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Файл:Элементы теории образования электрического тока в грунтовых и водных средах (проводниках второго рода). Монография
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ɫɬɜɢɣ ɜ ɩɪɢɪɨɞɟ ɧɟ ɫɭɳɟɫɬɜɭɟɬ. ȿɫɥɢ ɫ ɤɚɤɢɦ-ɥɢɛɨ ɬɟɥɨɦ (ɢɥɢ ɱɚɫɬɢɰɟɣ) ɩɪɨɢɫ-
ɯɨɞɢɬ ɢɡɦɟɧɟɧɢɟ, ɬɨ ɧɚ ɞɪɭɝɨɦ ɬɟɥɟ ɷɬɨ ɨɬɪɚɡɢɬɫɹ ɥɢɲɶ ɱɟɪɟɡ ɧɟɤɨɬɨɪɵɣ ɩɪɨ-
ɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ. Ɍɨɝɞɚ, ɪɚɡɞɟɥɢɜ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɞɜɭɦɹ ɱɚɫɬɢɰɚɦɢ ɧɚ ɷɬɨɬ
ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ
, ɧɚɣɞɟɦ «ɫɤɨɪɨɫɬɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ».
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɷɬɭ ɫɤɨɪɨɫɬɶ ɦɨɠɧɨ ɧɚɡɜɚɬɶ ɦɚɤɫɢɦɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɪɚɫɩɪɨ-
ɫɬɪɚɧɟɧɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ, ɬ. ɟ. ɜ ɩɪɢɪɨɞɟ ɜɨɨɛɳɟ ɧɟɜɨɡɦɨɠɧɨ ɞɜɢɠɟɧɢɟ ɬɟɥ ɫɨ
ɫɤɨɪɨɫɬɶɸ ɛɨɥɶɲɟ ɷɬɨɣ
. ɋɨɝɥɚɫɧɨ ɩɪɢɧɰɢɩɭ ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ ɫɤɨɪɨɫɬɶ ɪɚɫɩɪɨ-
ɫɬɪɚɧɟɧɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɜɨ ɜɫɟɯ ɢɧɟɪɰɢɚɥɶɧɵɯ ɫɢɫɬɟɦɚɯ ɨɬɫɱɺɬɚ ɹɜɥɹɟɬɫɹ
ɭɧɢɜɟɪɫɚɥɶɧɨɣ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ ɫɜɟɬɚ ɜ ɩɭɫɬɨɬɟ
: ɋ = 2,998·10
10
ɫɦ/ɫ.
ɇɚ ɩɪɚɤɬɢɤɟ ɛɨɥɶɲɢɧɫɬɜɨ ɫɤɨɪɨɫɬɟɣ, ɫ ɤɨɬɨɪɵɦɢ ɩɪɢɯɨɞɢɬɫɹ ɢɦɟɬɶ ɞɟɥɨ,
ɧɚɫɬɨɥɶɤɨ ɦɚɥɵ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫɨ ɫɤɨɪɨɫɬɶɸ ɫɜɟɬɚ, ɱɬɨ ɩɪɟɞɩɨɥɨɠɟɧɢɟ ɨ ɛɟɫɤɨ-
ɧɟɱɧɨɫɬɢ ɩɨɫɥɟɞɧɟɣ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɜɥɢɹɟɬ ɧɚ ɬɨɱɧɨɫɬɶ ɪɟɡɭɥɶɬɚɬɨɜ. Ɉɛɴɟɞɢ-
ɧɟɧɢɟ ɩɪɢɧɰɢɩɚ ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ ɫ ɤɨɧɟɱɧɨɣ ɫɤɨɪɨɫɬɶɸ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɡɚɢ-
ɦɨɞɟɣɫɬɜɢɹ – ɫɨ ɫɤɨɪɨɫɬɶɸ ɫɜɟɬɚ ɧɚɡɵɜɚɟɬɫɹ ɩɪɢɧɰɢɩɨɦ ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ
ɗɣɧɲɬɟɣɧɚ
, ɚ ɦɟɯɚɧɢɤɚ, ɨɫɧɨɜɚɧɧɚɹ ɧɚ ɷɬɨɦ ɩɪɢɧɰɢɩɟ, ɧɚɡɵɜɚɟɬɫɹ ɪɟɥɹɬɢɜɢɫɬ-
ɫɤɨɣ. ɇɚɩɪɨɬɢɜ, ɩɪɢɧɰɢɩ ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ Ƚɚɥɢɥɟɹ ɢɫɯɨɞɢɬ ɢɡ ɛɟɫɤɨɧɟɱɧɨɫɬɢ
ɫɤɨɪɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
. ȼ ɩɪɟɞɟɥɶɧɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɫɤɨɪɨ-
ɫɬɢ ɞɜɢɠɭɳɢɯɫɹ ɬɟɥ ɦɚɥɵ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫɨ ɫɤɨɪɨɫɬɶɸ ɫɜɟɬɚ, ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ
ɜɥɢɹɧɢɟɦ ɤɨɧɟɱɧɨɫɬɢ ɫɤɨɪɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ ɧɚ ɞɜɢɠɟɧɢɟ
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɪɟɥɹɬɢɜɢɫɬɫɤɚɹ ɦɟɯɚɧɢɤɚ ɩɟɪɟɯɨɞɢɬ ɜ ɨɛɵɱɧɭɸ ɦɟɯɚɧɢɤɭ, ɨɫɧɨ-
ɜɚɧɧɭɸ ɧɚ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɨ ɦɝɧɨɜɟɧɧɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ.
