第14講 麥克斯韋方程組(II)

1、主講：史琰DBtBEtDJH0VSSlSlSvdsdnDsdnBsdtBl dEsdtDJl dH0 SliSdtBl dEiEtB左旋左旋SLdSdtDl dHdHtD右旋右旋 nMaxwell方程組的邏輯關(guān)系方程組的邏輯關(guān)系n本構(gòu)關(guān)系本構(gòu)關(guān)系n時變電磁場的邊界條件時變電磁場的邊界條件n坡印亭能量定理坡印亭能量定理 n電磁位電磁位BEt 0B()0Bt0()()BEt DHJt0()()DHJt ()0JDtJt DDHJt0()()DHJt ()0JDtJt D00sin()yHEtzt0cos()xEa Etz000 xyzxaaaHExyztE 00 sin()yxxyyzza Etz

2、a Ha Ha Ht 00 xzHH00cos()yEHatz H00()DEPBHMJEDEBHJE0000000000* () ( )()* ()( )etemtmDEPEEEtEdBHMHHHtHd ()Fq EvB()fEvBEJB ()()()nnFn n FF n n ()()ntFn n FnnFF nFtAFtn tnAAA() ()tntntnAAFF tnFFF()()()()ttntn tnttnntnAAAAFF ttntnnttAFAAF nF1F2Sh1221()()SD dSDSnDn SDDn S VShSShdVQ0lim21 ()SnDD21nnSDDnnD

3、D21nnEE221121 ()0nBBnnBB21nnHH2211nblhllbnLSBE dldst 12212121()()()()lE dlEl lElllEElbnEElb nEEl 0lim0ShBBdsbh ltt 21()0nEE()LSDH dlJdst12212121()()()()lH dlHl lHlllHHlbnHHlb nHHl 0lim0ShDDdsbh ltt 0limSShJ dSJ bh lJb l 21()Sb nHHlb Jl 21()SnHHJ12ttSHHJ12ttHH2211ttBB2121212100SsnEEnDDnHHJnBBn理想介質(zhì)的邊界

4、條件理想介質(zhì)的邊界條件 理想介質(zhì)：理想介質(zhì)：=0 無歐姆損耗的簡單介質(zhì)無歐姆損耗的簡單介質(zhì) 理想介質(zhì)表面無自由面電荷和自由面電流理想介質(zhì)表面無自由面電荷和自由面電流12121212()0()0 ()0 ()0nHHnEEnBBnDD121212120000ttttnnnnHHEEBBDD00SSnHJnEn Bn D0( , ,0, )sincos()xH x yta Haxtay00sincos()sincos()SzxyJnHaa Haxtaya Haxtayn StSJt ),()cos(sin)sin(sin)cos(sin000yxcaytaxaHaytaxaHaytaxHytSS0

5、00( , ,0, )sincos()cos( , ,0, )sincos()coszzaHD x ytaaxtayayaHE x ytaaxtayay881 60cos(15 105 )20cos(15 105 )(/)xEatztzV m82cos(15 105 )(/)xEa Atz V m8182 80 cos(15 10 )cos(15 10 )xxEatEa AtmVA/80yEHEazt 881 0.1592 cos(15 105 )0.0531 cos(15 105 )(/)yHatztzA m82 0.1061 cos(15 1050 )(/)yHatzA m812 0.10

6、6 cos(15 10 )yHHat,E H , , iJiJiDHJEtBEt ()()()EHHEEH ()iVVBDJEdVHEE EEHdVtt ()iBDEHHEE EE Jtt 在體積在體積 上積分可得上積分可得()iVVSBDJEdVHEE E dVEHdStt ()ABA BBAttt()2AA AAtt ,DE BH 1()()221()()22BHHHH HB HttttDEEEE ED Etttt 11()22iVSVVJEdVEHdSB HD E dVE EdVt iJSEH11()22iVSVVJEdVEHdSB HD E dVE EdVt SdHESHESS11()22iVVVVJEdVEH dVB HD E dVE EdVt 11022E DB Ht ()0SEHdSHES00iJ ()11 22 iVSVVJEdVEHdSB HD E dVtE EdV 11022E DB Ht ()SVEHdSE EdV HES0iJ ()11 22 iVSVVJEdVEHdSB HD E dVtE EdV 110()22SVVEHdSB HD E dVE EdVt ()SPEHdSHES0iJ b2zJIEab2IHabEH2bIaJz2232rISEHab 22232222rSSS dSS a dSI