冯恩信电磁场与电磁波课后习题答案2

《冯恩信电磁场与电磁波课后习题答案2》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

⚪1.1X=2£+3-2=2+22,:(a)A5Ḅᜧ()(b)A5Ḅᓫ!"#$c&AB■,$d&Nxᨴ$e&43-.Ḅᜳ0$f&Aᙠ53Ḅᢗ5஺78$a&A5ḄᜧA=|A|=JA8+A+4=722+32+12=V14=3.74B=|fi|=+Bj+B=712+12+22=76=2.45$b&A8Ḅᓫ!"#21^=-=—$2x+3D=0.535%+0.8029-0.2672B1/?=-=I$9+-22&=0.408%+0.408$-0.8162$c&A8A-B=AB+AB+A.B„=2+3+2=7VVyy$d&AxBAAxyz,VyzAxB=AxA,A823-1=—5£+3>2B,BஹB1-2(e)A5-.Ḅᜳ0a᪷MNᨴ=ABcosaQAB7cosa==0.764a=40.19°AB9.163(f)Aᙠ33Ḅᢗ5AB7A-b==2.86B2451.2᝞T"#AஹBCᙠWX☢Z[\A•(5*0=0஺[\8_"#Aஹ5CᡠᙠX☢abX☢A=Ax+AyxyB=Bx+ByxyC=Cx+Cyxy

1xyzExW=B*BB=(BC-BC)x+(BC-BC)y+(BC-BCyzyzyzzyzxxzxyyxCCCxy:=(BC-BC)zxyyxA(BxC)=0xBC)”2=01.34=£cosa+fsinaஹ5=_icoscfsin/?C=£cos=+(sinZ,[\def"#ghᓫ!"#Zief"#hᐳ☢Ḅ஺[\81)ef"#ghᓫ!"#A=k=++A8=Vcos2a+sin2a=18=k=+8+B=7cos2^+sin2/7=1C=W=+C+C=7cos2/?+sin2/7=12)ef"#hᐳ☢ḄxyzBxC-BBB.=2cos᜛sin/xyC*CCyzA-(5xC)=0x2cos/?sinm•2=01.4A=x+2y-zxB=ax+y-3znX_LoZa஺78n,ZpqZN=0A-B=a+2+3=0ᡠra--51.5[\ef"#4=5£-5$ஹB=3x-7y-z^C=2£-2$-2sᡂfe0sḄeᩩvZwᑭᵨ"z{e0sḄ☢z஺[\8|aA-B=2x+2y+zA+(-B)+C=0ᡠref"#Aஹ3Csᡂfe0s{e0sḄ☢za

2Ay1--0=222S=AxB-5A/5+5+20/2=10.62-71.6P~Q~Ḅ!"#ᑖa53+129+222—39+2,P~ᑮQ~Ḅ"#ᐸ஺78P~ᑮQ~Ḅ"#aR=r-r=(2x-3y+z)-(5x+l2y+z)=-3x-15yQpP~ᑮQ~Ḅa-=k=+&=15.31.7"#A=41—39+25=2£+$—?gḄᓫ!"#஺78_"#C"#A=4£—3?+23=22+$-2gZᑣA-C^4C-3C+C.=0(1)XVd=2Cr+Cy-C=0(2)(1)+(2)Q6C,-2Cஹ.=0—>C-3C(3)yx(1)+3x(2)Q10C-=0.G=5C,.(4)᝞T"#6hᓫ!"#ZᑣC=++=+925C=1ᡠrC,=-,==0.16971+9+25C=3C,=0.507xC=5cx=0.845:C=0.169x+0.507y+0.845£1.80ᙶ᪗Ḅ"#E(x,y,z)=x,F(x,y,z)=ᑖᵨᙊ£ᙊᳫᙶ᪗Ḅ2ᙶ᪗ᑖ#⊤¦஺78ᙠᙊ£ᙶ᪗

3cos஺si”o-cos஺si”o-Tcos஺=-sin0cos஺0=-sin0cos஺00=-sin^9001§00100ᡝi(p,(p,z)=cos¨sin(p(p*COS0sin஺o-cos஺sin஺o-~Q'sin஺%—-sin(pCOS00©sin஺cos஺01=cos஺[0|_00014010_F(p,

4cos஺sin஺022cos᜛%sin஺cos0002si”00100E(x,y,z)=2cos¯+2sing9(2)F](x,y,z)=2Q=-/,"(xx+yy)F(X,y,z)=-3sin°+3cos
2ᑭᵨ(2)±²Q3«(x,y,z)=3஺=-,³(x?-yx)Jx+y1.10ᙊᳫᙶ᪗Ḅ"#£஺,´᜛&=5ᡝ,£஺,´᜛&=6ᵨ0ᙶ᪗Ḅᙶ᪗ᑖ#⊤¦஺78᪷MsinOcos஺cosOcose-sine%Ay=sinOsin᜛cosOsin᜛cos஺%(1)4_cos஺sin஺0J4Q>,/sinBcos஺cos®cos°-sin^9R5sin஺cos°=sinOsin஺cosOsin/cos஺0=5sinOsin஺A.COS0sin஺005cos஺ᡝi(x,y,z)=x5sin6cos᜛+f5sin6sinQ+25cos6

5x=rsinOcose¸|a=(3+2)2+(5+4)0+(-4+3)2=5Ç+90-9¼AA¼PsZP(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)A8-.Ḅᜳ00-cos-1(—B)=cos-1(———)=68.40AB38.077(e)A3ḄᜧA=M+d+&=7.071B=
B/B+B=5.385পAᙠ53Ḅᢗ5-AJA6=(3Q+50-42)------(2஺+4஺+32)=2.61.13"#ZÐᙊ£ᙶ᪗Zᙠ~P(l7/2,2)"#aA=2Õ+30,ᙠ~Q(2,Ö3)"#a8=-3஺+102:(a)4+8(b)A(c)A5-.Ḅᜳ0஺78×ᣚᑮ0ᙶ᪗ACOSe-sin^90APAsin஺COS00Av(PA0014A-3x+2y-100-3B0003x+10£00110(a)A+B-2y+10£(b)A=9(c)A8-.Ḅᜳ06=cos-1(2^)=cos-1(©^-)=125.7°AB15.441.14ÅÆᙠᙊᳫᙶ᪗~¬(10,Ç/4,Ç/3)Q(2,4/2,I)-.ḄP~ᑮQ

7~Ḅ"#஺78᪷Mᙊᳫᙶ᪗0ᙶ᪗Ḅᐵx=rsin^cos^

87:V/=x—+y—+z—=3x2y2zx+2x3yzy+x3y2zdx,4E1.17᪗#fx,y,z
=xy+2z2ᙠ~$1ì,1&íî=I2+2ÕᔣḄðᓄ᳛஺vT+ô+õ7:yx+xy+4zz/=-,1=(xx-2y+z)y/x2+y2+l—2x+4zᔖ7x2+/+lᡠr(1,1,0=6ZO/5J&1.18ᵫ÷জ=£ù+£ú+£d,ᑭᵨᙊ£ᙶ᪗0ᙶ᪗ḄᐵZûüýþÿAᜐI&VO=p——+᜛-+--z---dppd(p^°ᙠᙶ᪗Vজ=x——+y——+z——(1)X=pCGS(p(y=psin஺(2)ஹz=zP=^x2+y2y<(p-arctg—(3)xz=zx=Qcos஺(஺sin஺(4)y=/sine+0cos°(5)ᵫ021ஹ031234bp=COS^9(6)dx

