Electromagnetic Fields and Waves

765 Pages·2010·9.94 MB·English

ElectromaFgineelatdnisdcW aves
IncludEilnegc tCriircc uits
ThiErddi tion
PauLlo rrain
UniverdseiM toen treaanldM cGilUln iversity
DalRe.C orson
CornelUln iversity
Fran<;Looirsr ain
rn
w.H .F reeamnaCdno mpany
New York
Coveirm agLei:n oefsE anodf H ina no ptiwcaavle guSiedpeea .g6 e6 8.
Backc oviemra gDei:ff erenctiiuraictStie.npe ga ge
144.
LibraorfCy o ngrCeastsa loging-in-DPautbal ication
LorirnaP,a ul.
Electromfiaeglndest iacn d waves.
Inlcudiensd ex.
1.E lectromfiaeglnd2es.tE. il ce ctromwaagvneest.i c
I.C orsDoanl,Re . IIL.o rnr,aFi ran"ois
IITIi.t le
QC66E54.L671 897 5304.11 ' 86-83013
ISB0N- 716-71823-5
ISB0N7- 16-6791-(83p bk.)
Copyr©i g1h89t8b y FreemaannCd o mpany
W. H.
Nop arotft hbioso mka yb er eprodbuyac nemyde chanical,
photogroarep lheicct,pr rooncioecsr is nt, h feo romfa
phonogrraepchoircnd oirn g,mib atye s torienadr etrieval
systterma,n smoirto ttehde,rc woipsifeeo dpr u bloirc
privatwei tuhwsoreui tt pteernm isfsriotomhn pe u blisher.
Prinitnte hdUe n itSetda tofeA sm erica
2 3 4 58 69 07 V B 6 5 4 3 2
() H I)
CONTENTS
Preface
viii
1
VECTOORP EARTORS
2
PHASORS
29
3
ELECTFRIIECL ID S
42
Coulomb'Gsa uLsLasaw'w s a nd
4
ELECTFRIIECL IDIS
64
TheE quiaootnfPs o isasnLodan p lCahcaeCr.og nes oenr.v ati
Conductors
5
ELECTFRIIECL IDISI
84
EleMcutplrotilcie s
ELECCT FRIIE LIDVS
6 101
Ene,rC gpayaictaanncFdeo ,r ces
ELECTFRIIECL VD S
*7 119
ElectrAi:cR C CC iirrccuuiittss
8
ELETCRICF IELVDIS
* 149
EleCcitrrBciuc:Ci i ctruTsieh to rems
ELECTFRIIECL VDISI
9 172
DielMeatcetrrAii:Bac ol usCn hda ragntedhEs el eFclturxi c
DenDs ity
10
ELETCRICF IELVDISI I
192
DielMeactterBri:Ric ea Dalilse leCcotnrtiCiconsnu,di itatyti ons
anI nfatcearen,Sd t oErnegedyr
11
ELETCRICF IELDS IX
211
ImagLeasp.lE aqcuieao'itnsRn e ctaCnogourldairn ates
Astermiesaktnsh atth ceh aptcearnbs es kipwpietdh looustic nogn tinuity.
•
VI CONTENTS
12
ELECTFRIIECL XD S
225
Lap'lsEa qcueaitSniph oenrC iocoarld. Pi onoianssts' eEsquation
froE
*1 3
RELATIIV ITY
238
TheL oernTtrzao nrsmfaatnSidpao cnie m-et
*41
RELA TIIVII TY
251
ThLeo reCnotnzt raanTcdit Dmiieo lna TthiTero anon.rs mfation
ofaV leocity
*51
RELATIIVIITIY
265
MasMso,m enFtour,mac ,neE dn geyr
*16
RELATIIVVIT Y
284
ThFei elMdo voEifln egaCc htarrigce
*71
RELATIVVI TY
308
MawxelElq'usa tTiheFo onusr.- PAo tential
18
MAGNETFIICE LID S
326
TheM agnFeltDuiexcn Bs ainttdyhV ece tPoort eAn tial
19
MAGNETFIICE LIDIS
348
TheV ecrPt ooteAn.At mpirea'elCs i uricLtaawl
20
MAGNETFIICE LDS III
360
MagnMeattieAcr :Tihe aM lasg nFeltDuiexcn Bs ainttdyh e
MagnFeiteSiltcdr ength
H
*21
MAGNETFIICE LIDVS
