《电动力学》讲义第01章电磁现象的普遍规律

123...4567121.1(Coulomb)..........................21.2............................31.3(Gauss)............................31.4.........................41.5.............................41.6..............................51.7.......................51.8.........................61.9...................................62{62.1.................................62.2..............................72.3|(Biot|Savart)...................82.4............................82.5...............................82.6.............................92.7.............................92.8...................................113(Maxwell)113.1.........................113.2...........................123.3.................................123.4Maxwell..........................133.5.........................133.6(Lorentz)...........................133.7...................................144144.1...............................144.2.................................154.3...............................154.4..............................164.5.........................164.6...................................1715175.1.......................175.2.............................175.3.............................185.4...................................196196.1.....................196.2......................206.3.....................216.4...................................25IIII²E(x;y;z;t)²B(x;y;z;t)IIEBx1.1(Coulomb)1785IQ0QFF=QQ04¼0¢rr3=Q0Q4¼0r2¢rr=E(x0;x)Q(x)0Q00Q~x0~x~rI²|²||2x1.2I...E(x0;x)=Q04¼0r2¢rrF/1r(2+±)±2:7£10¡15IE(x0;x)=14¼0Xiq0ir2i¢ririIE(x)=14¼0¢ZZZV½(x0)r3rdV0ρ(~x0)0P(~x)~x0~x~rVx1.3(Gauss)IVSISE¢dS=10ZZZV½dVVSr¢f=lim¢V!0Hf¢dS¢VIr¢E=½0III3x1.4dVdx=¡E;dEdx=½0d2Vdx2=¡½0VdVpVvcxvcxpxdxasplasmaareaanodesheathdoublesheathPotentialaxisx1.5E(x)=14¼0¢ZZZ1½(x0)r3rdV0ISE¢dS=10ZZZV½dVISE¢dS=14¼0IS[ZZZ1½(x0)r3rdV0]¢dS=14¼0ZZZ1½(x0)(ISrr3¢dS)dV0er¢dSr2=sinµdµdÁ=d­x0S(x0=2S)ISrr3¢dS=0x0S(x02S)ISrr3¢dS=4¼dΩrdSEQS14¼¢ISrr3¢dS=½0x0=2S1x02SISE¢dS=10ZZZV½dV4x1.6ILE¢dl=14¼0IL[ZZZ1½(x0)r3rdV0]¢dl=14¼0ZZZ1½(x0)(ILrr3¢dl)dV0=14¼0ZZZ1½(x0)(ILrr3¢dr)dV0=14¼0ZZZ1½(x0)[ILd(¡1r)]dV0=0LQrdldrdl=drr¢dr=rdrL(Stokes)HLf¢dl=RRS(r£f)¢dSIr£E=0x1.7E(x)=14¼0¢ZZZ1½(x0)r3rdV0r¢E=½0r¢E=14¼0¢ZZZ1½(x0)[r¢rr3]dV0r6=0r¢rr3=r(1r3)¢r+1r3(r¢r)=¡3r3+3r3=0r=jx¡x0j·½(x0)=½(x)r¢E=½(x)4¼0ZZZr·[r¢rr3]dV0=½(x)4¼0ZZZr·(¡r0¢rr3)dV0=½(x)4¼0ZZr·(¡rr3)dS0r=x¡x0dS0ISrr3¢dS=Id­=4¼5r¢E=½0x1.8E(x)=14¼0¢ZZZ1½(x0)r3rdV0r£E=0r£E=14¼0ZZZ1½(x0)(r£rr3)dV0=14¼0ZZZ1½(x0)[r(1r3)£r+1r3(r£r)]dV0=14¼0ZZZ1½(x0)[¡3rr5£r+1r3£0]dV0=0r£rr3=¡r£(r1r)=0x1.9IE(x)=14¼0¢ZZZ1½(x0)r3rdV0IIr¢E=½0Ir£E=0Page451,2,3{x2.1II6J=dQdtdScosµ¢eI=dIdScosµ¢eII=ZSJ¢dSIJ=½v=nqvIJ=Xi½ivi=Xiniqivix2.2I²III²ISJ¢dS=¡ZZZV@½@tdV²ISJ¢dS=ZZZVr¢JdV=¡ZZZV@½@tdV@½@t+r¢J=0IddtZZZ1½dV=0I@½@t=0)r¢J=07x2.3|(Biot|Savart)I|||dF=Idl£BIr2B(x)=¹04¼ZZZJ(x0)£rr3dV0¹0IJdV0=J(dS¢dl)=(JdSn)dl=IdlB(x)=¹04¼ZIdl£rr3x2.4I(Ampere)²ILB¢dl=¹0I²IILB¢dl=¹0ZZSJ¢dSIStokesr£B=¹0Jx2.5IIISB¢dS=0Ir¢B=0II8x2.6B(x)=¹04¼ZZZJ(x0)£rr3dV0r¢B=0B(x)=¹04¼ZZZJ(x0)£rr3dV0=¡¹04¼ZZZJ(x0)£r(1r)dV0=¹04¼ZZZr(1r)£J(x0)dV0=¹04¼ZZZr£[J(x0)1r]dV0=r£[¹04¼ZZZJ(x0)rdV0]=r£AA=¹04¼ZZZJ(x0)rdV0r¢B=r¢(r£A)=0x2.7AbiotB=r£A;A=¹04¼ZZZJ(x0)rdV0r£B=¹0Jr£B=r£(r£A)=r(r¢A)¡r2AIr¢Ar¢A=¹04¼ZZZr¢[J(x0)r]dV0=¹04¼ZZZJ(x0)¢r1rdV0r=jx¡x0j=q(x¡x0)2+(y¡y0)2+(z¡z0)29rxx0r¢A=¡¹04¼ZZZJ(x0)¢r01rdV0=¡¹04¼ZZZfr0¢[J(x0)1r]¡1rr0¢J(x0)gdV0=¡¹04¼ISJ(x0)1rdS0+¹04¼ZZZVr0¢J(x0)rdV0I²VVSJ(x0)²r0¢J(x0)=¡@½(x0)@t=0r¢A=0Ir2Ar2A=r2[¹04¼ZZZJ(x0)rdV0]=¹04¼ZZZr2J(x0)rdV0=¹04¼ZZZJ(x0)r21rdV0=¡¹04¼ZZZJ(x0)r¢rr3dV0r6=0r21r¡4¼±r¢rr3=r(1r3)¢r+1r3(r¢r)=¡3r4(er¢r)+3r3=0r=jx¡x0j·¿1J(x0)¼J(x)r2A=¡¹04¼J(x)ZZZr·r¢rr3dV0=¹04¼J(x)ZZZr·r0¢rr3dV0=¹04¼J(x)Ir=rr3¢dS010r=x¡x0dS0ISrr3¢dS=Id­=4¼r2A=¡¹0JIr£B=r(r¢A)¡r2A=¹0JIIIx2.8II|IIPage464,5(Maxwell)x3.1r¢E=½0r£E=0r¢B=0r£B=¹0JI()I()11x3.21831E=¡ddtZSB¢dSILE¢dl=E=¡ddtZSB¢dS=¡ZS@@tB¢dSddt=@@t+v¢rP233r£E=¡@B@tIddtx;y;z@@tx;y;zIddt@@tLddtx3.3Ir£B=¹0J0=r¢(r£B)=¹0r¢J=¡¹0@½@t=?½p=r¢P=0I²@@t!0r£B=¹0J+@f@t²f0=r¢(r£B)=r¢(¹0J+@f@t)=¡@@t(¹0½¡r¢f)=¡@@t(¹00r¢E¡r¢f)f=¹00E;JD=0@E@tr£B=¹0(J+JD)12x3.4Maxwell1864201900Gibbsr¢E=½0r£E=¡@B@tr¢B=0r£B=¹0J+¹00@E@tII½JI½J²²x3.5II²²r¢B=0IrIx3.6(Lorentz)If=½E+J£BIf=eE+ev£BIII13x3.7IIIIMaxwellIPage466,10x4.1Ip=qlIP=§pi¢V=npIZZZV½PdV=¡ISP¢dS½P=¡r¢PI¾PdS=¢Q=¡(P2¡P1)¢dS¾P=¡n¢(P2¡P1)InI14x4.2r¢Ef=½f0;r¢E0=½P0;E=Ef+E0r¢E=10(½f+½P);½P=¡r¢Pr¢E=10(½f+½P)=10(½f¡r¢P);r¢(0E+P)=½fID=0E+Pr¢D=½fIPEP=Âe0EÂeIDD=E=r0;r=1+Âerx4.3Im=iaIM=§mi¢V=nmIZZSJM¢dS=IM=ILnia¢dl=ILnm¢dl=ILM¢dlJM=r£MIP=§eixi¢V;JP=§eivi¢V=@P@t15x4.4r£Bf=¹0Jf+¹00@E@t;r£B0=¹0JM+¹0JP;B=Bf+B0r£B=¹0Jf+¹0JM+¹0JP+¹00@E@t;JM=r£M;JP=@P@tr£(B¡¹0M)=¹0Jf+¹0@D@tIEHH=B¹0¡Mr£H=Jf+@D@tIMHM=ÂMHÂMIBB=¹H¹=¹r¹0;¹r=1+ÂM¹¹rx4.5DHr£E=¡@B@tr£H=Jf+@D@tr¢D=½fr¢B=0IConstitutiveEquationD=EB=¹HJ=¾EI16x4.6IIIPage467,9IIIII²±²x5.1ILE¢dl=¡ddtZZSB¢dSILH¢dl=If+ddtZZSD¢dSISD¢dS=QfISB¢dS=0x5.2ISD¢dS=Qf=ZZZV½fdVD2¢dS2+D1¢dS1+(D1¢±S1)+(D2¢±S2)=½f±h¢S17ID±S1/±h!0±h¾f(D1¢±S1)+(D2¢±S2)!0(D2¡D1)¢n¢S=½f±h¢S=¾f¢SISn¢(D2¡D1)=¾fIn¢(B2¡B1)=0x5.3ILH¢dl=If+ddtZZSD¢dSH2¢dl2+H1¢dl1=Jf¢(±h£dl2)+[@D@t¢(±h£dl2)]I@D@t±h!01.2.[@D@t¢(±h£dl2)]!0(H2¡H1)¢dl=Jf¢(±h£dl)=(Jf±h)¢(n£dl)=®f¢(n£dl)If´(H2¡H1)¡®f£n[(