9yd(px1y1.----r=(—sin஺(7)dx1+(6)2x+ypX(8)Sy1d(pxx1—----=—cos(p1+(-)2X+yPXᵫপ-(5)24<=>?ᐭAB?Cজ=x——+y——+z——DᦔF,5A.ஹ?/B.5ஹ?ᐢ=(஻cos°-0sin(p)--+(/?sine+0cos᜛)——■+z-——dx,K&Ldp3জd(p60iao.——=----—+-----=——cos஺(-----Sin69Ddpdxd(pdxdppḄP=QR+SQ=Q5"+UV3᜛4dpdyd(pdydppd(pWᵫ(6)-(9)234„,/.ஹ/212.ஹCজ=(pcos^9-^sincp)(——cos஺-------sin(p)dppd(p+(?n”0c°se)(ᔩi"+'"cos஺)+2^dppd(pA=Q_cos2°+`a3°-0"3b”-`Q3c”dppd(pdppd(p+Q_sin4+`d+@fcos°si”+g_cos°si”+2ᳮdppd(pdppd(p7B?~1?5jVO=p——+(p-----+z——dppd(pk1.19lf(p,(p,z)=Pcos஺Ḅop஺r59B1:473v7;஽-0CGS(p_0£n(p

101.20ᵫCজ=£ᚪ+ft+ut6ᑭᵨᙊᳫᙶ᪗zᙶ᪗Ḅᐵ6|}ḄA᝕~)1~)1H)VO=r—+^-—+(p------------drrd0rsin6:x=rsinBcos஺vyrsinOsin/z=rcosdzy(P=arctg—xx=rsincos(p+0cos0cos(p-(psAn(py=ᡝsinOsin*+AcosOsin°+0cos°2=/cos6(3sin஺_50drdO3জd(pSx,drdxdOdxd(pdxᓾ50dr3জdO3জd(p—=-----1-------1------ᔊdrdy83dyd(pdydrdO5Qd(p—=-----1-------1------EdrdzdOdzd(pdzSr.—=sinecos஺dx5r-=sinsin^5r一=cos6a7a^5xM=—COSCOS^9r¥--cosOsin/r

11dO1.=-sin᜛dzr丝sin(p&rsin஺丽cos^9ঝrsin஺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)rdOC/জ0=r——1+e”---&---+0-----1-------)-drrdOrsin஺d(p

121.21l/(r,஺,஺)=/sinBcos᜛Ḅop஺Vf=r—+0—+(p------—drr30rsin^d(p=r2rsin0cos(p+0rcos^cossin1.22lopVp,Vr,Veb,ᐸ஽ᦪ஺V7—Op-NP=PW=PᓽV757'VY=Y—=rdrN*=Iᓃ=rkekrdr1.23ᙠᙊᳫᙶ᪗6ᡝ()()=ᡝ6ᐸ஽ᦪ6ᡝ(7)`rᔠ/Ḅᑖ¡6ᓽᶭ£=0»I᪷¦§ᡲ©ª«ᳮ-dl=j|VxF-JS/srrdrsin0q)Vy—VvkG_1deaVAriri—VAr—=0r2r2sin^drded(pk-)00°ᡠ_"5xF-dS=0is1.23(1)V^=-^(TVO-OVT)³(2)VF(জ)=/(জ)Vজ஺v

13জ(P+/´জ7Uµজ(PTdxT2dxdy-T2dyTdzT2¶ᵬ¸3=-d=B9জ”35.STº»—7{x—জ+y—জ+z—জ}---r{x——+V——+z——}*?2dxdydzT-dxdydz=J(+V(D—

144COS஺-sin஺0A,A6sin஺cos*0A.×001A4A=A“cos(p-Asin(pxvA=Asin(p+Acos(pypif>Sp=CGS(pdxd(p1.—=---sinedxpd(p1=—cos(pSyPc7_dpdAd(p"ஹdpSAQ(pÙV-A=---4----+—---—+—:---+--dpdxd(pdxdpdyd(pdy8I஺=cos(p—(Acos°-sin(p)---sin(p(A/cos°(sin(p)p+sin°⁐(A,sin°+AcosÚ+1cos9´(4sin᜛+Acos᜛)+Ûdppd(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%ÞdpppḄ᝕1/,,ஹ1Ê஺d\.-----(ß)+-+--pdppḄ

15τ-n1o1á(2)V-A=——(r2A)+--------—(sin^4J+r2drrrsin஺à9rsindd(p5r-axar-=sin<9sin695y力一及种=-cosecos0raY=-cosOsin᜛r生e及竺2&ed(p_cos(pdyrsinOã஺AÎsinOcos஺cos0cos(p(sin°A,Aஹ.=sinOsin°cosgsin஺cos஺£cos஺(sin60A,S

16e+sin6sin0(sin஺sin(pA+cosOsin(pA+cos(pA)r0&]a+cos8sin°----(sin6sinç,.+cos6sin(pA+cos(pA)0r30COS஺O/•B.4BAAஹ+---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—Aredrdrdr22Òj33+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)r0r19ᓝ((sirr0Ar+sinBcosì)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<91\—(4)+—4+--------(An)+-----An+---------drrrsin3^0rsinOrsindd(p=U(/4)+/•ZMஹ13Arorrsin஺69…)+wî

171.26ïðñᑡḄᦣpa)F=yzx+zyy+xzz>—'b)F=p+p(pF=22+rcos06+r(p:cF]^.xa)V•F=--4---+--=z+ᐗõökcU1Ò,Îஹ1᜜_1b)VF=----(pF)H-------4----=(pdppḄEpC•ᡝ=ù2(ú5)+^—û(sin/)+1ᔲ=±-sine+^~^c)r~drrsin^ddrsin^d(prsing1.27ïðᦣpC•(஻),VI,V•(þÿ)
ᐸ஺:.())=2Pdp-15,Vr=VF=——(r2r)=3r2&C)=k•VJr=k-ekr\^(k-r)=k'=kᓲজ%1U/*\1.28ᵫজ-&--------'--------72"#\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?জa
1sজஹ.1dsজஹz=cos(p,-sin^cos᜛()-sin°(cos஺)dp~dppd(ppd(pdp.ia,•EDஹ+sm஺(sin஺)pd(pd(pa20.d13஺জ18জஹz——=(sin஺G+cos9----)(sin°——+cos0-----)dydppd(pdppd(pHজ51a(D13,.MD\x=sin~cp——7+sin0cos°——(----)+cos°-----(sin஺——)dpdppd(ppd(pdp1d,50ஹ+COS(P--——(cos(P——)pd(pd(pv72T23Pজ.e/aজஹ.ie/Q"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(pS+siMjVGsiniJ"+si”cosHYdppdppd(pdpp~d(p.21d2a>+sm-P'6621dজ1520)13জ21a?জ+cos(p-----+cos^sin^---------cos^sin^—d——+cos~(p—r-——r-pdppd(pdpp-dtpp~d(p~d?জ1501a2(D1d,,ஹ1ᕒজ=-[+-----+r—r=----(p——)+—r——5~dp~pdpp~d(p~pdpSpp-d(p~1.29]^a)f(r)=x2zb)f(r)=pc)f(r)=r`abc