374
MagnMeattiecBr :Fi earlrso maagnMndae gtniCesitmri ccu its
22
MAGNETFIICE LVD S
387
The MaFgonroecnCet hsia cra gnCedus r rents
23
MAGNETFIICE LVDIS
412
ThFea raIdnadyuL catwi on
*42
MAGNETFIICE LVDIIS
437
EleCcitrrCciuc:Mi u ttasun aSdlfe- lnIductance
*25
MAGNETFIICE LVDISI I
452
EleCcitrrDciuc:Idi n utscC tiirvacenu Tdiart nfossr mers
26
MAGNETFIICE LIDXS
471
MagnEentgeiyarc n d MacMraogsnFceootrpicicec s
27
MAXWELELQ'USA TIONS
492
('ONTENTS Vll
28
PLANEEL ECTROMAGWNAEVTEIISC
514
UnifromP lanei FnWr aSevpaeec Nseo n,c ocntdoaurnsd,
Conductors
*29
PLANEEL ECTROMAGWNAEVTEIISCI
536
WavieGnso oCdo ntdouarcnsid Pn l asmas
30
PLANEEL ECTROMAGWNAEVTEIISCI I
554
RfleecatniRdoer nfa cAt:Tihe oB na sLiascwa nFdr neessl '
Equations
31
PLANEEL ECTROMAGWNAEVTEIISCV
578
RecflteainoRdnfer acBtN:iono unf nroimP laWnaeva ensTdot al
Rfleection
32
PLANEEL ECTROMAGWNAEVTEIVSC
594
RfleecatniRdofer na cCt:Rifl eoenc atniRdoer nfa catttih oen
Sufcaroefa G ooCdo nductor
33
GUDIEDW AVEIS
610
GenePrraiplnl.c eT ishCeo aaxniMadil oc srtLriinpe s
34
GUIDEWADV EISI
626
TheH olwRl eoctaWnagvuelgauri de
*35
GUIDD EWAVEISI I
646
TheP laOnptairWc aavle gAu:Tihe Ed ieeg nvEaqluuaet ion
*36
GUIDD EWAVES IV
662
TheP laOnptairWc aavle gBu:Tihe Gd uedi eWdav e
37
RADIATII ON
675
ThPeo teVna tniAdaa nltdshF ei eEla dnBsd
38
RADIATIIIO N
692
TheE leDcitprToirnlcase m iAtntteinnnga
39
RADIATIIIOIN
712
ThHeaf l-aWvAen teAnnntaeA,nrr na,aya sntdhM ea gnetic
DipAontleen na
AppenA diSxIP REFIXAENSD T HEISRY MBOLS7 30
AppenB diCxON VERSITOANB LE 731
AppenCd iWxAV ES 732
ANSWERS
739
INDEX
745

1
CHAPTER
VECTOR OPERATORS
1.1V ECfORA LGEBRA 2
1.1I.N1V ARIANCE 3
1.2T HEG RADIENVTf 3
ExapmleT:H EE LEVATIOOFNA POIONNTT HES URFACE
OFT HEE ARTH 5
1.3I NVARIANOCFET HEO PERATOVR 6
14. FLUX 7
ExapmleF:L UIFDL OW 7
1.5T HED IVERGENVC E. B 8
16. THED IVERGENTCHEE OREM 9
Examples 10
1.7T HEL INIEN ETGRALf �'B CONSERVATFIIVEEL DS 10
dl.
18. THEC URLV xB 11
ExapmleF:L UISDT REAM 13
19. STOKEST'HSE OREM 13
Exapml:eC ONSERVATIFVIEE LDS 15
1.0 1THEL APLACIOAPNE RATOVR2 15
1.1O1R THOGONACLU RVILINCEOARO RDINATES 15
1.1C1Y.L1I NDRICCOAOLR DINATES 17
1.21 S1P.HERICCAOLOR DINATES 18
1.31T 1H.EG RADIENT 20
1.41 T1H.ED IVERGENCE 20
1.51 T1H.EC URL 22
1.61 T1H.EL APLACIAN 23
11.2 SUMMARY 24
PROBLEMS 26
This incthraopidtsue crmtt eoohar entylth p o se wrheaoar nedtoy e erts
profiictnih euenso tefv ecotpoerr ators.
Wes hfarlueleq nrtelftyeot r hfi ee ldesl eoccfht arraigncced us r rents.
Foerx amwpesl heca,ol nls tihfdeoe rbrce et wteweeoln e cchtarrtigoce s
arfirsoea mni nterbaecttweieioetonnhn eoerft hceh aragntedhs fie e ld
oft hoet her.
