电磁场与电磁波部分答案1(陈抗生第二版)

1I.CHAPTER11.1E(t)=Eyy0=y010−3cos(2pi×106t+2pi×10−2x)V/m(1)¯µ¥þE3Ÿo•ºÅ÷Ÿo•DºÅÌõŒºªÇf=?§ƒ ~êk=?§ƒ„vp=?")µE3y•§Å÷−x•D§Å̏10−3§f=106§k=2pi×10−2§vp=ω/k=108m/s"1.2ÑežCþêL«µ(1)V(t)=6sin(ωt+pi/6)V(t)=6cos(ωt+pi/6−pi/2)=6cos(ωt−pi/3)(2)V=6e−jpi/3(3)(2)I(t)=−10sin(ωt)I(t)=−10cos(ωt−pi/2)(4)I=−10e−jpi/2=10j(5)(3)A(t)=3cos(ωt)−2sin(ωt)A(t)=3cos(ωt)−2cos(ωt−pi/2)(6)A=3−2e−jpi/2=3+2j(7)(4)C(t)=10cos(1000pit−pi/2)C=−10j(8)(5)D(t)=1−sin(ωt)Ϗ3ü«ªÇ§ÏdvkéAEêL«/ª¶(6)U(t)=sin(ωt+pi/6)cos(ωt+pi/3)U(t)=sin(2ωt+pi/3)+sin(−pi/6)2Ϗ3ü«ªÇ§ÏdvkéAEêL«/ª¶1.3ÑeEêL«žL«µ(1)C=3+4jC(t)=Re((3+4j)ejωt)=3cos(ωt)−4sin(ωt)(2)C=4e−j1.2November24,2017DRAFT2C(t)=4cos(ωt−1.2)(3)C=3ejpi/2+4ej0.8C(t)=3cos(ωt+pi/2)+4cos(ωt+0.8)1.4Ñež¥þEêL«/ªµ(1)V(t)=(3cos(ωt),4sin(ωt),cos(ωt+pi/2))V=(3,4e−jpi/2,ejpi/2)=(3,−4j,j)(2)E(t)=(3cos(ωt)+4sin(ωt),0,8(cos(ωt)−sin(ωt)))E=(3−4j,0,8+8j)(3)H(t)=(0.5cos(kz−ωt),0,0)H=(0.5e−jkz,0,0)1.5ÑeE¥þƒAžL«µ(1)C=(1,−j,0)C(t)=(cos(ωt),cos(ωt−pi/2),0)(2)C=(j,1,0)C(t)=(cos(ωt+pi/2),cos(ωt),0)(3)C=(e−jkz,jejkz,0)C(t)=(cos(ωt−kz),cos(ωt+kz+pi/2),0)1.7OŽeIK|Fݵ(1)u=x2y2z2∇u=(2xy2z2,2x2yz2,2x2y2z)(2)u=2x2+y2−z2∇u=(4x,2y,−2z)(3)u=xy+yz+xz∇u=(y+z,x+z,x+y)(4)u=x2+y2+2xy∇u=(2x+2y,2y+2x,0)(5)u=xyz∇u=(yz,xz,xy)1.9¦e¥þ|ÑÝ!FݵNovember24,2017DRAFT3(1)A=(x2,y2,z2)∇·A=2x+2y+2z(9)∇×A=∣∣∣∣∣∣∣∣∣∣x0y0z0∂∂x∂∂y∂∂zx2y2z2∣∣∣∣∣∣∣∣∣∣=0(10)(2)A=(y+z,x+z,x+y)∇·A=0(11)∇×A=∣∣∣∣∣∣∣∣∣∣x0y0z0∂∂x∂∂y∂∂zy+zx+zx+y∣∣∣∣∣∣∣∣∣∣=0(12)(3)A=(x+y,x2+y2,0)∇·A=1+2y(13)∇×A=∣∣∣∣∣∣∣∣∣∣x0y0z0∂∂x∂∂y∂∂zx+yx2+y20∣∣∣∣∣∣∣∣∣∣=(0,0,2x−1)(14)(4)A=(5,6yz,x2)∇·A=6z(15)∇×A=∣∣∣∣∣∣∣∣∣∣x0y0z0∂∂x∂∂y∂∂z56yzx2∣∣∣∣∣∣∣∣∣∣=(−6y,−2x,0)(16)II.CHAPTER22.1½{^²1V‚§ÿÙ©Ù>´ëꏵR′=0.042Ω/m(17)L′=5×10−7H/m(18)G′=5×10−10S/m(19)C′=30.5pF/m(20)¦DÂ~êk§A{|Zc"November24,2017DRAFT4)µω=2pi∗50(21)k=−j√(R′+jωL′)(G′+jωC′)=(1.38−j1.45)×10−5(22)Zc=√R′+jωL′G′+jωC′=(1.52−j1.44)×103(23)%%2.1R=0.042;L=5e-7;G=5e-10;C=3.05e-11;w=50*2*pi;%50Hzk=-1j*sqrt((R+1j*w*L)*(G+1j*w*C));zc=sqrt((R+1j*w*L)/(G+1j*w*C));2.2DтA{|Zc=50Ω§K1{|ZL=75+j75Ω§¦µ(1)K1B¶(2)K1?