冯恩信电磁场与电磁波课后习题答案汇编

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3cos஺si”o-cos஺si”o-Tcos஺=-sin0cos஺0=-sin0cos஺00=-sin^9001³00100ᡝi(p,(p,z)=cos´sin(p(p*COS0sin஺o-cos஺sin஺o-~Q'sin஺%—-sin(pCOS00µsin஺cos஺01=cos஺[0|_00014010_F(p,

4cos஺sin஺022cos᜛%sin஺cos0002si”00100E(x,y,z)=2cos½+2sing9(2)F](x,y,z)=2Q=-/,"(xx+yy)F(X,y,z)=-3sin¾+3cos
2ᑭᵨ(2)¿ÀY3·(x,y,z)=3஺=-,Á(x?-yx)Jx+y1.10¤ᙊᳫᙶ᪗¨©Ḅ./£஺,Â᜛v=5ᡝ,£஺,Â᜛v=6ᵨ¥9ᙶ᪗¨©Ḅᙶ᪗ᑖ/⊤²஺@A᪷SsinOcos஺cosOcose-sine%Ay=sinOsin᜛cosOsin᜛cos஺%(1)4_cos஺sin஺0J4Y>,/sinBcos஺cos®cos°-sin^9R5sin஺cos°=sinOsin஺cosOsin/cos஺0=5sinOsin஺A.COS0sin஺005cos஺ᡝi(x,y,z)=x5sin6cos᜛+f5sin6sinQ+25cos6

5x=rsinOcoseÆf஺@A(a)%+>=(3+2)2+(5+4)0+(-4+3)2=5~+90-9jAAjPsZP(Pz(b)AxB-ApA&=35—4=312-170+22BᓫB243

6(c)6=]1(3p+50—42)=+(2p+40+32)AA/32+52+421(2஺+40+32)=(2஺+4஺+32)BA/22+42+325.385(d)A%867Ḅᜳ90-cos-1(—B)=cos-1(———)=68.40AB38.077(e)A%3Ḅᜧ(A=M+d+&=7.071B=
B/B+B=5.385পAᙠ5<Ḅᢗ>-AJA6=(3Q+50-42)------(2஺+4஺+32)=2.61.13./©sßᙊ¯ᙶ᪗¨sᙠP(l7/2,2)./fA=2å+30,ᙠQ(2,æ3)./f8=-3஺+102*:(a)4+8*(b)A(c)A%567Ḅᜳ9஺@Açᣚᑮ¥9ᙶ᪗¨ACOSe-sin^90APAsin஺COS00Av(PA0014A-3x+2y-100-3B0003x+10£00110(a)A+B-2y+10£(b)A=9(c)A%867Ḅᜳ96=cos-1(2^)=cos-1(µ^-)=125.7°AB15.441.14ÓÔᙠᙊᳫᙶ᪗¨©¹(10,~/4,~/3)%Q(2,4/2,I)67ḄPᑮQ

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8@:V/=x—+y—+z—=3x2y2zx+2x3yzy+x3y2zdx,4E1.17᪗/fx,y,z
=xy+2z2ᙠú1û,1vüý=þ2+2åᔣḄ
ᓄ᳛஺vT++:yx+xy+4zz/=-,1=(xx-2y+z)y/x2+y2+l—2x+4zᔖ7x2+/+lᡠ(1,1,0=6ZO/5J1.18ᵫজ=£"+£#+£d,ᑭᵨᙊ*ᙶ᪗-./ᙶ᪗Ḅᐵ1234567Aᜐ;I&VO=p——+᜛-+--z---dppd(p^°?ᙠ./ᙶ᪗1AVজ=x——+y——+z——(1)X=pCGS(p(y=psin஺(2)ஹz=zP=^x2+y2y<(p-arctg—(3)xz=zx=Qcos஺O஺sin஺(4)y=/sine+0cos°(5)ᵫS2ஹS3TUVbp=COS^9(6)dx

