S O L U T I O N S M A N U A L to accompany E L E C T R I C I T Y A N D MA G N E T I S M MUNIR H. NAYFEH MORTON K. BRUSSEL University of Illinois JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore Copyrigh1t9@8 b6y J ohWinl ey& SonsI,n c. Thisma. terima.ayl b er eprodfuocret eds tionrg instructpiuornpoaslbe ysp eoplues intgh et ext. 7 ISB0N 4 718 0692 Printientd h eUn iteSdt atoefsAme rica 9 7 10 8 6 5 4 3 2 1 CHAPTER 1 + + + + 1.1 Thec rossp roduAcxt B isp erpdeincultaorb otAh a ndB . Sincwee w anat univte ctowre,j usdti vibdyet he + + + magndie t:u -n- +A BX/ IXA Bl + + X y z A X B = 2 -6 -3 l5x- lO+y 3oz 4 3 -1 IAX s1= /1s2 + 102+ 302 35 3x- HencTIAe =, 1s x l-O+y 30; 72v + 6z 3'i 1. 2 Thep ositivoenc toorfst hesteh repeo inatrse + -A A + A -A rl 2x y+ z,r 2 = 3x+ 2y z,a nd + r -x+ 3y+ 2z. Thep ositivoenc toofra na rbitrpaoriynits 3 + A A A r = xx +y y+ zz. Ifa llv ectolrasyi nt hep lanet,he tnh e followtirnigp clreo spsr oduvcatn is.h es whicghi velsl +x Sy+ 13z- 30 O. 1. 3 Thep oistiovne ctoorfst hespeo inatnsd a na rbitrpaoriyn t + A + A -,,- A arerl Jx+ y+ 2z, r2 = X ,._y 4z, and - t = xx yy+ zz. Thee quatiooftn h ep lanies g overnbeytd h e condit(ito nt )•(r-r) =w h0i cghi vetsh ee quation 2 2 1 2x +3 +y 6z+ 28 =f o0rt hep lane. r dtnltl=/ rd/rr V(l/r)= r d(l/r)/d=r - ;/2r 1.5C onsitdheesr u rfadceef inbeyfd where f(x,y=, 2zx)z2 -3xy- 4x =- O7. Recatlhla Vtf i sn ormtaol surfafc(ex ,y=, Oz,)t hen afA afA afA Vf - x+- y+- z ax ay az At( 1,,-2)1 weh aveVf: = (8+ 3 -)x 43-y +8 z A A 7x- 3y +8 z.T heu nivte ctnoorr mtaolt hes urfaactte h si point is: n= Vf = 7i- 3i+ s:£ 7;_- 3i+ 8:i "fvTT /22 2 2 ✓122 + 3+ 8 1.6B yd efiniwteih oanv He/ ds = IV t1 -NowV t=2xy3z; + max x2z3y+ 3x2yz2;,t huast X 2, y = l, z = -1w eh ave A A A Vt= -4x - 42yz . H+e n1ce, idstm /adxsi maulmo ng 2 2 2 (-4i- 4y+ 12�)//+4 4 + 12 direction and 2 2 2 IVtl/ 4+4 +12 =✓176 2 1.7U sinEgq .1 .57 + 3 +3 3+ -3 + 03 V•(r/)r = V(lr/ )•r+V •r/r rA• r + = 0 4 r 1.8U sintgh ev ectiodre ntgiitvyei nnE q.( l.6w0e)h ave = + + + + + + + + t+ V•(xA B =) B•(xV A ) -•A(Vx B) O, sincex =�V V x o. + 1 .A9 i si rortatniaoli fV X wAh icghi ves - x(c+ 1 ) -y(a- )4 +� (b 2)= 0. Therefa=o r4,e b 2, C= -1. HencA+=e (x +2 y 4+z )x( 2x +3 -y -z)y + + (4X - y 2 )+ Nzo wA z--."v�w-- � xA� + YA�+ Az . Thus ax ay �z ar,, + + - = X 2y 4z Partiailnltye grwaittrehe spetcoxt : ax 2 + =�+ 2xy 4xz+ f,(zy). Now�=2 x 3-y - zt,h us 2 ;)y partiailnltye grawtiitnrhge spetcoyt gives 2 + = 2xy - 3y2 -/yz +g (xz),. No�w = 4x - y 2z, thus az partiailnltyea gtrinwgi trhe spte tcoz gives: + 2 = 4xz- yz z +h (xy,).Co mparitnhge3 ',s wes eet haitf f(y,z)= -32/y2 + 2 z-yz, g(,xz)= 2x/2 +4 xz + 2,z h(,xy) x2/2 + 2xy- 3y2/2 thewne g eta wh erVe A=+. Thaits = x2/2 +2 xy +4 xz- 3y2/2 + 2 z-yz + cao ntsatn. + + + 1.10V •A l 1 a 2 + 0a w hicghi veas= -2. + + 2A E= r/r= r/ri sc onserv(astpihveer ciocoarld inaartee s + + E impeldi)i fV Ex = O.Notteh at= E; r 3 r re rsinei + + a a a VX E 2 ar TI � r sine 0 + + V X E (rileE /a�- rsini8il E /38=) Q. Wec anq uicyk l 2 r r rsin8 seet hat�s pheriyc syamlmlet(r8i,c�i ndepe)n rdaednital fielidsc onservatTihvuVes X. ( r/=r )o . + A A il A lil A l il E =r /=r -V= (- r - + e ----.