‡XêΓL¶(3)7ÅXê†lmK11˜‡7Ł: ˜")µYL=1/ZL=0.0067−j0.0067(24)ΓL=ZL−ZcZL+Zc=0.412+j0.353(25)VSWR=1+|ΓL|1−|ΓL|=3.37(26)d=ϕ/pi+14λ=0.306λ(27)%%2.2zc=50;zl=75+1j*75;yl=1/zl;gammaL=(zl-zc)/(zl+zc);gammaMag=abs(gammaL);gammaAng=angle(gammaL);VSWR=(1+gammaMag)/(1-gammaMag);d=(gammaAng+pi)/4/pi;November24,2017DRAFT52.3K1ZL=80Ω§DтZc=50Ω§K1þ>؏5V§¦lmK1l=λ4,l=λ2,l=3λ8?Ñ\{|Zin±9Umax,Umin,Imax,Imin")µZin(z=−l)=ZcZL+jZctan(kl)Zc+jZLtan(kl)(28)Zin(z=−λ4)=31.25Ω(29)Zin(z=−λ2)=80Ω(30)Zin(z=−3λ8)=44.9+21.9jΩ(31)(32)ϏΓ(0)=ZL−ZcZL+Zc=0.23§ÏdK1?>؁Œ§>6§kµVSWR=1+|Γ(0)|1−|Γ(0)|=1.6(33)Umax=5V(34)Umin=Umax/VSWR=3.125V(35)Imin=Umax/ZL=0.0625A(36)Imax=Imin×Imin=0.1A(37)November24,2017DRAFT6%%2.3zl=80;zc=50;kl=2*pi/4;zin1=zc*(zl+1j*zc*tan(kl))/(zc+1j*zl*tan(kl));kl=2*pi/2;zin2=zc*(zl+1j*zc*tan(kl))/(zc+1j*zl*tan(kl));kl=2*pi*3/8;zin3=zc*(zl+1j*zc*tan(kl))/(zc+1j*zl*tan(kl));gamma=(zl-zc)/(zl+zc);vswr=(1+gamma)/(1-gamma);Vmin=5/vswr;Imin=5/80;Imax=Imin*vswr;2.4ÛDтZc=50Ω§K1{|ZL=4.5+2.19j§¦DтÝl=λ/8,λ/4,3λ/8?Ñ\{|º)µZin(z=−l)=ZcZL+jZctan(kl)Zc+jZLtan(kl)(38)Zin(z=−λ8)=9.75+j53.4Ω(39)Zin(z=−λ4)=449−j219Ω(40)Zin(z=−3λ8)=8.12−j45.1Ω(41)(42)November24,2017DRAFT7%%2.4zl=5*cos(25.99/180*pi)+1j*5*sin(25.99/180*pi);zc=50;kl=pi/4;zin1=zc*(zl+1j*zc*tan(kl))/(zc+1j*zl*tan(kl));kl=pi/2;zin2=zc*(zl+1j*zc*tan(kl))/(zc+1j*zl*tan(kl));kl=3*pi/4;zin3=zc*(zl+1j*zc*tan(kl))/(zc+1j*zl*tan(kl));2.6e¡ü^Dт=˜^DÑõnjºDт1µA{|Zc1=50Ω,Umax=100V,Umin=80V¶Dт2µA{|Zc2=75Ω,Umax=150V,Umin=100V")µéuDт1§kµVSWR=Umax/Umin=1.25(43)P1=U2max2VSWR∗Zc=80W(44)(45)éuDт2§kµVSWR=Umax/Umin=1.5(46)P1=U2max2VSWR∗Zc=100W(47)(48)ÏdDт2DÑõnj"November24,2017DRAFT8%%2.6Vmax=100;Vmin=80;zc=50;vswr=Vmax/Vmin;P1=Vmaxˆ2/(2*vswr*zc);Vmax=150;Vmin=100;zc=75;vswr=Vmax/Vmin;P2=Vmaxˆ2/(2*vswr*zc);2.7DтA{|50Ω§ªàm´§ÿ©àÑ\{|j33Ω§¦Dт>Ýlλ")µéuªàm´DтkµZin=Zcjtan(kl)(49)kl=arctan(ZcZL)(50)l/λ=arctan(ZcZL)2pi=0.157(51