Ɍɚɤɭɸ ɦɟɯɚɧɢɤɭ ɧɚɡɵɜɚɸɬ ɧɶɸɬɨɧɨɜɫɤɨɣ, ɢɥɢ ɤɥɚɫɫɢɱɟɫɤɨɣ. ɉɟɪɟɯɨɞ ɨɬ ɪɟɥɹ-
ɬɢɜɢɫɬɫɤɨɣ ɦɟɯɚɧɢɤɢ ɤ ɤɥɚɫɫɢɱɟɫɤɨɣ ɮɨɪɦɚɥɶɧɨ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɢɡɜɟɞɟɧ ɩɟɪɟ-
ɯɨɞɨɦ ɫɤɨɪɨɫɬɢ ɫɜɟɬɚ ɤ ɩɪɟɞɟɥɭ ɫ > ɜ ɮɨɪɦɭɥɚɯ ɪɟɥɹɬɢɜɢɫɬɫɤɨɣ ɦɟɯɚɧɢɤɢ.
ɉɨɫɤɨɥɶɤɭ ɭɠɟ ɜ ɤɥɚɫɫɢɱɟɫɤɨɣ ɦɟɯɚɧɢɤɟ ɩɪɨɫɬɪɚɧɫɬɜɨ ɨɬɧɨɫɢɬɟɥɶɧɨ, ɩɪɨ-
ɫɬɪɚɧɫɬɜɟɧɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɪɚɡɥɢɱɧɵɦɢ ɫɨɛɵɬɢɹɦɢ ɡɚɜɢɫɹɬ ɨɬ ɬɨɝɨ, ɜ
ɤɚɤɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɺɬɚ ɨɧɢ ɨɩɢɫɵɜɚɸɬɫɹ
: ɭɬɜɟɪɠɞɟɧɢɟ, ɱɬɨ ɞɜɚ ɪɚɡɧɨɜɪɟɦɟɧɧɵɯ
ɫɨɛɵɬɢɹ ɩɪɨɢɫɯɨɞɹɬ ɜ ɨɞɧɨɦ ɢ ɬɨɦ ɠɟ ɦɟɫɬɟ ɩɪɨɫɬɪɚɧɫɬɜɚ ɢɥɢ ɧɚ ɨɬɞɚɥɟɧɧɨɦ
.
91
ɪɚɫɫɬɨɹɧɢɢ ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɩɪɢɨɛɪɟɬɚɟɬ ɫɦɵɫɥ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ ɭɤɚɡɚɧɨ, ɤɤɚ-
ɤɢɦ ɫɢɫɬɟɦɚɦ ɨɬɫɱɺɬɚ ɷɬɨ ɭɬɜɟɪɠɞɟɧɢɟ ɨɬɧɨɫɢɬɫɹ.
Ɉɞɧɚɤɨ ɜɪɟɦɹ ɜ ɤɥɚɫɫɢɱɟɫɤɨɣ ɦɟɯɚɧɢɤɟ ɹɜɥɹɟɬɫɹ ɚɛɫɨɥɸɬɧɵɦ, ɬ. ɟ. ɫɜɨɣɫɬ-
ɜɚ ɜɪɟɦɟɧɢ ɫɱɢɬɚɸɬɫɹ ɧɟɡɚɜɢɫɹɳɢɦɢ ɨɬ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ – ɜɪɟɦɹ ɨɞɧɨ ɞɥɹ ɜɫɟɯ
ɫɢɫɬɟɦ ɨɬɫɱɟɬɚ
. ɇɚɩɪɨɬɢɜ, ɩɨɧɹɬɢɟ ɚɛɫɨɥɸɬɧɨɝɨ ɜɪɟɦɟɧɢ ɧɚɯɨɞɢɬɫɹ ɜ ɝɥɭɛɨɤɨɦ
ɩɪɨɬɢɜɨɪɟɱɢɢ ɫ ɷɣɧɲɬɟɣɧɨɜɫɤɢɦ ɩɪɢɧɰɢɩɨɦ ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ
ɦɟɯɚɧɢɤɟ
ɫɥɨɠɟɧɢɹ ɜɟɤɬɨɪɨɜ
, ɨɫɧɨɜɚɧɧɨɣ ɧɚ ɩɨɧɹɬɢɢ ɚɛɫɨɥɸɬɧɨɝɨ ɜɪɟɦɟɧɢ, ɢɦɟɟɬ ɦɟɫɬɨ ɡɚɤɨɧ
, ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɦɭ ɫɤɨɪɨɫɬɶ ɫɥɨɠɧɨɝɨ ɞɜɢɠɟɧɢɹ ɪɚɜɧɚ ɜɟɤ-
ɬɨɪɧɨɣ ɫɭɦɦɟ ɫɤɨɪɨɫɬɟɣ, ɫɨɫɬɚɜɥɹɸɳɢɯ ɷɬɨ ɞɜɢɠɟɧɢɟ.