19Iᡭf/a)v2/==2zA242஽2b)j◤*ᓝ/MJB,1o
27ஹ13,.eᨵஹ12c)V-/=-7—(^—)+-;-------(sm6>^-)+———------r~drdrᔆsin6sdOr'sin'03(p~r1.30`uFpp+gp+zzvVᵫ᜛W1,0<^?<>r,0

20<]A.dixz2d_1.31ᵫ(VxA>£=]jm^-----"#VxA玄ASTOASdx.4A,:1)=2
/)
AzḄ
ᙠ(x,y,z)Ḅ¡¢£¤r--5AQAaAdl=-AA-(Aஹ,+-^Az)Ay+(AG+--Ay)Az+/dzdya4dA--VAzAyH-AyAzdz-------dyjA-dl/G¥+¦As&dy2)§=9,/AxḄ
ᙠ(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)=\/AxAyḄ
ᙠ(x,y,z)Ḅ¡¢£¤¨--5A3AV(\A'dl=-Aஹ.Ay—(4+--Ay)Ar+(A+--Ax)Ay+V;dydx--Ax+AxAydydx(SA-dT2==©+ªAsdydx«¬DxA7=x3(---◍--•’-+-04ஹ+ry(--S-AL+6-AV-)+z(---d-A--x-+d-Av-)dzdydxdzdydx

21戈

22左2((z人X。dg旦V-2XA=今笈-4女--2a4&y0-XA-(VxA)=(yx-xy)-(-2£)=0µ¶·¸
¹H=A(x,y)x+A,(x,y)ys<<(-Esin6))0rorrsin0c>92Ecos32£cos^----0---------------0-------=0Frsin▬d1JdVxE=/singE3gprᔆsinØQ

23rrersin0(p1add/sin஺draed(pEcos0-rEsin00o0Ú@(-£sin஺+4sin6)=00r1.37ÂÃx(জM)=OVxA+VOxAo:

24Jû’—lm4JvJ(x-x')2+(y-y,)2+(z-z')2j_24rᡠY-1rF(r)=-VO(r)=-V(--)=~~~-4m-4k1.39]^-R=0,VxR=M(x)b(y)b(z),°±Fc᪷îïðñᐻzᳮF(F)=-VO)(r)+VxA(r)ᐸজô4᮱|r-r'|g£ேy┳-dV
V•=0,জ=0Vxᨴ=23(x)b(y)b(z)1fffV'xF(r'))=-111-iz~i~'-dV'4!J,J|r-rI1%&'dx,dy'dl4%-x')2+(y-y')2+(z-z')2II)=z---=----(Pcos஺-3sin஺)4041ᡠ3F(r)=VxA(r)rrdrsin0(p1ddr2sin<9dr304rAe03ndAsin஺)-(------)=---(PrdrdO4"

25829:⚪2-1.=>?@AᨵCDEᵯ₹%=1C,%=2CI/=4CI«4=8CIᑖNO(1,0,0)I(0,1,0),(-1,0,0,),(0,-1,0)E,P(0,0,1)EḄᵯRST஺UV=-X+Z',R=-y+z',R=X+Z',R=y+z2}4E=1{A[+qq+᜛4ᑍ)_3f+6)+15241%R\R2RR4ᐔst2-2.=>_ᵯ₹`T
qḄᙳᒴ_ᵯ₹dᡂ᝞gᡠhḄijklIPPEḄᵯRST஺P⚪2-2gUV(a)ᵫoឋᨴ=E+r2+s+t=஺(b)ᵫoឋ2=E+u2+v=0(c)wxᙶ᪗{᝞gᡠhI|ᩩ~▲_ᵯ₹ḄᵯR
t=t+t=Vj(-)}=-47r%aLTte^a~
aḄ~ᙊ_ᵯ₹ḄᵯR
ᵯR
£=t+t=02-3.?@A▲Ḅ~
aḄ~ᙊᵯ₹`T
᜛ஹIP_ḄᵯRST஺U:ᙠ▲Ḅ~ᙊT
஺4᜛ḄᩩIᩩ▲Ḅ_ᵯ₹Iᵯ₹_`T
=Rad஺,8ᑖ,?@A▲Ḅ~
aḄ~ᙊᙠ_ḄᵯRST
y

26⚪2-3g⚪2—4g2-4.?@A▲ḄT
aḄᵯ₹`T
P@¡EḄᵯRST஺UVᙠX,ᜐT
Ḅ▲ᩩIᡂ▲Ḅ_ᵯ₹Iᵯ₹_`T
p,=p.dx,,ᙠE(x,y)ᜐḄᵯR
I-ஹ1ppdx'dE(x,y)=--"ߟ2ᑍPᐸA஺="¤+¥0=¦2yl(x-x')2+y2x'ᑖ▲ḄT
aḄḄᵯ₹ᙠE(x,y)ᜐḄᵯR
Ps"jU-x')x+yy.§(x,y)4%.'(x-xT+V-c/x+a/2x-a/2ஹஹ+y2{arctg-------------arctg-----------)}yy2-5.=>?@Aᵯ₹ᑖ¨
r2,raPs-b,r-ar
REᑮᙶ᪗ªEḄ«¬Ia,b
ᦪ஺PᵯRST஺UVᵫᵯ₹ᑖ¨ᐹᨵᳫoឋIᵯRᑖ¨±ᐹᨵᳫoឋI¡~
rḄᳫ☢Iᑭᵨµ¶·ᳮs‘0¹º»
<^EdS=47ir2Ers~
rḄᳫ☢ᑁḄᵯ½
4-\ra5IᵯRST

277~TA"a5sanE=r+5ba22-6.ᙠᙊ¾ᙶ᪗{Aᵯ₹ᑖ¨
~\rar
REᑮzḄ«¬Ia
ᦪ஺PᵯRST஺UVᵫᵯ₹ᑖ¨ᐹᨵoឋIᵯRᑖ¨±ᐹᨵoឋI¡~
r,ᓫOTḄᙊ¾☢Iᑭᵨµ¶·ᳮsD஺¹º»
ᑮ2.À=27irE,.~
rஹµ
1Ḅᙊ¾☢ᑁḄᵯ½
2ÁÂ----;raI3IᵯRST
r2----;ra2-7.ᙠ&Åᙶ᪗{Aᵯ₹ᑖ¨
p(.x,y,z)=<0;|x|>aPᵯRST஺UVᵫᵯ₹ᑖ¨ᐹᨵ☢oឋ,ᵯRᑖ¨±ᐹᨵ☢oឋI¡oḄÆkÇÈ☢,ᑭᵨµ¶·ᳮIÉÊ☢
SḄᵯ˽
Eஹ2sIÆkÇÈ☢ᑁḄᵯ½
2xS/?oNaIᵯRST

28-Ñ|<஺E=\£°x4x>a2-8.ᙠ&Åᙶ᪗{Aᵯ₹ᑖ¨
)…)=3\x[,\x\ு<஺aPᵯRST஺⚪2—8gUVᵫᵯ₹ᑖ¨ᐹᨵ☢oឋIᵯRᑖ¨±ᐹᨵ☢oឋI¡oḄÆkÇÈ☢,ᑭᵨµ¶·ᳮIÉÊ☢
SḄᵯ˽
Ô2S,ÆkÇÈ⊈ᑁḄᵯ½
XXx2S;|x|aooIᵯRST
x2X2-----;0