+-- )�• ar ra e rsrnae� - Thu1s/r -il/ar= -d/drO.r- d= dr/wrh icihn tegrates to = -tnr+ c. Appyilng( r a)=0 givecs =t nat;h us = tna- tn=r -tn(r/)a. 1.12N otitchea itf w ec an finad s calfaurn cti(oxn), syuch thaAt= Va sr equiirnet dh es ecopnadr otf t hipsr oblem, then + itw oulbdea necesys aanrds ufficcioenndtii otnt haAt be conservatiHvoew.e vweerw ,i lglo a heaadn de xpliyc sihtolw + + thaVt Ax= 0 tos hotwh aAt i sc onservative: A 2 2 VX A +x[il(3-xyz) /il-yil (3x- z)/ilz) 2 3 -y[il(3-xyz)/xil -il(6yx z+) /ilz] 2 3 +�[il(-3zx)a/x il-(6yx -)z/il]y 2 2 �(--1( -1)-)y (3z-(3z))+ ;(6-x( 6)x)= o.T herefore + + Vx A= 0 + A isc onservatNiovwwe ef. i nd such that + A V. 4 + 3 A 2 A 2 A A (6x+y z )(x3 x+ z)y+ (3xz- y)z 3 2 3 Integrga at�ia/nx 6xy z+ give�s = 3xy +XZ + g(y,z), 2 - 2 Integraat�ia/ny g 3x z give�s =3xy z-y+ h(x),.z 2 3- IntegirnagHt /az 3xz- ygive�s x= z zy+ f(x,y). Byi nspectoifto hne set hreree altiso nwec ane asislhy ow 2 3 + tha�t( x,y,z3)xy xz -zy+ C, + ax ay+ -az 3, V•r= -+ - = Thes urfaicnet egral ax lly az +A I= (! r•ndcaa nb ew rittiennt ermosf a voluimnet egral using S thed ivergetnhceeo rIe =m rv•dtv = fd3v= 3Vw herVe i st he V V voulme oft hes urf,a ce aA aA aA 1.14a ) V•=A � + __:j_ + __z = 4 4-y+ 2z, ax ay az b)Fromh eroen ,i ti se asietsots wittcohc ylindrical + cooirndatweshe reV •A= 4 -ps4i¢n + 2z, Inc ylinrdical coorndaitexs2, + y2 = 4i st hes amaes p = 2, From ftihgeu re A A theu nivte cotrsn ormtaols isp , normtaols isz ,a nd 1 2 s .!� normatlo 3 is-_z. t Thed i vergetnhcoeer esmt ates o 1 -rl!is; + f V• Adv= A• d = (4- 4psi¢n 2z)pd pd¢dz (,·. V :....__- �. 3 2'1T 2 ; f dzf d¢f pdp(4 -ps4i¢n + 2z=) 84'1T 0 0 0 I I t,/ Noww ec alcultahtese u rfaicnet egral ·,.J + + 1A •ad 'j 5 + y p icos+• y sina.n,dA 4xx - Zy2 + 2;z 2A 2A A A (4xx - 2y+ yzz )• ( xcos+• y sni•p)d� z (4pco2s• -z/si3n•)pd�z - + + 2 3 Thigsi veAs• da= 8(co•s 2sin•) d• zdatp = 2 1 + + 2A A A•da(zz )•( z)pd.dwph icihse quatlo9 pdp d.a tz = 3. 2 A+ •d+a (z2z A )• (A- pzd).pd whicihsz eraot z = u.Additnhge 3 threceo ntrtiibounwseg et 1 x.aJ = 9 2 fpd p 2lf f d .+ 2f8 (lfc o2•s - 2si2•n)d3f• d z S O 0 0 + 0 whicghi ve8s4 lft,h es amaes f V•Adv. 1.15a ) Wef irsfti ntdh e unit nTohrecm yalli.n drical surafcei sd escrbeidb yf (x,)y x2 + 2y -16= o. We n A A use = ll/flVflT.h eg raidenotf f isll f= Zxx 2+y y.T he magnitouftd hee g raedniti s lvfl Bute verywhere /2 II ont hes ufrcaew eh aev 2 + 2 y 4,t herefVofr =e 8. Hence n =( x� y+y )/4. b) + + A SubtsitutfionrgA andn inA •nw eg etA •n(xz+ yx)4/. Writitnhgii sn c ylindrcioocrdailn atweegs e t + A + A (pzcos• Thu/s•A nda= fA• npdtdz lf/4 5 f f (zcos+• 2sin.co=s 5.()5d+t

Solutions Manual for Electricity and Magnetism

Similar Solutions Manual for Electricity and Magnetism