9yd(p_x1y1.----r=O—sin஺(7)dx1+(2)2x+ypX(8)Sy1d(pxx1—----=—cos(p1+(-)2X+yPXᵫপ-(5)TVZ[\]ᐭ_`]জ=x——+y——+z——5ᦔ7,AA.ஹ]/`.Aஹ];ᐢ=(஻cos°-0sin(p)--+(/?sine+0cos᜛)——■+z-——dx,f&?gdp3জd(p60iao.——=----—+-----=——cos஺O-----Sin695dpdxd(pdxdppḄk=lm+nl=l5"+pq3᜛4dpdyd(pdydppd(prᵫ(6)-(9)TUV„,/;;.ஹ/212.ஹজ=(pcos^9-^sincp)(——cos஺-------sin(p)dppd(p+(]n”0c°se)(ᔩi"+'"cos஺)+2xdppd(pA=Qcos2°+yz3°-0"3{”-yl3|”dppd(pdppd(p+Qsin4+y}+@#cos°si”+cos°si”+2ᳮdppd(pdppd(pC`]~1]AVO=p——+(p-----+z——dppd(p1.19f(p,(p,z)=Pcos஺Ḅ஺rAD`1E473v7?F஽-0CGS(p_0£n(p

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11竺为=——sin஺r丽sin0菽rsin^丽_cos஺
rsin^丽&=0V(D=x—+y—+£^4(0জdr஺জS33জd(o-------+---------+-------)(rsin0cos(p+6cos0cos஺!°sin(p)drdxd0dxd(pdx+(-#--D---d-r-+-8--জ---5--0-+--8-জ---Q-(-o)(rsinOsino+3cos6sin(p+0cos°)drdydOdyd(pdy5^)Qr30Q0(50d(D+($%+$$+&')(/cose—Osin஺)dr&90dzd(pdz3জ=(——sincos(rsincos(p+0cos0cossin(p)dr+(——cos0cos(/))(ᡝsin᜛cos(p+0cos0cos9-0sincp)rdO150-(------------sin*)(rsincos(p-^-0cos0cos(p-(p^.(p)rsin஺d(p+D+(,—sinsincp)(Fsin6sin9+6cos6sin0+°cos(p)+(!_cos6sin°)(/sin6sin᜛+-cos6sin᜛+0cos(p)rS31a0+(------------cos(p)(rsin8sin9+6cos6sin0+°cos(p)rsin3d(pao+(——cos0)(rcos஺!3sin0)dr1.+(--------sin0)(rcos<9-^sin3)rdO/Mজ0=r——1+e”---&---+0-----1-------)-drrdOrsin஺d(p

121.21/(r,஺,஺)=/sinBcos᜛Ḅ஺?Vf=r—+0—+(p------—drr30rsin^d(p=r2rsin0cos(p+0rcos^cossin1.22Vp,Vr,Veb,ᐸA஽ᦪ஺?V7—Op-NP=PW=PᓽV7AC'VY=Y—=rdrN*=Rᓃ=rkekrdr1.23ᙠᙊᳫᙶ᪗1A2ᡝ(¡)¡(¡)=¢ᡝ2ᐸA஽ᦪ2£¤ᡝ(7)yr¥¦§ᔠ©ª/Ḅ«¬ᑖ®2ᓽᶭ°=0»I£¤?᪷³´ᡲ¶·¸ᳮ?-dl=j|VxF-JS/srrdrsin0q)Vy—VvkG_1deaVAriri—VAr—=0r2r2sin^drded(pk-)00¼ᡠ"5xF-dS=0is1.23£¤(1)V^=-^(TVO-OVT)½(2)VF(জ)=/(জ)Vজ஺v£¤?

