still if

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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 mea3 you discover them either in the book or in this manual.

Sincerely,

David K. Cheng

Electrical and Computer Engineering Department

Syracuse University Syracuse, NY 13210

(For the use of instructors only.)

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-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.

N0-201.10129.1 FGHIJ·AL-89818

..

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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 built upon abstract models that demand a good mathematical background. Second, before the course on elec-

tromagnetics, 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 ~Destlonsare 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 maywish 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~1ngtypes. 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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()- _..t!.j, +^Col,.,J, +~ ^C1"" v.l..^J,*1{"~~-~l"tL) ^.

~ ~~:~_ ^iI^F^{: -4i,} ~~UJ;h;"~~~~;;rr:~'H,})J.·

- - - - r ~ 4}~.Q .~ll =- . ^Qd ^.

.Q (r) IS 'r : ,-0 -,I"(d'",..)v.

6) j"~, ^l'1rrJr =-^{Q .}

14-

(18)

1'.4-1 tA) 0"l9;"'/pointcJ,Q,.,. ^Q. ^a-l y -= d/J Q"cI/1'Yt~!Jes Q &t Y= ^(1+''')dlJ ^J ?t-:tl, t.J¹ ^• ^{• • •} -Q. .fy-.(~+'n)J/3 , "-O~ :ttl~l~···

b) 0",'9;_11,',.. cJ.ar"!Jt ~ tAl 8 - JO·^{Q h J} """fI&~"^/,'nc.

Cha.r,.s ~ QI-B - I.O·GnJ -'/0·; -~QI 9.'O~ -~D:QnJ-150°

•

.v•

...----... ^---......

...---da---'"

t o e o - - - - D - - - - -

, h'

Q·--d- Q_, J. = _ ._d

Q. ( - h)

4 ) V - - - - ' - - - . 4"~ At dR;

b) fa _^-£ "V I

• • ~A ^131'

_ t.l(J,a-d

--•.",'''-.J^a^_

..,

(19)

1'4-{3

') 4-14 Tj,~ solu#ion V()r.,Y)= V_O sal'-s/lel V"v=o ana all bound4'-Y Cl1nt;/llioltl. • LJnirLi. SD!u"'''Dn.

V(x~)') ^...~^s'-',:."~[A" ^Sf;'/':"'1 "A,.CoS/':"Y]-

. [5^t^rtoJJ

AI y-o^I vc~o,-~-r_,. ^B_It^S"n r;:)C, -... 'n- It"₀_I _"ct_V.I1.

At Y-b, Vi-.."')- V, - Is,."'/,..[A"Sl,J,':a,ri+8..cos/' ":"]

It ~

~ A: 1'·"1.n", ^«e ^COJIt~^_{"'II'^ItHJ

n 4 " 4 0^I "he".

A" - J^ntr_,,~I,~li(v, _-~^coshIt:"). ⁿ ^ocJJ

l·o~ ^{n even.} ^.

0. 4-IJ 7ntl. J'olul-ion /r fhq,sup..rposif;ot)01 Mol _~or

£')C~"'pl. 4-'Qrui //,aI -lor F,'9- 4-12 ro/-qf~J ~o· ^;n thQ c./ocl<\IV"~" dl,..cJ"on. (In btlM CG~.S ~ ^$houlJ h. r⁴pla c «J _{~.Y ~/.2.J}

1nsiJ.: Vlr,~)^.. '~.Lf (il[Sin"+⁺^si"n("~I)J, ^r«⁶

" ,,=.u

OulsiJ.: V(r,+)·~r ~(#[s;nnl +I;""(~~:~l. ^r>6.

1t. .~tI

l_-_"J4 ,n VCr,,~)=-^E.,.c.tI~+ ,.~^t! B,^uo~cos "r-". _ _^...l ^(Af ^,.»,⁶ ⁾

,..1 ^It⁰ ^\ E-ca.£.,V--l;,"c••_~

A+ ,-h. V('~#)·"'!,l-I;4I~ '~I, ,"'c.~".L

flfJ " r

---. _{~ ·~h·;} B,."0 /Or n/a'.

Oullicl.Nt.cy!ittJ.,.: V(r,4-) .. -_~,.o-~)^c•^.I+'

r >b E- r ,. ,.

(I;~)^{- -} iV -i,.4 {,..·Oc.'II.,E.(fI·I,;,,~·

)4-10 For r~1>~ ~('i~J^..-t.~c.J~"i,,.r·"coln1,

.. n.'

",h~ ~C~;).r A",,"cos"f.

Af r~b: V.('6.)-~.("+)It-'--..- -t,II+',li'=A,S,j ,,,J,....A,.~,., n~l.

-~, L..·-(r~L..- r."8,"·'_-~rA,; ftl"l;"'·'L-f."A"b":/~.

'II,

(20)