2
Fig1.- 1A. v ecAtoa rn idt tsh ree
componveencttA oxrxAs,, .Ay,,z
whi,cw hhetnh eayrp el aceendtd o
enda,re eq uivtaolA e.Tnh teu nit
vectoyr,s p oiinntt h peo sitive
X, Z
direcotfti hoceno so rdianxaetse
anadr oefu nimta gnitude.
field
Mathceam,la ltayi iasf unctthidaoetns carp ihbyesqsiu caanlt ity
scafilealrd s
aatl plo iinsntp sa Icne . thqiusa nitsi tsyp eacs iifinegdl eb y
numbfeoerra pcoh.i T netmper,red aetnu,sa inetdly epcottreiancrt ei al
examopfsl ceasql uaarn tthicatativn ea sfrr yoo mnp eo inatn ottiohn e r
vecfiteolrd s
spaIcne . thpeh ysqiucaaniltasv i ettcoysr p,e cbiybfi oeatd h
numbaenrd d iatr ieocWni.nv de loacnigdtr ya vitfaotraicroeen al
examopfsl uevcseh c fiteo.lr d s
unit
Vecqtuoarn wtiibltedli e essi gbnyba otledidfta actylepi eac, n d
vectors
wiclalra r yc irXcy,u, m flex:
Z.
lighitftaatycpleei. c
Scaqluaarn tibtedi eessi gbwnyia ltle d
Wes hafloll tlhoew cuussutaoolfum s irnigg htC-ahratneds ian
coordsiynsatatesiem Fng si 1. - t1hp:eo sizt-idvieri etsch dteii roenc tion
ofa dvaonfac r ei ghts-chrraeonwtd ai tnte hsdee ntsheta utr tnhse
posixat-xiiivnsett hope o siyt-xiaitvshe r otuhgeah n 9.g0 l°e
1.V1E CTORA LGEBRA
Fig1u-rs1eh oawv se cAt aonrid tt sh rceoemn peosnA xt>A yA,z .I wfe
defitnwevo e ctors
(11-)
univteo crts
wheXry,e, arteh e alotnhge y,oa nzd- axes,
z X-,
respleytc,ht einv e
A + B= (Ax+ B x)+x (A y+ B y)+Y( A z+ Bz)i, (21)-
A -B= ( Ax- Bx)+x (A y- By)+Y( A-zB z)i, (31)-
A .B AxB+xA yB+yA zB=z A B co1>s, (1-4)
=
3
Fig1.- 2T.w ov ectAoa rnsBd a nd
thuen ivte ctonro rmtaotl h e
placnoen taCA,i an niBdn.g T he
posidtiirveec ftoi4Jroa nnsd
C
follthorewi ghntds- chrareuwl e.
Thev ectporro dAuX cB t i esq ual
toA Bs i4Jn anBd X A -AX
c, =
B.
x
y z
AXB= A( Av Az = A Bs i<pnc= (1-5)
C,
Bx By Bz
1-2,
aisF ni g.w here
(61)-
magnitAu,d e B.
is the of ansdi mifloarr ly
Thqeu anAt i,.wt hyBi icsh readB ,i""tsA h secd aooltrad ro,t
porduocfAt a nBd,w hiAl BeX, r e"adAc roBs,is"ts h eviecrot ro r,
cropsrso duct.
1.1I.n1va riance
A,B ,
The quanatni<pdta irieens d epoefn dctehhnoeoti fc c oeo rdinate
�yms.tS eucqhu ansta irstea itieodb ei nva.rA i vaencttsoatryh ,e
graviftoartocinaeo b nra,iil cis kn vabruiitatc nsot m,p oanreneno; tt s
tehyd epoennt dhc eo ordsiyntaetme.
A,B ,
Bothd oattnh cder opsrso daurfceut nsc otofin olnys a n<pda nd
<ltrheau lsis nov a.r iant
A B A B-,
Thseu amn tdh deie ffre,n +c eand arteh emsveelcvteosr s
anidn variant.
1.T2H EG RADIENT
VI
scaploaifrnnu ctt-ion
iass caqluaarn staityte ym,p e,rt ahitaaust r e
A
f
funcotfi octnoh oer dCionnastaies dsce.arp l oairn t-ftuhnactt iiosn
4
y
/1
/
, ,',' ------- +t" il
.
-----/-
.r - I
dx !
I I
I I
I
Fig1.- A3 .sc alar-point function
changesft off rdofom v etrh e
+
distdaln.c e
()'- -- -- "--- ,-+'-,c-,,--
f
contianndudio effunesbtr l.iWe aew itsohk nohwo wc hanogveteshr e
dl 1-3.
infinidtiesstiaimnFnagci l.e Thdei fferential
of of of
df=-dx+ -dy+ -dz
ox oy oz (-17)
is stchapelr aord utchttew vooe fc tors
=d xi + d yY+ d zi (-18)
dl
and
of of of
Vf= + y+ i.
oxi oy oz (-19)
f
Thsee cvoencd,wt hoorcsoem poanretenhr teas to fce hsa onfgw ei th
gradient
distantchceeo oarldaoeixnnsgia,c sta elt lheed offT. h sey mbol
(1-10)
irse "add.e "l
Nottehv ea lutehm eao gfn iotftu hgdere an dti:e
IVfl_- [(-oOxf)2 + ( -oOfy)2 + ( -oofz)2 ]1/2. (1-11)
Thus
df= V f·d l=I V fldlllc o8s, (1-12)
8 Vf
wheriets h aen gle tbheet wveeeacnntd dol .r s