13জOk+/¾জ7p¿জOkTdxT2dxdy-T2dyTdzT2ÀᵬÂ3[-d[`9;জ”35.STÃÄ—7{x—জ+y—জ+z—জ}---r{x——+V——+z——}*?2dxdydzT-dxdydz=J(+V(D—

144COS஺-sin஺0A,A2sin஺cos*0A.Ý001AVA=A“cos(p-Asin(pxvA=Asin(p+Acos(pypif>Sp=CGS(pdxd(p1.—=---sinedxpd(p1=—cos(pSyPc7dpdAd(p"ஹdpSAQ(pßV-A=---4----+—---—+—:---+--dpdxd(pdxdpdyd(pdy8I஺=cos(p—(Acos°-sin(p)---sin(p(A/cos°Osin(p)p+sin°⁐(A,sin°+Acosà+1cos9¾(4sin᜛+Acos᜛)+ádppd(p—Acos2(p-—Acossin^--sin^cos^—A,+-sin2dpdppd(ppIdA11aAi+-----sin-(p+—sin^cosq)A+—coscp------cossin(pApd(pppd(pp+sin>—>4+sin^cos^—+-cos^sin+-cosM,+—dpdppd(ppEa+&i%ädpppḄ᝕1/,,ஹ1Ð஺d\.-----(å)+-+--pdppḄ

15τ-n1o1ç(2)V-A=——(r2A)+--------—(sin^4J+r2drrrsin஺æ9rsindd(p5r-axar-=sin<9sin695y力一及种=-cosecos0raY=-cosOsin᜛r生e及竺2&ed(p_cos(pdyrsinOé஺AÔsinOcos஺cos0cos(pOsin°A,Aஹ.=sinOsin°cosgsin஺cos஺£cos஺Osin60A,n

16e+sinOsin0—(sinOsin+cos6sin@4஻+cos(pA)&]a+cos8sin°----(sin6siní,.+cos6sin(pA+cos(pA)0r30COS஺O/•`.4`AAஹ+---r----(sin᜛sin(pA+cosesin((A+cos(pA)rorsin®ᓾa+cos6—(cos0A-sin0A)redrsin஺3\.\ஹ--------(cos6A-sin0A)rer30-sin26cos2(p—A+sincoscos2(p—A-sin0cos(psin(p—Aredrdrdr22Øj33+sinOsirrcp-A+sin^cos^sin-cp—A+sinOsin0COSQ—ro&Sr+cos20—A-cos^sin^—r&dr+—(sin^cos^cos2(p—A+cos2^cos2cp—A-cos0cos(psin(p—A)rorSOdOSO+—(sin^cos^sin2(p—A4-cos2Osin?(p—A+cos0sincpcoscp—A)rer303030--(sincos0—A-sin20—A)rer3030+—(cos2^cos2(pA-sin^cos^cos2ᜐ®)rr+—(cos2᜛sin20A-sincossin2(pA)r0r19ᓝO(sirr0Ar+sinBcosò)rτ33+-----(-sin®sin°cos0——A-cos^sin^cos^——A+sin2(p——A)rorsingd(pd(pd(p+——(sin8sin(pcos(p—A,+cos0sin(pcos(p—A+cos2(p—A)0rsingd(pd(pd(p1d------(sin6sin2M+cossin2(pA+sin᜛coscpA^)ersin®1d------(sincos2(pA+cos^cos2(pA-sin^9cos(pA^r0rsin஺32sin஺3cos<91b—(4)+—4+--------(An)+-----An+---------drrrsin3^0rsinOrsindd(p=p(/4)+/•ZMஹ13Arorrsin஺69…)+wô

