Уравнения Максвелла (55
..pdfɦɭ ɩɪɨɫɬɪɚɧɫɬɜɭ. Ⱥɧɚɥɨɝɢɱɧɵɟ ɢɧɬɟɝɪɚɥɵ ɨɬ ɩɨɫɥɟɞɭɸɳɢɯ ɱɥɟɧɨɜ ɩɪɟɨɛɪɚɡɭɸɬɫɹ ɜ ɢɧɬɟɝɪɚɥɵ ɩɨ ɛɟɫɤɨɧɟɱɧɨ ɭɞɚɥɟɧɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɨɛɪɚɳɚɸɬɫɹ ɜ ɧɭɥɶ ɜɫɥɟɞɫɬɜɢɟ ɨɬɫɭɬɫɬɜɢɹ ɧɚ ɷɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɡɚɪɹɞɨɜ ɢ ɬɨɤɨɜ. ɉɨɷɬɨɦɭ
³dV P& |
³dV r&U, |
(15.16) |
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& |
1 |
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&& |
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³dV M |
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³dV[r j]. |
(15.17) |
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2c |
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ɢ M& ɡɚɱɚɫɬɭɸ ɨɬɨɠɞɟɫɬɜɥɹ- |
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ɇɚ ɨɫɧɨɜɚɧɢɢ ɷɬɢɯ ɪɚɜɟɧɫɬɜ P& |
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ɸɬ ɫ ɩɥɨɬɧɨɫɬɹɦɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɞɢɩɨɥɶɧɵɯ ɦɨɦɟɧɬɨɜ. Ɉɞɧɚɤɨ ɢɡ ɢɡɥɨɠɟɧɧɨɝɨ ɜɵɲɟ ɹɫɧɨ, ɱɬɨ ɬɚɤɚɹ ɢɧɬɟɪɩɪɟɬɚɰɢɹ ɧɟɬɨɱɧɚ.
ɂɡ ɫɨɨɬɧɨɲɟɧɢɣ (15.1) ɢ (15.2), ɫ ɨɞɧɨɣ ɫɬɨɪɨɧɵ, ɢ (15.14) ɢ (15.15), ɫ ɞɪɭɝɨɣ, ɫɥɟɞɭɟɬ, ɱɬɨ ɜ ɫɥɭɱɚɟ ɩɪɨɢɡɜɨɥɶɧɨɣ ɷɥɟɤɬɪɨɧɟɣɬɪɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɞɥɹ ɨɩɢɫɚɧɢɹ ɪɚɫɩɨɥɨɠɟɧɢɹ ɢ ɞɜɢɠɟɧɢɹ ɡɚɪɹɞɨɜ ɜɦɟɫɬɨ ɩɚɪɵ ɮɭɧɤɰɢɣ U(r&,t) ɢ &j(r&,t) ɦɨɠɧɨ ɢɫɩɨɥɶɡɨ-
ɜɚɬɶ ɩɚɪɭ ɮɭɧɤɰɢɣ P&(r&,t) ɢ M& (r&,t) . ɉɪɢ ɷɬɨɦ ɞɥɹ ɪɚɡɧɵɯ ɝɪɭɩɩ
ɡɚɪɹɞɨɜ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɪɚɡɧɵɟ ɩɚɪɵ ɮɭɧɤɰɢɣ. ȿɫɥɢ, ɧɚɩɪɢɦɟɪ, ɫɢɫɬɟɦɭ ɡɚɪɹɞɨɜ ɪɚɡɛɢɬɶ ɧɚ ɞɜɟ ɩɨɞɫɢɫɬɟɦɵ I ɢ II , ɩɥɨɬɧɨɫɬɢ ɡɚɪɹɞɚ ɢ ɬɨɤɚ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɫɭɦɦ U U(I) U(II)
ɢ &j &j (I) &j (II) , ɚ ɡɚɬɟɦ ɞɥɹ (ɷɥɟɤɬɪɨɧɟɣɬɪɚɥɶɧɨɣ) ɩɨɞɫɢɫɬɟɦɵ I
ɮɭɧɤɰɢɢ U(I) ɢ &j (I) ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (15.1) ɢ (15.2) ɜɵɪɚɡɢɬɶ ɱɟ-
ɪɟɡ ɮɭɧɤɰɢɢ P&(I) ɢ M& (I) , ɬɨ ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɟɪɜɚɹ ɩɚɪɚ (14.3) ɭɪɚɜɧɟɧɢɣ Ɇɚɤɫɜɟɥɥɚ ɧɟ ɢɡɦɟɧɢɬɫɹ, ɚ ɜɬɨɪɚɹ ɩɚɪɚ (14.4) ɡɚɩɢɲɟɬɫɹ ɜ ɜɢɞɟ:
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& |
& |
(I) |
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1 w(E& |
4SP&(I) ) |
4S & |
(II) |
, |
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°rot (B |
4SM |
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c |
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wt |
c |
j |
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(15.18) |
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® |
& |
&(I) |
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° |
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4SU |
(II) |
, |
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¯div(E 4SP |
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ɢɥɢ ɠɟ ɜ ɱɟɬɵɪɟɯɦɟɪɧɨɣ ɮɨɪɦɟ:
31
w |
Fkl 4Smkl(I) 4cS jk(II) . |
(15.19) |
wx |
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l |
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ɂɦɟɧɧɨ ɬɚɤ ɢ ɞɟɥɚɟɬɫɹ ɜ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɟ ɫɩɥɨɲɧɵɯ ɫɪɟɞ ɩɪɢ ɪɚɡɞɟɥɟɧɢɢ ɡɚɪɹɞɨɜ ɢ ɬɨɤɨɜ ɧɚ ɬɚɤ ɧɚɡɵɜɚɟɦɵɟ ɫɜɹɡɚɧɧɵɟ ɢ ɫɬɨɪɨɧɧɢɟ.
32
ȾɅə ɁȺɆȿɌɈɄ
ǽȜȝȜȐ ǻ.Ǯ.
ȁȞȎȐțȓțȖȭ ǺȎȘȟȐȓșșȎ
Издательство «Прометей» 115035, Москва, ул. Садовническая, д.72, стр.1
Тел/факс: 8 (495) 799-54-29 E-mail: info@prometej.su
ǽȜȒȝȖȟȎțȜ Ȑ ȝȓȥȎȠȪ 23.07.2012 ȑ.
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