)%%2.7l=atan(50/33)/(2*pi);2.102.93ÛDтþÿµZscin=j100,Zocin=−j25,dmin=0.1λ,VSWR=3§¦K1{|º)µZscin=jZctan(kl)(52)Zocin=Zcjtan(kl)(53)Zc=√ZscinZocin=50Ω(54)|Γ|=VSWR−1VSWR+1=0.5(55)ϕ=(0.1−0.25)∗4pi=−1.885(56)ZL=Zc1+Γ1−Γ=24−30.5j(57)November24,2017DRAFT9%%2.9Zsc=100j;Zoc=-25j;vswr=3;Zc=sqrt(Zsc*Zoc);GammaMag=(vswr-1)/(vswr+1);GammaAng=(0.1-0.25)*4*pi;Gamma=GammaMag*cos(GammaAng)+1j*GammaMag*sin(GammaAng);Zl=Zc*(1+Gamma)/(1-Gamma);2.10®²ZL=30+j60,Zc=50§^Œ£ÄüŒC>Bšì?1š§¦ë:K1åldÚá´|‚Ýl")µ8˜zK1{|zl=ZL/Zc=0.6+j1.2§3ã¥éK1{| ˜§X㥤«§¿\\š>´§Œlã¥ÖÑDтݏ100.26o§ë:?BJ܏j1.63§Ïdµd=100.26180λ2=0.279λ(58)l=λ2piarctan(Zc1.63)=0.0875λ(59),˜|)ùpئ"2.12Áy²µU2U1=Zc2Zc1)µZ1,Z2þ>6©OI1,I2§ålZ2λ4?>Ø>6©OUA,IA§KkµUAIA=0jZc2j/Zc20U2I2(60)U1I1=0jZc1j/Zc10UAIA(61)U1I1=0jZc1j/Zc100jZc2j/Zc20U2I2(62)=−Zc1/Zc200−Zc2/Zc1U2I2(63)U1=−Zc1Zc2U2(64)2.15Áy²§ü0Ÿmåld0Cλ/4ž§Ñ\7Å'l1Cε2r"November24,2017DRAFT10Fig.1.ã)µéuý˜¥Åλ>^ŧ3ƒé0>~êεr0ŸDž§ÅCλ√εr§=0Ÿݏλ4√εr0Ÿ§Ù>ÝE1/4"Ó¶‚A{|zc=1§@oéuk0ŸÓ¶‚A{|z′c=1√εr§Ïdmå0ž§ƒuλ/2Dт"K1{|zl=1§²Lλ/2DтC†§Ñ\{|Ezin=1§=7Å'1¶November24,2017DRAFT11måCλ/4ž§Ñ\{|Œ±dnÚOŽµza=z′2czl=1εr(65)zb=12za=εr(66)zin=z′2czb=1ε2r(67)III.CHAPTER33.2ØmH=zy0+yz0,D‘žmCzíº)µÏ´Ã˜m§¤±Jc=0§Ïdkµ∂D∂t=∇×H(68)=∣∣∣∣∣∣∣∣∣∣x0y0z0∂∂x∂∂y∂∂z0zy∣∣∣∣∣∣∣∣∣∣(69)=0(70)Ïd§DؑžmCz"3.9b½E=(x0+jy0)e−jz,H=(y0−jx0)e−jz§¦^z!ωtL«S(t)±9")µE(t)=(cos(ωt−z),cos(ωt−z+pi/2),0)(71)H(t)=(cos(ωt−z−pi/2),cos(ωt−z),0)(72)S(t)=E(t)×H(t)(73)=∣∣∣∣∣∣∣∣∣∣x0y0z0cos(ωt−z)cos(ωt−z+pi/2)0cos(ωt−z−pi/2)cos(ωt−z)0∣∣∣∣∣∣∣∣∣∣(74)=(0,0,cos2(ωt−z)−cos(ωt−z+pi/2)cos(ωt−z−pi/2))(75)=(0,0,cos(2ωt−2z)+12−cos(2ωt−2z)−12)(76)=(0,0,1)(77)Ïd:=z0(78)November24,2017DRAFT125µŒ±ùo)=0.5∗Re(E×H∗)(79)=∣∣∣∣∣∣∣∣∣∣x0y0z0e−jzje−jz0jejzejz0∣∣∣∣∣∣∣∣∣∣(80)=(0,0,1)(81)=z0(82)3.10>|rÝE=Eyy0=y0Eymsin(mpixa)cos(npiyb)§¦^|rÝH§]ž·<ÉõÇ6S(t)†²þ·<ÉõÇ6")µH=1−jωµ∇×E(83)=1−jωµ∣∣∣∣∣∣∣∣∣∣x0y0z0∂∂x∂∂y∂∂z0Eymsin(mpixa)cos(npiyb)0∣∣∣∣∣∣∣∣∣∣(84)=(0,0,1−jωµmpiEymacos(mpixa)cos(npiyb))(85)E(t)=(0,Eymsin(mpixa)cos(npiyb