Конспекты лекций по электродинамике. Розман Г.А. - 66 стр.

åäèíèöó âðåìåíè â åäèíèöó îáúåìà. Åñëè ðàññìàòðèâàòü íå
äèôôåðåíöèàëüíóþ ôîðìó, à èíòåãðàëüíóþ, òî ðàáîòà ñòîðîííèõ ñèë
ñîâåðøàëàñü áû çà ñ÷åò èõ ýíåðãèè, ðàññðåäîòî÷åííîé âî âñåì îáúåìå.
               Äæ
     Òàê êàê      = Âò , òî ìîæíî ãîâîðèòü î ìîùíîñòè ñòîðîííèõ ñèë,
                ñ
çàêëþ÷åííûõ â åäèíèöå îáúåìà.
     Ðàññìîòðèì êàæäûé ÷ëåí ñëåâà â (**):

                j2   l 1 l  1 R⋅s
                = R=ρ =    ⇒ =    =
               σ     s σ s  σ  l
                Êë 2  Îì ⋅ ì 2 Êë 2 ⋅ Îì ⋅ ì 2    À2 ⋅ ñ 2 ⋅ Îì
                       ⋅      =                 =               =
               ñ2 ì4    ì         ñ2 ⋅ ì4 ⋅ ì       ñ2 ⋅ ì3
                     U
                 I=
                     R             À2 ⋅ Â ⋅ ñ    Äæ
               =                =             =      .
                              A À⋅ ì ⋅ ñ ñ ⋅ ì3
                                         3
                 R = ; [R ] =
                     U
                      I       B


      j2
         - ýòî òà âíóòðåííÿÿ ýíåðãèÿ, êîòîðàÿ âûäåëÿåòñÿ â åäèíèöå
      σ
îáúåìà â åäèíèöó âðåìåíè â öåïè ïðè ïðîõîæäåíèè òîêà. Åñëè â öåïè
íåò ïðîâîäèìîñòè, ýòîò ÷ëåí ðàâåí íóëþ.
     Ðàññìîòðèì ñìûñë âòîðîãî ÷ëåíà:
                                                                 [ ]
             ∂ εε 0 E 2 + µµ 0 H 2   ∂ µµ 0 H 2  [∂ ][µ ][µ 0 ] H 2
                                   =            =                   =
             ∂t          2           ∂t    2           [∂t ][2]


                                         Ãí ⋅ À 2
                                       2
                               Ãí  À               Äæ
                           =         =          =        ,
                               ì⋅ñ  ì  ñ⋅ ì  3
                                                    ñ ⋅ ì3
òàê êàê Ãí ⋅ À 2 = Äæ .

     Àíàëîãè÷íî:




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