电磁场与电磁波课程作业解答(老师版)

“”“”——“”201191-5222222=666xyzxyuuuuaaaxyzzxyzaxyzaxyza∂∂∂∇=++∂∂∂++vvvvvv()(1,1,1)p−666pxyuaa∇=+−zavvv3()3pxuaaau∇yza∴==+−∇vvvv63pu∇=1-18122222272yxzAAAAxxyxyxyz∂∂∂=++=++∂∂∂vz∇⋅z yx0 1/1/1/2111222111222124VAdvAdxdydz−−−∇⋅=∇⋅=∫∫∫∫vv3s1s2s3s4s5s6241481481)(414141)(41)()3(3654232222122665544332211=+=−⋅+⋅+⋅+−⋅+−⋅−+⋅=⋅+⋅+⋅+⋅+⋅+⋅=⋅∫∫∫∫∫∫∫∫∫∫∫∫∫sxxsxxsyysyyszzszzsssssssadydzaadydzaadxdzaxadxdzaxadxdyayxadxdyayxsdAsdAsdAsdAsdAsdAsdAvvvvvvvvvvvvvvvvvvvvvvvvvv2∫∫⋅⋅∇=⋅svdvAsdA)(vvv 11-2122xyaxaAyxvvv+=xydldxadya=+vvvl4aaa−a−xyl3l2l122Adlxdxxydy⋅=+vv1∫∫+⋅+=⋅lyxyxladyadxxyaxaldA)()(22vvvvvv∫+=ldyxydxx)(22∫=ldxx02dyyyadyxyl2222∫−±=,sinθay=θcosax=∫∫∫∫∫+++=432122222llllldyxydyxydyxydyxydyxy32422422422422223022sincossincossincossincosadadadadπππππππθθθθθθθθθθθθ=+++∫∫∫∫42440211(1cos4)|088aadaππ4πθθθ=−==∫2∫∫⋅×∇=⋅slsdAldAvvvv2-4204lRdydEaRρπε=vvdzdEvzRav30cos4lrrdzrdEdEdERRρθπε=⋅=⋅=v/230024lrrdzERρρπε∴=∫l/2xyz0)(,,prϕ 2221/()Rrz=+2dzzrrElr2/32/0220)(42−∫+=∴ρπερ2202/022202/32/02204242)(42rlrlzrrzrdzzrrEllllr+=+⋅=+=∴−∫περπερπερρ2-7(36)/4sxyz6aa=−+−vvvvaa(36)/4sxyzaaaa=−+vvvv6QsdDs=⋅∫vv2sDSSρ⋅=⋅12sDρ=911901108.33(36)1221036sssxyEaaaaaρεπ−−×z∴===−+××vvvvvvz2-811110110(7.51015)rxyDEEaaεεεε===++vvvavvv2134ttxEEaa==+vvyvv21015nnDDaε==vvzv2020201535nnzrDEaεεεεza∴===vvvvy25rε=1346xyzEaaa=++vvvv12.5rε=2022005(34)(1520)trtxyxDEaaaεεεε==+=+vvvvvvaz2343xyEaaa∴=++vvvvz20(152015)xyDaaaε=++vvvv222z 32-1040502.510/0.2zzzUVEaaaVdcm===×vvvvm20z543.5102.510=0.88/zzJEaaAmσ−==×××vvvv40.8815101.33sIJdSmA−==××=∫vvdvEdvtsdHEsvvme∫∫∫++∂∂=⋅×−2)()(σωωvvv0=∂∂tdvEsdHEsv∫∫=⋅×−2)(σvvv——32452/86.21)105.2(105.3mkWEp=×××==−σσmWdvpPv63.65102.010151086.21243=×××××==−∫σσ301.33102565.63PIUmWσ−==××=342/65.6310/(15100.21021.86/pPVkWmσσ−−==××××=32-21188()0.03sin(10)0.04cos(10)3334xyEtatzazππππ=−−+−vvvπ+8850.03cos(10)0.04cos(10)3634xyatzazπππππ−+−+vv=−()xyxyEzaEaE⋅⋅=+vvv5()()36340.030.04jzjzxyeaeππππ−+−−=+avv20EjHωµ∇×=−vv0()jHzEωµ=∇×vv=0///0xyxyaaajzxyzEEωµ∂∂∂∂∂∂vvv 4⎥⎦⎤⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛∂∂−∂∂+⎟⎠⎞⎜⎝⎛∂∂−∂∂+⎟⎟⎠⎞⎜⎜⎝⎛∂∂−∂∂=zxyyzxxyzayExEaxEzEazEyEjvvv0ωµ5()()3436010.040.03jzjzxyeaeaππππη−−−+⎛⎞=−+⎜⎟⎝⎠vv88015()0.04cos(10)0.03cos(10)3436xyHtatzatzπππππη⎛⎞=−−++−−⎜⎟⎝⎠vvvπ2-2210cos()xEEtkzω=−vav0jkzxEEea−=vv0EjHωµ∇×=−vv0000///()e00xyzjkzjkzaaajjHxyzEzEeωµωµ−−∂∴=∂∂∂∂∂∂=∂vvvv00jkzykEeaωµ−v=00()cos()ykEHttωωµ=−vkzav20000xyzavxyzxyaaSEHEH=×=vvvvvEHa=v=2200cos()zkEtkzaωωµ=−vzyjkzxjkzakEaekEaeEHESvvvvvv020000*2)()(21)(21ωµωµ=×=×=−zavakESSvvv0202)Re(ωµ== 