)cos(ωt),0)(86)H(t)=(0,0,1ωµmpiEymacos(mpixa)cos(npiyb)cos(ωt+pi/2))(87)S(t)=E(t)×H(t)(88)=∣∣∣∣∣∣∣∣∣∣x0y0z00Eymsin(mpixa)cos(npiyb)cos(ωt)0001ωµmpiEymacos(mpixa)cos(npiyb)cos(ωt+pi/2)∣∣∣∣∣∣∣∣∣∣(89)=(mpiE2ym2ωµasin(2mpixa)cos2(npiyb)cos(ωt+pi/2)cos(ωt),0,0)(90)=(−mpiE2ym4ωµasin(2mpixa)cos2(npiyb)sin(2ωt),0,0)(91)=0(92)IV.CHAPTER44.3®þ!²¡Å3þ!x0¥D§Ù>|rÝLˆªE(t)=y0Ey=y010cos(ωt−kz+pi/6)mV/m§óŠªÇf=150MHz§x0ëꏵµr=1,εr=4,σ=0§Á¦µNovember24,2017DRAFT13(1)ƒ ~êk§ƒ„vp§Åλ§Å{|η¶(2)t=0,z=1.5m?§E,H,S(t),ˆõµ(3)3z=0?§E1˜gÑyŒŠ£ý銤žt´õº)µ(1)k=ω√µε=2pif√µrµ0εrε0=2pi(93)vp=1√µrµ0εrε0=c/2(94)λ=2pik=1(95)η=√µrµ0εrε0=η0/2(96)(2)E=(0,10e−j(kz−pi/6),0)(97)H=1−jωµ∇×E(98)=1−jωµ∣∣∣∣∣∣∣∣∣∣x0y0z0∂∂x∂∂y∂∂z010e−j(kz−pi/6)0∣∣∣∣∣∣∣∣∣∣(99)=(−10kωµe−j(kz−pi/6),0,0)(100)=(−10ηe−j(kz−pi/6),0,0)(101)H(t)=(−10ηcos(ωt−kz+pi/6),0,0)(102)S(t)=E(t)×H(t)(103)=∣∣∣∣∣∣∣∣∣∣x0y0z0010cos(ωt−kz+pi/6)0−10ηcos(ωt−kz+pi/6)00∣∣∣∣∣∣∣∣∣∣(104)=(0,0,100ηcos2(ωt−kz+pi/6))(105)=(0,0,50η)(106)November24,2017DRAFT14t=0,z=1.5ž§E(t)=(0,−5√3,0)(107)H(t)=(10√3η0,0,0)(108)S(t)=(0,0,150η0)(109)=(0,0,100η0)(110)(3)ωt+pi/6=pi§E1˜gý銁Œ§t=2.78ns4.7gd˜m²¡Å²þU6—ݏ0.26µW/m2§²¡Å÷z•D§ÙóŠªÇf=150GHz§>|rݏE=Emcos(ωt−kz+pi/3)"Á¦3z=10m?§t=0.1µsž§E(t),H(t),S(t)´õº)µH(t)=Emη0cos(ωt−kz+pi/3)(111)S(t)=E2mη0cos2(ωt−kz+pi/3)(112)=E2m2η0(113)Em=√2η0∗0.26∗10−6=14∗10−3V/m(114)z=10m§t=0.1µsž:E(t)=0.007V/m(115)H(t)=1.86∗10−5A/m(116)S(t)=1.3∗10−7W/m2(117)4.8¦e|4z5Ÿµ(1)E=(je−jkz,e−jkz,0)ŕz•D§ϕy−ϕx=−pi/2§EymExm=1§Ïd´m^4z"(2)E=(0,(1+j)e−jkx,(1−j)e−jkx)ŕx•D§ϕz−ϕy=−pi/2§EymExm=1§Ïd´m^4z"(3)E=((2+j)e−jky,0,(3−j)e−jky)ŕy•D§0<ϕx−ϕz^Ål˜íR†•°¡D§®°Yëêεr=80,σ=1S/m,µr=1§²¡>^Å3°²¡?|rE(t)=x01000e−kizej(ωt−krz)§óŠÅ300m§Á¦>|rÝ̏1µV/mžl°¡ål§¿ÑT ˜þE,H")µÏσωε=σλ2picε=224.7>>1§Ïdµkr=ki=√ωµσ2=1.987(120)>|rݏ1µV/vžݏ÷vµ1µV/m1000V/m=e−kiz(121)z=10.43m(122)E(t)=x0ej(ωt−20.7)µV/m(123)Å{|µε˜=ε(1−jσωε)=−jσω(124)η=√µε˜=2.1ejpi/4(125)H(t)=y01|η|ej(ωt−20.7−pi/4)=y00.356ej(ωt−21.5)µA/m(126)November24,2017DRAFT