.
They are deSigned to review and reinforce the essential material
1n the chapter without the need for a calculator. You may wish
to use them as a vehicle for discussion in class.
I have tried to.m~ke the problems in each chapter meaningfUl
and to avoid trlvlal number-plu~1ng types. This solutions
manual gives the solutions and answers to all the problems'in
the book. I hope it proves to be a useful aid in teaching
from the book. Answers to odd-numbered problems are included
in the back of the book.
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Let J. t -1jU1l. -t -Il/u~. r(~-I{f-Il/u.)
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y
81.1t
h)
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4
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£ - ? it
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Let
Clf-
~~ ~
&
Jt
'0
.:
y - 22. S
:t nA/Z
(M).
4"
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.. l.s(), ./0-' COI(to'"t - ~ r + ..
1) (V~,'
,,_/
wi -lea.
e;
·
£,. = s,,,.
(m).
£-
ii.,£",sinfl(
+ .,£.Sin(tlH'/r)
-4xE".+ ~Ey.
!.x S'
I £ . " mCr4+YJ-s/"eccDJf+cos4s/nyr
Ie -
; : Cos '"
+/ ' -
rt.f r .
Sill
.
'?.-" ~ . v"0l~
CDS t \1. (, .s;\ sin'",
( .!x..
e: - .s:
£,.
I
£;j
I.. £r _\1+( £. _,J_2~~_f,
l e:. . Sift r)
£. 4/" vI
E,.E.. Sllt',vvhich is the ~fuQliDn of an 4/lijJse.
I,. Ord., 10 "'."J Ih", /,orllmakN 01 fhtz (lIllI's e ,
rofaie fhtZ coorcl/nah 4W'el x-y Cou"hrc/oc.'wlsfl
hy t:tn DI19'. 8 .}" x~y~ Auume /oj, e «'Iuo/ion t>f
fhe ellipse in
Y
.jfbrMl
of lit.,
hew cODrJ"nd/.~ 1-0 h.
(-!if + (-:fJ -I.
0
whera
"
E. ' == E GIIf. + I: ~"n. (!)
"ox£ sin_ -IlvCMII.@
~
£
y
"
",
...s~h$l"'k""n!J @ oncJ (j) in @ Q"d NZ,Qrran9;"9 :
1 __
£
'f
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Q!
s""'._' .,. £ 2(r;n'fI .,. co,.. ,_Z£ £ :sin,,£.,S(.L - .!.\_,
h*"7
Q~
Y
II-
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slot. .,
J
1
@
£.1. sin''''
co,·. __./__
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£:lit& sl" . .,.
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b'
1
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j,a
(Z) tbtJ @ Cdn
2.
Q'
COJt
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•
h. so/v.J -lor fIt,.~ unknowns:
8 = .1.,..
a. ..
4
sin
+
a..
£'p. CD.
b*
Y
ohM;"
CO"'PQrln9 (!) dnd @.
4
7
w. I. __,__
1·
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M '.1 y=,\
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LQn
j e ('''sacZIt) 'foE! (I-~.Cl') · s/" '"
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In parHculQ.t> i, £,,,= £,.:
-t. '
4Z
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1- ·
·
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LeI an 411/l'f;c,ally po/arizecl pla.n. wave h. r e-«
p,..stlnl_d ~Y fh. p/'asor (wi~h p"'pagalion
lac lor e-JJ,~ omiH.J):
s = s;e, % 41 £J ei~
0.)
wber« £I
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£i » and ~
are
arb,.Ir41'Y
co"'fanls.
Ri~J,t-honJ circula,.,y PO'tlriz~dWtJ"":£"c-Cre(a..-iay).
L.Ft-hllnJ circultlr/y polarlzeJ WII".: ~ • ~, (;Il"'i iiy ) .
I
i-,
£ '1:, . . z' ( £, t ) ·£, e '"
£.1.,i j£.ej.A), .
rr
f{£,
£ ... £,." -+ ~ .
fhen
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E" e cs, - ia~)
:a
- l.