29ᡠ3I@ῚAßEḄᵯR
£=t+t=ᱏ.¡Âë=ìC
íᳫÜᢣᔣ@ῚAÜḄð½஺2-10.=>ᵯRᑖ¨
—x'-b/2b/2-x;xb/22-11.=>ᙠᙊ¾ᙶ᪗AIᵯRᑖ¨
Cr£=ᐸAC
ᦪ஺Pᵯ₹ᑖ¨஺0,,rbUVᵫñ♦uØ᜛/%,ᙠV•E=V-(——)=0(ᙠᙊ¾ᙶ᪗{)rᙠV-E=0/?=0ᙠ=2,r=bᨵ☢ᵯ₹.ᵯ₹☢`T
sC/a;r-aQP,=2=£

30(h-d)\rPᵯ₹ᑖ¨஺U:ᵫ஺জØ¡᜛//óᵯ₹`T᜛=¡£0ᔆ2জ(b-a);rZ?P÷ø÷¶ùúV2@=o᜛=0ü☢ýúua,r=bḄᑖÿ☢
Ḅ☢ᵯ₹஺_50E=-V(D=-r—dr'0;r/?£,Jo!a\r=a☢ᵯ₹Ps=D=%£'“=(n—£a/b,,r=bo2-13.ᑖ!"#$%ᙊ$ᙳᒴ)ᵯ₹ᙠ+)
Ḅᵯ,஺A.4kldlL(a)(b)23(a)#$ᙳᒴ)ᵯ₹ᙠ+)
Ḅᵯ,#$4ᩩ6ᙳᒴ)ᵯ₹Ḅᵯ,জ3)89:=/-In'J2+(1)2+L/24=4J2+(1)2-L/2

31ᐸDJ2=2+(L/2)2Z#$ᙳᒴ)ᵯ₹ᙠ+)
Ḅᵯ,E7z2+L2/2+L/2জ(z)=~^TnJ4ylz2+1}/2-L/2LbMᙊ$ᙳᒴ)ᵯ₹ᙠ+)
Ḅᵯ,জব=AO=ߟ"4R஺0J.2+2sJ.2+12o2-14.!"⚪2-5TUḄᵯ₹ᑖVḄᵯ,஺23⚪2-5TIIIḄᵯ₹ᑖVḄᵯWEfr37~TYra/+5a2O(r)=J5c5%r_`r

321lr\-f11,~*ri??,rrR2rr1ly3*1l~*nr1—a-[1----:-]5-a—[1-1--------]K,rrR4rrজE47r%&RRR234qqa(x+y)-ryy2+4-~]-r=4fr22ᐔ—^—rsin6(cos(p+sincp)24c*216.ᵯWE£=3x+4y-5£,q(0,0,0)j(1,2)Ḅᵯ஺⚪2—16b23V=জ(a)-জ(஺)=j£-dlaba213a(0,0,0)ᑮ6(1,2,1)Ḅ//|(0,0,0)ᑮ(1,0,0)-+/2(1>0,0)ᑮ(1,2,0)-+&(1,2,0)U(1,2,1)121V=\E-dl=++^Edl=J3a+_J5dz=6baI/1l/0002322E=-Vজজ=-(3x+4y-5z)V=0(0,0,0)-

33_32-17.ᙠᳫᙶ᪗DᵯWE=^ᡝ]qL]᜛JjL6,%,MḄᵯ஺ᔆ23ᑮL,஺2,᜛2MḄ/11L஺©]91MᑮL“]஺]஺2M+4L஻,஺1]᜛2MᑮL஺,஺2,82M+/3L஺,£]02MᑮS]£]᜛2Mv=•/=,§•/=Jh127322-18.ᙠᙊ¨ᙶ᪗DᵯWEE=-p,qLa,@,0Mj3,°2]°MḄᵯ஺23La,%,0Mᑮgb,gp,0M/]La,0,0MᑮL6,gpஹ,0M+஺3,gP,0Mᑮ2xLª᜜,0M2-19.¬Ea,ELḄᙊ¨®¯°ᙳᒴ᩽ᓄ]᩽ᓄ#ᔣE+ᔣ]᩽ᓄEᡝ=³£L³E´ᦪM஺q®¯DḄ¶·ᵯ₹஺23L1M®¯DḄ¶·ᵯ₹¸E“=-V•ᡝ=0L2M®¯⊤☢Ḅ¶·ᵯ₹☢E᜛=ᡝᙠᙊ¨®¯°Ḅº☢
¶·ᵯ₹☢E»;ᙠ
¼½☢
¶·ᵯ₹☢ᑖE஺1=¾j.2-20.q
⚪DḄ¶·ᵯ₹ᙠ+)
¿ÀḄᵯW஺23
¼½☢
¶·ᵯ₹¿ÀḄᵯWᵫÁ⚪]ᙊÂ$ᵯ₹¿ÀḄᵯWEᒹ(1-)Yz'>0Ä(z')=ÅDaEᙊ¬._
ÅÆÇᣚ,z'=z-L/2,£=j,É
½☢
¶·ᵯ₹¿ÀḄᵯWE

34஺(1z-L/2—U/---------=\,Z>L/2<247(-L/2)2+a2ZEz\(z)=_Ì(]+z-L/2\,Z-LU<2%J(Z+—/2)2+a2ᓃ2Ð)=Z+L/2■)-z<-L/22+a2
¼½☢
¶·ᵯ₹¿ÀḄÑᵯWE4z+L/2Z-L/2]Yz>L/22%J(z+L/2)+/7(-£/2)2+Q~Z%2+}L/2z-L/2E=];-L/2

352-23.ã▲Ḅ)ᵯ₹,`®ᵯ´ᦪE£Ḅᙳᒴ®¯D])ᵯ₹0E´ᦪ]q®¯DḄᵯW஺23åã▲Ḅ)ᵯ₹æz+çn]ᑭᵨêë[ᳮ]ì᧕qᮯDḄᵯWEE=
îpEWᑮ)ᵯ₹Ḅïð.a2718P2-24.¬EaḄᙳᒴÝᵯᳫñ]ᵯ₹☢£E´ᦪ]᜜ᒹzòóEdஹ®ᵯ´ᦪE£Ḅ®¯]q®¯ᑁ᜜ḄᵯW஺2:ᵫ`ᵯ₹j®¯ᑖVᐹᨵᳫ_÷ឋ]¬ErḄᳫ☢]ùᵨêë[ᳮ
Åúûü6ᑖE4ý4᝞”,2ᵫr஺=ᡠ....-A6Za+d2-25.ᳫᑖaஹb,!"#Ḅ"ᵯ&ᦪ£,ᑁஹ᜜ᳫᵯ+ᑖV,0஺.ᳫ!Ḅᵯ/0ᳫ☢2Ḅᵯ₹☢45஺678ᑁ9ᵯ₹qᵫ;ᵯ₹<"#ᑖ=ᐹᨵᳫ@AឋCrḄᳫ☢EᵨGHIᳮᳫ!Ḅᵯ/4Lᡭᳫ!ḄᵯNOP4QV1ᡠE,1~T77ab