171.26õö÷ᑡḄᦣa)F=yzx+zyy+xzz>—';;b)F=p+p(pF=22+rcos06+r(p:cFcd.xa)V•F=--4---+--=z+ᐗûücU1Ø,Ôஹ1᜜e/1b)VF=----(pF)H-------4----=OpdppḄEp•ᡝ=ÿ2(5)+^—(sin/)+1ᔲ=±-sine+^~^c)r~drrsin^ddrsin^d(prsing1.27ᦣ•(஻),VI,V•()ᐸ"#$%&'஺):.(,)-)=2Pdp-15,Vr=VF=——(r2r)=3r2&M)=k•VJr=k-ekr\^(k-r)=k'=kᓲজ9"1U/=\1.28ᵫজ-:--------;--------7267\72জ7¥(P¥)+P2?2):஻জI?জPজ=-----------------7SO_9dজ+d(p3জeজ.12cos᜛----sine-----dxdxdpdxd(pdppd(p3জdp3জdcp3জ.3জ1d^>——=----+=1——=Sin69——+COS0-----dydydpdyd(pdppd(pa2od.isao.12ஹzw——=(cos஺sin°----)(cos°----sme-----)dxdppd(pdppd(p

182a?জa1sজஹ.1dsজஹz=cos(p——-sin࠷os᜛S(-----)-sin°-----(cos஺——)dp~dppd(ppd(pdp.ia,•TDஹ+sin^——(sin^—)pd(pd(pa20.d13஺জ18জஹz——=(sin஺S+cos9----)(sin°——+cos0-----)dydppd(pdppd(pVজ51a(D13,.ZD\x=sin~cp——7+sin0cos°——(----)+cos°-----(sin஺——)dpdppd(ppd(pdp1d,50ஹ+COS(P--——(cos(P——)pd(pd(pv72T23]জ.e/aজஹ.ie/^"জ=coscp——--sin^cos^?——(----)-sin^-----(cos஺——)dp~dppd(ppd(pdp.1d.3জஹ+sin^——z(sin^—)p~d(pd(p.a2o.8/iao)ஹ1s/.soஹ2+sin-9——-+sm°cos(p——(----)+cos᜛------(sincp——)6p~dppd(ppdtpdp+COS(P--——(cos(P——)pd(pd(p`+siMjcSsiniJ"+si”cosHfdppdppd(pdpp~d(p.21d2a>+sm-P'6621dজ1520)13জ21a?জ+cos(p-----+cos^sin^---------cos^sin^—j——+cos~(p—r-——r-pdppd(pdpp-dtpp~d(p~d?জ1501a2(D1d,?ஹ1ᕒজ=-7+-----+r—r=----(p——)+—r——5~dp~pdpp~d(p~pdpSpp-d(p~1.29ija)f(r)=x2zb)f(r)=pc)f(r)=rlmn)o

19Iᡭr/a)v2/==2zA242஽2b)v◤*ᓝ/MJB,1{27ஹ13,.kᨵஹ12c)V-/=-7—(^—)+-;-------(sm6>^-)+———------r~drdrᔆsin6dOr'sin'03(p~r1.30l&'Fpp+mp+zzcᵫ᜛W1,0<^?<>r,0

20<]A-dixz2d_1.31ᵫ(VxA>£=]jm^-----67VxA玄ASTOASdx.4A,):1)¤¥=2/$¦§$¨)©AzḄ"ªᙠ(x,y,z)Ḅ¬®¯r--5AQAaAdl=-AA-(Aஹ,+-^Az)Ay+(AS+--Ay)Az+/dzdya4dAV----AzAyH-AyAzdz-------dyjA-dl/S°+±As&dy2)¤²=9,/$¦§$Ax©Ḅ"ªᙠ(x,y,z)Ḅ¬®¯l-dAdAqA-cll=-AAx-(A_+--Ax)Az+(A+--Az)Ax+A.Az/zdxdz8A.dA------A^xAz+-x-AzArdx-----dzSA-dl1dA.dA-________==______i__|_____L.¨sdxdz3)¤¥=\/$¦§$Ax©AyḄ"ªᙠ(x,y,z)Ḅ¬®¯³--5A3AV(\A'dl=-Aஹ.Ay—(4+--Ay)Ar+(A+--Ax)Ay+V;dydx--Ax+AxAydydx(SA-dT2==´+µAsdydx¶·D73◍’04ஹrSA6AdAdAxA=x(-----•-+-+y(---L+-V-)+z(------x-+-v-)dzdydxdzdydx

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