-
(a:.f -a,jZ) +£
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(a.; + Qyj)
wAe,... E•., and E._ cue I"'9/'I-hA"J and 1..lf-hand
ell'-pflc.dlly pola";ZI.J waves respflclivttl),.
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wave can h. written as
~~ • £ lA,c ., j iiy )
- £ (ii~f +~jJ)+£ (ti.1
= ('c- ~ £'•.,. .
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For
COil du c li"E In II
kc1=:s
.I
W~€,-W~E.(I- ; , : )
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8".$'
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b) f
- I (Mil..)
c) f
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· .ii- a:z 0 • 210
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e-···'·
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(AA,,)
roC - 0.1.
e»
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d.=fJjiijlll+(i!iV-I} - 14- (Nfl"')
~ -wJiii [JI+{-4i!.flj'/&- 300" (raJlm)
~..
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by
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=iia '7E,. , a
It
0'-/4
if
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unJlGnt jnJ.~"J~~
of
r:
l- s.e, + 4,£"
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r 2'11".. r '
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PD)'nf,'''' v.e/o,tJ. - £ Ie
Power
P
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ot CF'O,,-Sfl.CflDnal
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l;-£.(4~-i4¥)('-IJ~.
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2- 0 :
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[ ~(.) ., t: (a)]
r
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e
£.f-~ +j iiy)~iJ: Q./~/t-/'anJc:ircu"rly
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r
d,·recbeon.
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f, (%~t) -lR.. [Et (%).,. £,.{~)j .J.,t
= lR.. ~[(a.-J4j,)c·i".+ (-.. 4ja,) ~~zJ(illlt
- 01.... £.[-2j (.", -j~s,·nlJ.lci•• ,
c)
- 2£. Si,,~.(. . ~;,.tJt-aycoltJt).
Given
P.'-17
£; lx,z)" Q1 fO e-i t ,1T. ., ~~
(v/",).
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A -
2"
T1" - tii
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0.
'2 r (",)
I - f: - 4.1'.,0· (Hz.);
h)
W-J.."'f .Jc~ -JJI f0 9 ("tAcI/s)
E; (x,z ;t)- ~fO CO'(J.(O't - '.-I~)
(VI_)
fi,.l~Z). ,;. iilM·xl,.
ci",-f-~o.'+a.4'
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2
v -y
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~ IS"
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c)
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1=
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cJ)
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ii,. ex-, s) -
;f aM
II
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0 - . . . I:.,.(X".) -= -ii., fOC
aM' .. i;, D.' .,. ~ D.,·
i,(~~)
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(AI".).
l, (1t,,2) - t; ex"s) "f,Ca"s) -a,ID(e-i,S. e11S) c-j ""
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• - 5yilO e-i ' " ~,." IS
("Im).
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--(i'./~",COI'. -i". ,f-or si"ts)':I'. (AI",).
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(i.ivc"
a.)
1; (y,d- S(ay.., a.Jj)Ci.{Jiy;j)
kY=-'fl,
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Jc .l~;.,Jt; =12. (rlAcJlm).
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(,..).
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t
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#;(y,2it) -
c:.)
cJ)
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6; -
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(vI",),
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(A/",).
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ii, lYJ z) = i,. (y" z) + ii,. (,/,,2)
=
a. (- ,~)c:os 'z
-e ;Ufy
P. 1-/9 4) frDm £". (.-,0A) and (I-'O"):
£, (:c., z;t) ii, lx,s;t)
iiy~£;.s;" fJ,a cos .;J.rin(wt -~,1t s,h9,).
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.,. i.. (2
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~ 0'. sill -I (;4$fJ,aCOS(}I)Sin(",t -AUl"S,.)j,
ii, (x"z; t)- "0,
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r _ - £. .~z -iJaZ
t=t - ~ to e
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•
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