36ᳫ☢2Ḅᵯ₹☢45sV10஺=")=஺"(ᔆ=஺)=/(r=஺)=..,aab£/1=b)=D(r=b)=sE(r=/?)=--~nrab2-26ᳫᑖaஹb,!ᨵX"#"ᵯ&ᦪ£|ஹ£,"2#Z☢c,ᑁ᜜ᳫᵯ+ᑖ1,0஺.ᳫ!Ḅᵯ/0ᳫ☢2Ḅᵯ₹☢45["#ᑖZ☢2Ḅ\]ᵯ₹☢45஺678ᑁ9ᵯ₹qᵫ;ᵯ₹<"#ᑖ=ᐹᨵᳫ@AឋCrḄᳫ☢EᵨGHIᳮ^=_0ᳫ!Ḅᵯ/q--------\a

37᜛',(r=c)=/(E,(r=c+)—<(r=c_))2-27ᙊmnᵯoᘤᑁ᜜ᑖaஹb,!"#Ḅ"ᵯ&ᦪ£,"#Ḅqr/s.ᵯoᘤḄὊN஺678ᙊmnᵯoᘤu5L,ᑁᵯvq,ᑭᵨGHIᳮ^E.x—^—27T£rLbiᑁ᜜!ḄᵯNV=f—Jr=-^-ln-J27i£Lr2TTSLa__=x2ᐔEL1bInaᡠᵯ/^⊤ᔆV1E--------,bln-raᑁ⊤☢Ḅᵯ/£=abᡠV=aE

38-aaஹb᝞"#Ḅqr/sᑣᵯoᘤḄὊNV=aE

39-ba2-28_ᑁ᜜ᑖaஹbḄ"#ᳫ"ᵯ&ᦪ£,ᙠᳫ_ᵯvqḄᵯ₹஺1ᵨ"#ḄGHIᳮ.ᵯ/s52."#Ḅ᩽ᓄs50\]ᵯ₹஺671ᵫ⚪ᵯ/ᐹᨵᳫ@A᪀஺EᵨGHIᳮ"6=<7,ᙠrḄᳫ☢2ᵫ=

40q-------;rh7<=qj—

41D=D.=஺`=2%,ᓽE=/sE.=//232Z23ᡠE=3x+2e/sz.2t2Ì=3£+2j/q?2-31.aḄᳫᨵÚᙳbḄᳫnῚ,ᙠᐸ_ÚῚᨵ_ÚᵯvqḄᵯ₹ᙠÝᳫnῚ᝞Þᡠ᝞ᳫ2Ḅßᵯv0,.ᳫῚ[ᳫ᜜Ḅᵯ/s5஺671ᙠᨵᵯ₹ḄῚᵫ;@Aឋᵯ/s5=,RáῚᢣ44ᔣÝῚ/Ḅ+äåv஺2ᙠæ_çᨵᵯ₹ḄῚ;☟ᵯéêÝῚḄᵯ/s5ë஺3ᙠᳫ᜜ᵫ;ᳫì+◀îᳫ☢2᜜ᳫ᜜çᨵᵯ₹ᳫ᜜ᵯ/ᐹᨵᳫ@Aឋ·ᳫ2Ḅᵯvq,ᡠᳫ᜜Ḅᵯ/s5E=—rᳫᑮ/Ḅðñ஺r4ò/2-32.óᙊmnᵯoᘤᑁ᜜ᑖaஹb,!_ôᐙ"ᵯ&ᦪöḄ"#æ_ôᐙ"ᵯ&ᦪJḄ"#஺÷ᵯNVø.ᵯoᘤḄᵯ/0ᵯ₹ᑖ=஺678óᵯoᘤu5/ᑁ`_Ḅᵯvq,ᙠᑁ᜜!CrḄᙊm☢ᑭᵨGHIᳮᚆ.dM=qSᙠÚm☢2ᵯ/s5ᑖüì2ýþL/£ÿᱏ,+£E
=q22rᵫᩩE”=E=E,2rr

42=——জ——+£,r2b,ᑁ᜜Ḅᵯ!"V=\Erdr=-------------In—I24&+£2aᵫ'q=0*+,-./ln-arln2aᵯ₹ᑖ5"—L-;r=aWA.braIn—In—67p=<£947■=,as2390AB"ᵯCᦪ"jḄ-z<0AB"ᵯCᦪ"GḄ-H(1)ᵯK"qḄLᵯ₹Mᙠᑖ☢P9(2)ᵯ₹QRS"qḄᙳᒴQᵯ₹Mᙠᑖ☢P஺WᵯXYS஺Z[(1)ᵯK"qḄLᵯ₹Mᙠᑖ☢P\Lᵯ₹"]^_\A`"rḄᳫ-ᑭᵨdefᳮ(^DdS=qShPஹjAᳫ☢PḄᵯklmKᑖnoஹD,᪷qrsឋ-ᙠPஹjAᳫ☢Pᜧvᑖnw2x-ᨵ2m2(D[+A)=4᪷qᩩ=|2,,}'2.2£-+£E=q22I

43qE=%r24(4+£)r222ᵯ₹QRS"0ḄᙳᒴQᵯ₹Mᙠᑖ☢P\Qᵯ₹"Q_\A`"rᓫkSḄᙊ☢-ᑭᵨdefᳮ-dS=p,ShPஹjA☢PḄᵯklmKᑖnஹD,᪷qrsឋ-ᙠPஹjA☢Pᜧvᑖnw2x-ᨵ-+஺2=0᪷qᩩᵨ-=E“-}'4&ὡ-+S2E2h^p.I=E”=E2r=~"—£i+s
r22-34.☢"A,"dḄᵯᘤᵯ!"V,ᵯCᦪ"£S"tḄᑖnᢥ᝞aஹbᡠḄMᙠᵯ஺ᑖn¡¢£jᵯᘤ]ᵯX¤ᵯ₹ᑖ5஺⚪2.34Z[ah&B¦]ḄᵯXᑖn"§ஹ§-¨©§ஹ§ª«ᐵEt+E(d-t)=Ve0£E=sE(ᩩ)e00WZ\PE'=2K—E.0;'t+e(d-t)°t+e(d-t)rr᪷q⊤☢PḄᩩ±=஺“-ᙠPஹj⊤☢PḄᵯ₹☢RS"£Vp=±--------------st+n

44(b)ᵫ²-&B¦]ḄᵯX"E=V/d᪷q⊤☢PḄᩩ£=஺“-ᙠPஹj&B¦Ḅ☢PḄᵯ₹☢RS"Pos=±£0VIdᙠPஹj&Ḅ☢PḄᵯ₹☢RS"P”=▂Id2-35ᙠᑁ᜜A`ᑖn"஺³bḄᙊ´µ¶ᑁ·ᵯ₹-ᙠA`ᑖn"஺³bḄᙊ☢Pᵯkᑖn"V³0஺W¸ᙊ´µ¶ᑁḄᵯk³ᵯX஺Z[ᵫᵯ₹ᑖ5¹-ᵯkº»PḄ¼ᦪ-ᵯkª«½¾½e¿-¿"pdpkdpZÁᑖ¿জ(P)=c,ln/?+c2ᑭᵨᩩজ(a)=GIna+C2=Vজ(b)=qlnb+Q=°Vc1C2,aiaIn—In—hb}'Vbজ(p)=--In—l/pa2-36ᙠA`ᑖn"஺³bḄÊᵯᙊËÌᡂḄµ¶ᑁ-ᵯ₹ᑖ5"p=A"Cᦪ-ÎᵯCᦪ"£,ᑁᵯk"V,᜜ᵯk"0஺WḄᵯkᑖ5஺Z[ᵫᵯ₹ᑖ5¹-ᵯkº»᜛Ḅ¼ᦪ-ᵯkª«ÐÑ¿Id,"A----(r---)=----rdrdrsrZÁᑖ¿AজÒ=---r+C,Inr+c0£ᑭᵨᩩAজ(a)=---ci+jIna+Q=V