53-222200220(1)(1)4aVVRRQdvdvRdaaρρρπ==−=−∫∫∫R30815aπρ=RRa∫∫abcQ−Q+−=⋅=⋅RsdRRaRRDsdD022202114)/1(4πρπvv523010244435RRDRaπρππρ⇒=−30012()35RRRDaaρρ∴=−vv300110200/()35RRREDaaρρεεε==−vvvaRb≤158430222aRDsdDsπρπ=⋅=⋅∫vv3022215RaDaRρ∴=vv30220215RaEaRρε∴=vvbRc≤0Q=∑30D∴=v30E=vcR≤QQ=∑3042215RaDaRρ∴30420215RaEaRρε∴=vv=vv0Rc≥3300442200221515RRaaEdRdRRRρρϕεε∞∞===∫∫vvbRc≤303344020|15cRcRcaEdREdRcρϕϕε∞==+=+=∫∫vvvvaRb≤330022320022|1515bbRcRRaaEdRdRRcρρϕϕεε==+=+∫∫vv 63333000000002222111()15151515aaaaRbcRbρρρρεεεε=−+=−+cRa112|aRaREdRϕϕ==+∫vv=3002200()35aRaRRRdRaρρϕεε=−+∫|232000020000211()415620aaRRcbaρρρρεεεε=+−−+4v3-5oa1d2d1ε2εxy1ax11Ev22Ev2Dv1DD=2D0112DD2dεε=+Ud1201221xUDddaεεεε∴=+vv20111221xUDEaddεεεε∴==+vvv10221221xUDEaddεεεε==+vvv2210PSnnEEρε−=012012012211221()()PSrrUUddddεεεεερεεεε−−==++3-91aRv11Ev22Ev1tEE=2t21EE=vv1Dv1R2Ro1ε2εQ+ 7R12EEE==vvQsdEEs=⋅−∫vvv)(2211εεQREE=⋅+∴222112)(πεεQER=⋅+2212)(πεε2122(QER)πεε∴=+122122()RQEEaRπεε∴==+vvv211110101()()PPDEEρεε=−∇⋅=−∇⋅−=−∇⋅=vvvv0ε111102212()2()PSRRRQPaaaRρεεπεε=⋅=−⋅+vvvv=102212()2()QRεεπεε−[phone]()()2(PSRQPaR)εερπεε−=⋅−=−+vv2220220212()2()RQPDEaRεεεπεε=−=−+vvvv220PPρ=−∇⋅=v202122212()2(PSRQPaR)εερπεε−=⋅=+vv202122212()()2(PSRQPaR)εερπεε−−=⋅−=+vv0PSρ=31111121122(SnQDR)ερπεε==[phone](SnQDR)ερπεε−=−=[phone](SnQDR)ερπεε==+ 8222222122(SnQDR)ερπεε−=−=+3-15bxy0φ=0φ=0φφ=o⎪⎩⎪⎨⎧∞→===xxby00,000φφ(,)()()xyfxgyφ=Q0,yb=0φ=∴()sin()mygyBky=sin()0ykb=∴ymkbπ=()gy1()sin()mmmgyBybπ∞==∑1,2,3..........m=kk220yx+=xymkjkjbπ==Qx→∞0φ=()mxbmfxAeπ−=1,2,3..........m=∴(,)xyφ1sin()mxbmmmCeybππ∞−==∑0x=0φφ=01sin()mmmCybπφ∞==∑)sin(ybnπy0001sin()sin()sin()bbmmnmydyCyydybbnbπππφ∞==∑∫∫02[1cos()]nCnnφππ∴=−xbmoddmmeybmmyxπππφφ−∞==∑=)sin(4),(10 93-171α0ϕ=Uϕ=oqpbapqOr1U0pq0()ErrdUαα∴⋅=∫()UErarϕα⇒=vv()UDrarϕεα=vv()()sUrDrrερα==()()()ln()bssaUUQrdsbadrbarrbaεεραα∴==−=−∫∫()ln(QUbbaa)αε∴=−()()ln()QErabrbaaϕε=−vv()()()()ln(QrErrdbabaaαϕ)αϕφαε−==−−∫()ln(sQbrbaaρε=−)()ln(sQbrbaaρε)−=−2U00()UErarϕα=vv(,,)Mrzϕ00()()UUrrdrαϕαϕφααα−==∫0()()sUDrErrερεα===0sUrερα−=3()ln()QbabCUaεα−==2ϕ012222==∇ϕφφddr 10BA+=ϕφϕϕϕφφarAaddrEvvv−=−=−∇=1rADarAEDnsερεεϕ±==−==vvv1QababAdrabrAdsQbassln)()(−=−==∫∫εερababQAln)(−=εBababQ+−=ln)(εϕφBababrQaababrQEsln)(ln)(−±=−−=ρεϕv2U0⎩⎨⎧===000ϕαϕφUα/00UAUB−==rUarUEUUsαερααϕφϕ0000±==+−=v13ababQUln)()0()(−==−==εαϕφαϕφababUQCln)(αε−==ababUdrabrUdsQbassln)()(00αεαερ−=−==∫∫ababUQCln)(0αε−== 113-201Q−20204(2)QQEhπε=xyz•••Q-Q0Ezav00001164QQhEEπεπε∴==22''01)2QmvhhEQW−=−+0(2'0220()44hhQhhEQdRRπε=−−∫201122mvhEQ=04min012QEQvmπε=3-311JEσ=vv222JEσ∴=vv121222121221cos600.5/23sin602nnntttJJJJJAJEEEEσ⎧=⇒===⎪⎪⎨⎪=⇒==⋅⎪⎩m14.6rε=11rµ=130/smσµ=29.2rε=