ƍ
ȿɫɥɢ ɛɵ ɷɬɨɬ ɡɚɤɨɧ ɛɵɥ
ɭɧɢɜɟɪɫɚɥɶɧɵɦ
ɛɵ ɩɪɢɦɟɧɢɦ ɢ ɤ ɪɚɫɩɪɨ
ƍ
ƍ
ɫɬɪɚɧɟɧɢɸ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ.
ɗɬɨ ɨɡɧɚɱɚɥɨ ɛɵ, ɱɬɨ ɫɤɨ-
ƍ
ɪɨɫɬɶ ɷɬɨɝɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ
Ɋɢɫ
. 14.
ɂɧɟɪɰɢɚɥɶɧɵɟ ɫɢɫɬɟɦɵ ɨɬɫɱɺɬɚ
ɪɚɡɧɵɯ ɢɧɟɪɰɢɚɥɶɧɵɯ ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ
, ɱɬɨ ɩɪɨɬɢɜɨɪɟɱɢɬ ɩɪɢɧɰɢɩɭ ɨɬɧɨɫɢ-
ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɡɥɢɱɧɨɣ ɜ
. ȼ ɤɥɚɫɫɢɱɟɫɤɨɣ
, ɬɨ ɨɧ ɛɵɥ
-
ɬɟɥɶɧɨɫɬɢ ɢ ɨɩɵɬɭ Ɇɚɣɤɟɥɶɫɨɧɚ, ɤɨɬɨɪɵɣ ɭɫɬɚɧɨɜɢɥ ɩɨɥɧɭɸ ɧɟɡɚɜɢɫɢɦɨɫɬɶ
ɫɤɨɪɨɫɬɢ ɫɜɟɬɚ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɟɝɨ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ
. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɪɟɦɹ ɬɟ-
ɱɟɬ ɩɨ-ɪɚɡɧɨɦɭ ɜ ɪɚɡɧɵɯ ɫɢɫɬɟɦɚɯ ɨɬɫɱɟɬɚ, ɜɪɟɦɹ ɧɟ ɹɜɥɹɟɬɫɹ ɚɛɫɨɥɸɬɧɵɦ. ɋɨ-
ɛɵɬɢɹ, ɨɞɧɨɜɪɟɦɟɧɧɵɟ ɜ ɧɟɤɨɬɨɪɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ, ɛɭɞɭɬ ɧɟɨɞɧɨɜɪɟɦɟɧɧɵɦɢ
ɜɞɪɭɝɨɣɫɢɫɬɟɦɟ
. Ⱦɥɹ ɩɨɧɢɦɚɧɢɹ ɷɬɨɝɨ ɜɨɩɪɨɫɚ ɩɪɢɜɟɞɟɦ ɪɢɫɭɧɨɤ, ɢɫɩɨɥɶɡɭɟ-
ɦɵɣ Ʌ.Ⱦ. Ʌɚɧɞɚɭ ɢ ȿ.Ɇ. Ʌɢɮɲɢɰɟɦ.
