电磁波辐射（PPT讲稿）Radiation of Electromagnetic Waves

2. Show the solution A satisfies Lorenz condition V.d+100=0 A 证:令t=t t'(t,x,*)vA-ko j 4丌J V·J(x’,t)+/(x,t)V-] 4丌 V·J(x,t a Vt a/(x, !r 1a(r, t') at at V·J(x,)=V·J(x,t V't t V·J(x,p a(',t Vr It'=c VJE, !")=V JE,Il t=c

2.Show the solution 、 A satisfies Lorenz condition   2 1 A 0 c t   + =  证：令 ( , , ) r t t t t x x c    = − =  = A dV r J x t V       ( , ) 4 0     0 1 1 [ ( , ) ( , ) ] 4 J x t J x t dV r r   =  +        ( , ) 1 ( , ) 1 ( , ) ( , ) J x t J x t J x t J x t t r r t c t c t           =  = −  =             = − r r  ( , ) ( , ) ( , ) 1 ( , ) ( , ) t c t c J x t J x t J x t t t J x t J x t r c t = =      =   +               =   −        J (x ,t ) J (x ,t ) J (x ,t ) t c    =    −    =      

V·A V.J(, t)+J(x', tV'-lav 4丌 t=c ∫vY)m V′.( (x,t) C 4丌 S t=c m 1 dp(, t)Ot 00(x,t) at tEc at' at 4丌 V·A+ 1 ao 了(x ap( ,2ot4丌! -,.at 0电荷守恒定律

 A =          =  J x t dV r t c ( , ) 1 4 0         −   +    dV  r J x t J x t r ] 1 ( , ) ( , ) 1 [     0 1 ( , ) 4 t c J x t dV r   = =      J x t ( , ) dV r      ( , ) 0 S J x t dS r  =  =  2 2 0 1 1 1 ( , ) 4 V x t t dV c c t r t t          =       0 1 ( , ) 4 V x t dV r t       =     =     + c t A  2 1  0 1 ( , ) [ ( , ) ] 0 4 t c x t J x t dV r t    =      + =         0 电荷守恒定律