45Aজ(஺)=-b+GIn஺+Q=08AAV——3—a).V——(b-a)£A,£AV--(b-a)bজ(r)=—(b_r)+——J----In-£.baIna2-37ᙽᵯkᑖn"0³VḄA·▲ᜧḄᵯ᪀ᡂᜳÚ"aḄÚ´µ¶-W¸Ú´µ¶]Ḅᵯkᑖ5஺°=0a⚪2.37⚪2.38Z[ᵫ⚪Ü-ᙠᙊᙶ᪗]-ᵯkº»°Ḅ¼ᦪ-ᙠᵯᵯk¿",1I?জß=—■^=0pd(p~ᐸâZ"<1>=஺ã᜛+%ᵫᩩজ(᜛=0)=0;জ(᜛=a)=V,VåG=2“0=0aᡠ\-জ=—(pa2-38.æᵯᑴ_Ḅèéê᝞ᡠ-◀êìḄᵯk"V᜜-ᐸíêîᵯk"0,Wêᑁᵯkᑖ5஺Z[ᵨᑖᙌðKñ-ᵯkḄâZ"..mᐔ.H7T_na-ஹZsin--xsin—V(஺+')n,m=\஻,ᑭᵨᩩজ(z=0)=09জ(z=b)=V,Wõᦪ

46A=-----------—mஹn"᜻ᦪmnmn7r^shab
=0mஹn"Ꮤᦪ2-39ᙠ£=ḄᒴYᵯX]ùzM2᪷A`"aḄ·▲ᵯᙊ|-Wᵯk¤ᵯX஺⚪2.39Z[ᵫᑖúðKñ-·▲ᵯᙊ᜜ḄᵯkḄâZ"8]᜛,᜛=/In஺+d°+Zc,““"+dp~m
cosû஺+bsinmgp'
1mmm=\hজ
2=0=0,H᜛2>00üḄᵯkxý·ᵯᙊḄᵯk-ᓽ00/9-»oo=জ00—>oo=JE-xdx=-Ex=-£pcos^?2Oo0x⌕1Ḅᵯᙠ2ߟ82,ᑮ"ᦪG=-E,%%=0,=0,4o=஺o'ᵫ)*+☢Ḅ-+ᩩ/জ
2=a
=04=a2E,d^=00m012ᵯḄᱯ45জ
p,᜛=-£7
/7--cos^P2-40.ᙠ:▲ᜧḄ)ᵯ=>?@A)ᵯ=>hᜐ=DEF:▲GḄHᵯ₹2ᵯ₹HJK50,L)ᵯ=>?@ḄᵯM஺4:ᵨPQR2)ᵯ=>ḄSTᦔ5PQFḄVWᵯ₹HJK5-0ḄHᵯ₹2)ᵯ=>?@ḄᵯM5

47^=A4-42ᐔsrr2YZτஹrᑖ]5Hᵯ₹^ᐸPQHᵯ₹ᑮM`ḄAabc஺22-41ᵫ:▲ᜧḄ)ᵯ=>ᢚᡂ45°Ḅhij2ᙠkhijYlV`%,y02Z஺ᨵV`ᵯ₹q,ᵨPQRLᵯᑖq஺47᝞stuvᑖ58Wj2ᙠxWjYyzᩭḄ)ᵯ☢5P☢y|}~ᑮPQF,zᵯ₹ḄF5/,ᡭ⌲02᜜7WPQᵯ₹ᙠᙊᙶ᪗"YḄᙶ᪗572o2Xo2Z஺2i'o2Xo2Zo2—x,y,ZQhix஺,—/pZ஺2—y,—x,zyghx,zx2—yo2z஺00000PQᵯ₹5qஹ=-q\q=4%=-q஺=q%=-q\q=4%=~q2bM`x,y,z2ᵯ₹ᑮM`ḄAabc5=x-x,.x+y-y,y+z-zzi=0,…7;7-ᑣM`ḄᵯM5Er=4f,=ort⚪2-41s

48⚪2-42s2-425a,ᵯc5QḄ)*ᳫ▬AᳫfᜐᨵV`ᵯ₹q,L`ᵯ₹qᡠḄ¡஺47`ᵯ₹qᑮḄ¡(M)ᨵ¤¥ᑖ2V¥ᑖᦔ5PQᵯ₹"Ḅ¡2V¥ᑖᦔ5ᳫYḄ`ᵯ₹q”Ḅ¡஺ᵫPQR2PQᵯ₹dḄᜧ§¨Fᑖ]5aa'q=_/dfᵫᒹª)*ᳫḄ«ᵯc5Q,ᡠyᳫYḄ`ᵯ₹q"=Q-q'01`ᵯ₹qᑮḄ¡5ᡝ=*q+aq/f_aq!f-4ff22-43ᑁ᜜ᑖ]5aஹbḄ)ᵯᳫᑁAᳫ5d(d

49)ᵯᳫᑁḄᵯ54%·GᐸY·ஹGᑖ]5M`¸`ᵯ₹^PQᵯ₹ḄAa2ᵨᙊᳫᙶ᪗⊤º5r,=\r2+d2-2rdcos0r=+»2-2r¼)cos62(2))ᵯᳫᵯ5V®)ᵯᳫᵯ5V2½)ᵯᳫ᜜¾2)ᵯᳫ☢¿☢2À)ᵯᳫ᜜Ḅᵯ¿ᳫÁḄ2ᐸᵯÂÃজÄ.r)*ᳫᑁḄᵯ¾ᡂ¤¥ᑖḄÅÆ2V¥ᑖ¿ᑁᨵ`ᵯ₹Çᳫ5°Ḅᵯ2ÈV¥ᑖḄᵯÉÊV¥ᑖ¿ᑁ:`ᵯ₹Çᳫᵯ5VḄᵯ2ÈV¥ᑖḄᵯ5V஺01)ᵯᳫᵯ5V2)ᵯᳫᑁḄᵯ5জV%+V4Ë4஺Ì2ᐸY·ஹrᑖ]5M`¸`ᵯ₹^PQᵯ₹ḄAa஺2(3))ᵯᳫ?Ḅ«ᵯc5Q®)ᵯᳫ?Ḅ«ᵯc5Q2½)ᵯᳫ᜜¾2)ᵯᳫ☢¿☢2À)ᵯᳫ᜜Ḅᵯ¿ᳫÁḄ2)ᵯᳫᑁḄ«ᵯc5Q+q,ᐸᵯÂÃজÄV4^r0)ᵯᳫ?Ḅᵯ5஺=ÍÎÏ4fbÉ?2)ᵯᳫᑁḄᵯ5জ=~^—g_£}+u4Ð4·r22-44:▲ᜧ)ᵯ=☢?ᨵV)ᵯᳫ25a,ᙠᳫ*Ñ?@Aᳫ^)ᵯ=☢hᜐᨵV`ᵯ₹q,Lk`ᵯ₹ᡠḄ¡஺⚪244s47⌕)*ᳫ☢¨=☢?Ḅᵯᙳ5°2Óᨵ

50Q-qÔWPQᵯ₹2᝞sᡠº஺ÔWPQᵯ₹Ḅᵯc¨Fᑖ]522.aa.aq=1,Z=----q,z=-hhhh`ᵯ₹qᡠḄ¡5ÔWPQᵯ₹ḄᵯM¡2ᓽ-q2,a/halh1,r=Z---{------%------r-!------------;------%-----r]4ËÖ(/i-a2//i)2(h+a2/h)2(2/?)2¡ḄÑ@ᔣᔣ?஺2-45:▲ᜧ)ᵯ=☢?@=DEFV᪷5aḄ:▲G)ᵯᙊ2k)ᵯᙊÚHA)ᵯ=☢5h,L)ᵯᙊ¸)ᵯ=☢ÛvᓫGKḄᵯÝ஺47᝞Þ:▲G)ᵯᙊ?ᨵᵯ₹HJK82)ᵯ=☢ᵨPQFḄHᵯ₹ᦔ2PQᵯ₹HJK5-0஺ᵫ)*ᙊḄPQRL)*ᙊḄᵯজ2ßà2ᓫ)*ᙊ¸)ᵯ=☢ÛvḄᵯÝ5Q_Pi_=27rqজh+V/?2-a2,ln(-----------)a

51⚪2-45s2-46z>0uv5äᵯåᦪ5aḄäæ2z<0uv5äᵯåᦪ5çḄäæ2ᙠ+☢¤-A+☢5hḄÁFᑖ]EFᵯcᑖ]50¨µḄ`ᵯ₹஺ᑖ]èé¤W`ᵯ₹ᡠ¡஺47ᑭᵨPQR2èéz>0uvḄM2zᩭḄë⚪ᦔ5s246(b),èéz<0uvḄM2zᩭḄë⚪ᦔ5s2-46(c)஺È᪵?uvḄᵯ⊤º5Y᜜5çᑮM`ḄAa2஽5çḄPQFḄᵯ₹ᑮM`ḄAaîuvḄᵯ⊤º5Yq5ÖᑮM`ḄAa2஺5%ḄPQFḄᵯ₹*ᑮM`ḄAa஺ᑭᵨ-+ᩩ/,জ¨%=2.6S(%+4'2)/ð=(q'i+%)/£2(%V22)=@V42)²1,2g2GV£?,£1V£y<72=---------%+--------71J+?+£?§¨6ᡠḄö¡ᑖ]5

52qA4216÷//216Ë4/72(a)(b)(c)⚪2-46s2-47.¤É)*ᳫᑖ]5aஹb,¤)*ÛväæḄäᵯåᦪ5£,L¤)*ᳫÛvḄᵯÝ஺47øᑁ)*ᵯ₹5q2ᵫᵯ₹¸äæᑖqᐹᨵᳫÁឋ2û5rḄᳫ☢2üᵨýþÿᳮ
ᳫḄᵯ=-^-TᳫḄᵯb11V=fE,.Jr=/-(---)a4abᳫḄᵯqMsab(——=---------Vb-a2-48ᳫᑖaஹb,ᨵ
ᵯᦪJஹ£?,!☢C,#ᳫḄᵯ஺%&'ᑁ)ᵯ₹q
ᵫ,ᵯ₹-ᑖ.ᐹᨵᳫ01ឋ
3rḄᳫ☢
4ᵨ678ᳮ9:
=<\4m2ᳫḄᵯ47T£r2
2ᳫḄᵯᳫḄᵯ

534%2-49☢DA,FdḄᵯHIJKᵯᦪ£,LMtḄI
᝞PaஹbᡠT஺ᑖUVWXYZᵯHIḄᵯ஺⚪249P%&(a)'I-]^_ḄᵯᑖE«ஹb
cd£ஹbefᐵhEt+E(d-t)=Ve0sE=sE(i!ᩩk)e00#%lmn:V£VE=__________E=____-____1t+£(d~t)f+%(d—t)r᪷p⊤☢mḄi!ᩩka=஺“
ᙠmஹZ⊤☢mḄᵯ₹☢tM£VPஹ-±------------'t+£(d-t)rpAMSᵯsf=________—_______________________Vt+£(d-t)r(b)ᵫP9v
I-]^_ḄᵯE=VId᪷p⊤☢mḄi!ᩩkPs=஺“
ᙠmஹZI-]^Ḅ!☢mḄᵯ₹☢tMPo=±£V/ds0ᙠmஹZI-Ḅ!☢mḄᵯ₹☢tMP”=Id

54ᵯ0
஺z+£4=£஺4"}+~Vadad2-50ᙽzᔣ▲ḄᵯHIᜳ°=30°,-02=8Ḅᙊ☢,IḄᵯV,஺ᶍiᦔ
#ᙽIḄᵯᑖ.
ᵯ
lᓫMḄᵯ஺⚪2.50P%&ᙠᙊᙶ᪗h_
ᵯ8ᨵᐵ
ᙠᙽᵯHI1a2oV2O>==op-¤2¥¦Ḅ§%জ©᜛}=C¬᜛+c0ᑭᵨi!ᩩk
জ©°=}/6}=/
জ©9=0}=0:±/ஹ6Vজ©*}=

55ᵯ½¹W""geoE'V=É£oj©-/Ë"=27T£aV2o2-52.ᙊᳫÌᵯᘤᑁḄ᜜a,᜜Ḅᑁb,ᑁ᜜ÎᐙᵯᦪᑖÐஹ%Ḅ
!☢c,ᵯV஺#ᵯᘤ_Ḅᵯ½¹஺%&'ᙊᳫÌᵯᘤᑁmḄᵯ₹q,ᵫ678ᳮ9#:ᙠᑁ᜜ÑÒ9#:ᑁ᜜Ḅᵯbcb1.1.11..V=\Edr="+j©D/f}Jr=-rr2T-{—(-------)+—(--)}717Tacscbaac2ᙊᳫÌᵯᘤḄᵯC_4g&vaccbᵯ½¹w×Ø2஺=----2ᐔL------‘2£,©×}+/_Úaccb253MdḄᙊÌᵯᘤᑁḄ᜜a,᜜Ḅᑁb,ᑁ᜜ÎᐙᵯᦪᑖÛஹÜḄ
!☢C,ᵯV஺#ᵯᘤ_Ḅᵯ½¹஺%&'ᙊÌᵯᘤᑁmḄᵯ₹q,ᵨ678ᳮ,
ᙠᑁ᜜D,=—^ߟ27rrdᑁ᜜Ḅᵯbcbv=\Edr=J
O,/£|dr+©°
•/⎃}Þ=—11In—஺+—11In-8}ஹrJa8Caac<
''2ᑁ᜜Ḅᵯq2ᐔᔆ<1b6*2In—+In—acᵯ½¹w=-V2C=27r£'£2dv2~eIn-4-^ln-2-ac

562-54àáᵯ₹ᵯ¹ᙳq,Jᙠᵯᦪ£Ḅ_
Fd,#ã½஺%&àáᵯ₹Ḅã½ä<àáᵯ₹Ñ▲åæᑮè<àFdᜐ᜜êëḄì47rM2-55íîaXaḄHïᵯHIFðd,)ᵯ¹ᑖ±q,ñäᵯᦪ£ḄIòᐭᵯIôMxõ
ᑖ#IᡠöḄᵯê஺⚪2.55P%&']^Îᐙ÷ᑖÎᐙ÷ᑖᵯHImḄᵯ₹tMᑖ±0,2øi!ᩩk:A=,D=pÉᵫi!ᩩk:ὡ=/ᡈ4=2,û¥2s2]^Îᐙ÷ᑖÎᐙ÷ᑖᵯHImḄᵯ¹ᑖᜐ=S|£|=a(a-x)2|,=S202=aXPs2஺tᵫq=/+஺2᜛.ஹ2=ü஺”:஻(4<ÿ)£]+4X22-a(a-x)£]+axs2ᵯḄᵯᓃ=@/G+■/஺2)=|{----}22a(a-1+axc2ᵫᳮ!ᵯ₹#$%&ᡠ(Ḅ)x*ᔣᵯ,q2ad-)q=c2[a(a-x)e+axs]}2

57

58.301⚪3-145aḄↈᙊ9:ᵯ₹☢<=P,,@ᐸᙊBCDEF⚣᳛஺IJKᡂᵯMNᵯM☢<=஺OPᙊ9EF⚣᳛QIJᙊ9:45rᜐḄT=wVWᵯM☢<=J==PJgDgps3-2ᙠZ[\]*^_`[ᜧbᨵ8.5x1028ijᵫᵯk஺᝞mZDḄno☢io஺r,ᵯM1500A஺tu1vᵯM<=2vᵯkḄᙳxyT=OP1vᵯM<=J—1500-=1.5X106A//HS10x10-42vᵯkḄᙳxyT=J=pv,᜛=eN=1.6x10-9x8.5x1()28=]36x10"CIm3J1.5xlQ6=1.1x1(14m/s7-1.36x10'°3-3=30c:ᵯ₹ᙳᒴᑖET=20஻z/sᒴTKᡂḄᵯMḄᵯM=50,4tu:Ḅᵯ₹☢<=஺OPᵯM☢<==166.7uA/msL0.3VJs=PsVᡠEps=k==8.33pC/m2v203-4᝞mPᵯ₹<=7ᵯ₹ḄᙳT=P7+7%+=0dtP᝞mᵯ₹<=7ᵯ₹ḄᙳT=ᑣᵯM<=J=pU

59¢ᐭᵯ₹¤ឤ¦§¨7dt©pV-U+U-Vp+^-=Odt3-5ᵫ

61r2$ᵯ%&JI,Er=——r=-------a

62ᵫ⚪!V+V=—^ߟln-+—2"a2TC(J2I_V2L1ih,1icIn—+——In—a(yb2Y________1_PQE=—a

63E=-----b

64PQa

653-12ᙠ§3.327!᝞ᙠ®¯ᵯc®☢$ᵯ*!=°ᵯ±ᔣḄᵯ³஺@
´c®☢ḄᵯI஺µ¡[c®☢Ḅ!Ḅ®☢!´Q®☢Ḅᵯ"Aj=,ᑣᵫ/=¨SI^-brJ2ᵫQ¨/=2-7ibraTiobrc+aQjc®☢Ḅᵯ*V=fEJr=—ln^—,■¹$!y2஻+c°ᵯ±ᔣḄᵯ³/?=ᓃ=ºᵫ»£Iᐔ&>c3-13ᙊᳫ¯ᵯ5ᘤᑁa,᜜ᑁc,ᑁ᜜iᐙc)ᵯ¼ᦪᑖ£”£2!ᵯᑖḄᳮl!c)ᳮlᑖ:☢b,᝞ᑁ᜜ᵯ*V,=ᵯ5ᘤ7Ḅᵯ%½:☢Ḅᵯ₹"஺@ᵫ¾ᙊᳫ¯ᵯ5ᘤᑁiᐙc)ᳮl!ᨵᵯ´!
ᵯI஺ᙠᙊᳫ¯ᵯ5ᘤᑁÀ(rḄᳫ☢!´Qᳫ☢Ḅᵯ"/=஻!ᑣᵫ/=஺7¡6¨SI=J4TTT2ᡈJ=—4úᵯ%&,LIa

66ᑁ⊤☢Ḅᵯ₹"᜜ᑁ⊤☢Ḅᵯ₹"saV121Psi=஺2"(r=C)=_£2abbcklᑖ:☢ḄÍÎÏÐᵯ₹"(bl4-1Ps3=D2n-D\=£2E2-£\E\=n/d-J+bdº)ᓃabbc3-14=3-11⚪7ᵯ5ᘤḄᵯ஺@ᵫ3-2⚪¨E=________3V_______________CTgTd+CT]CT3d3+b஺2d323t´ᵯ5ᘤḄᵯ/=\=/=--------Òᜐ--------4+஺3d3+-hd3ᡠ¡G=-=------------9----Vb2b34+஺3d3+b஺2d33-15=3/3⚪7ᙊᳫ¯ᵯ5ᘤḄᵯ5½ᵯ஺@Qᙊᳫ¯ᵯ5ᘤḄᵯ5½ᵯÕÖὶḄ¯Ø᝞ÙᡠÚ஺4¹&4sl4)Þ1tzG111ºabbabbc3-16ᑖ=3-11⚪½3-13⚪7ᵯ5ᘤḄßὑá᳛஺@Í1Ð3-11⚪

67p=w=y2G=------------6WSV------------b2b3d]+%b3d3+CT]CT2d3(2)3-13⚪V24᩟2P=VI=—Rb-ac-b+aababct23-179ᙳaḄã¥ᵯä7ᐙᵯ᳛஺Ḅᵯ@å!◀ᵯçḄᵯV᜜!äḄᐸèéê9:☢ᵯë஺=ᵯ@å7Ḅᵯ஺@Q⚪ᵯᡠḄ¥¦9:ᩩ<[⚪2-33ì!PQᐸ@í[⚪2-33ì஺3-18îaḄêᵯᳫïðñᐭᵯ᳛O■Ḅᜧᙢ7!᝞ÙᡠÚ஺=õᙢᵯ³஺@
mᙢöÊḄᵯI,ᙠᜧᙢ7µ[ᳫd!ÇḄᳫ☢!ᙠQᳫ☢ᵯ"/="ì!÷ᯠᐵù᜼ᵯ%&E=J/a=------27ror~a1ᵯᳫḄᵯV=\Edr=-----J27roaO0PQᵯᳫḄõᙢᵯ³3-19ᙠᵯ᳛஺Ḅᜧᙢûᜐ!ìüdýþÿ
ᙳaḄ▲ᙊ஺ᙊᓫḄᵯ஺ᵨ☟ᵯ஺⚪!"#Ḅ$%&'(ᐸᵯᵯ*Ḅᐵ,G=-C£-!"#Ḅ$%&'ᓫḄᵯ*71SC=------------.—,D+A/D2-4a2In2a

68-(/ᙢᙊᓫḄᵯgG=-,--஺--+-(/஺2—4஺2In2a