ɇɚ ɪɢɫ. 14 ɩɪɟɞɫɬɚɜɥɟɧɵ ɞɜɟ ɢɧɟɪɰɢɚɥɶɧɵɟ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ Ʉ ɢ Ʉƍɫɨɫɹ-
ɦɢ ɤɨɨɪɞɢɧɚɬ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ X YZ ɢ Xƍɍ
ɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ Ʉ ɜɞɨɥɶ ɨɫɟɣ X ɢ X
ƍZƍ
. ɋɢɫɬɟɦɚ Ʉ
ƍ
. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɫɨɛɵɬɢɟ ɩɪɨɢɡɨɲ-
ƍ
ɞɜɢɠɟɬɫɹ ɜɩɪɚɜɨ ɨɬ-
ɥɨ ɜ ɬɨɱɤɟ Ⱥ ɧɚ ɨɫɢ Xƍɢ ɫɢɝɧɚɥ ɧɚɩɪɚɜɥɹɟɬɫɹ ɜ ɞɜɭɯ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɧɚɩɪɚɜ-
92
ɥɟɧɢɹɯ. ɉɨɫɤɨɥɶɤɭ ɫɤɨɪɨɫɬɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɫɢɝɧɚɥɚ ɜɨ ɜɫɹɤɨɣ ɢɧɟɪɰɢɚɥɶɧɨɣ
ɫɢɫɬɟɦɟ ɪɚɜɧɚ ɜ ɨɛɨɢɯ ɧɚɩɪɚɜɥɟɧɢɹɯ
, ɬɨ ɫɢɝɧɚɥɵ ɜ ɫɢɫɬɟɦɟ Ʉ
ƍ
ɞɨɫɬɢɝɧɭɬ ɪɚɜɧɨ-
ɭɞɚɥɟɧɧɵɟ ɨɬ ɬɨɱɤɢ Ⱥ ɬɨɱɤɢ ȼ ɢ ɋ ɜ ɨɞɢɧ ɢ ɬɨɬ ɠɟ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ. Ɉɞɧɚɤɨ ɞɥɹ
ɧɚɛɥɸɞɚɬɟɥɹ ɜ ɫɢɫɬɟɦɟ Ʉ ɩɪɢɯɨɞ ɫɢɝɧɚɥɚɜȼɢɋɛɭɞɟɬɨɬɧɸɞɶɧɟɨɞɧɨɜɪɟɦɟɧ
ɧɵɦ, ɯɨɬɹ ɫɤɨɪɨɫɬɶ ɫɢɝɧɚɥɨɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ Ʉ, ɫɨɝɥɚɫɧɨ ɩɪɢɧɰɢɩɭ ɨɬ-
ɧɨɫɢɬɟɥɶɧɨɫɬɢ, ɪɚɜɧɚ ɬɨɣ ɠɟ ɋ. ɂɡ ɪɢɫ. 14 ɥɟɝɤɨ ɜɢɞɟɬɶ, ɱɬɨ ɬɨɱɤɚ ȼ ɞɜɢɠɟɬɫɹ
ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ Ʉ ɧɚɜɫɬɪɟɱɭ ɩɨɫɥɚɧɧɨɦɭ ɜ ɧɟɟ ɫɢɝɧɚɥɭ
, ɚ ɬɨɱɤɚ ɋ – ɩo
ɧɚɩɪɚɜɥɟɧɢɸ ɨɬ ɫɢɝɧɚɥɚ, ɩɨɫɥɚɧɧɨɝɨ ɢɡ Ⱥ ɜ ɋ, ɩɨɷɬɨɦɭ ɜ ɫɢɫɬɟɦɟ Ʉ ɫɢɝɧɚɥ ɩɪɢ-
ɞɟɬ ɜ ɬɨɱɤɭ ȼ ɪɚɧɶɲɟ, ɱɟɦ ɜ ɬɨɱɤɭ ɋ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɗɣɧɲɬɟɣɧ ɜɧɟɫ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɟ ɢɡɦɟɧɟɧɢɹ ɜ ɨɫɧɨɜɧɵɟ
ɮɢɡɢɱɟɫɤɢɟ ɩɨɧɹɬɢɹ
ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɚɩɩɚɪɚɬɚ ɞɥɹ ɨɩɢɫɚɧɢɹ ɩɪɨɰɟɫɫɨɜ
ɜɨɨɛɳɟ ɢ ɜ ɫɢɫɬɟɦɟ ɤɚɬɨɞɧɨɣ ɡɚɳɢɬɵ ɜ ɱɚɫɬɧɨɫɬɢ
, ɤɨɬɨɪɵɦɢ ɧɟɥɶɡɹ ɩɪɟɧɟɛɪɟɝɚɬɶ ɩɪɢ ɜɵɛɨɪɟ ɢɥɢ ɪɚɡɪɚɛɨɬɤɟ
, ɩɪɨɢɫɯɨɞɹɳɢɯ ɜ ɩɪɢɪɨɞɟ
.
-
Ɉɬɦɟɱɚɹ ɜɚɠɧɨɫɬɶ ɪɚɫɫɦɨɬɪɟɧɢɹ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɬɟɤɚɸɳɢɯ ɩɪɢ ɩɨɞɡɟɦɧɨɣ
ɤɨɪɪɨɡɢɢ ɫɬɚɥɶɧɵɯ ɫɨɨɪɭɠɟɧɢɣ
, ɭɱɢɬɵɜɚɹ ɤɥɚɫɫɢɱɟɫɤɢɟ ɡɚɤɨɧɵ ɷɥɟɤɬɪɨɯɢɦɢ-
ɱɟɫɤɨɣ ɤɢɧɟɬɢɤɢ, ɫɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɜɵɲɟɨɩɢɫɵɜɚɟɦɨɣ ɥɨ-
ɝɢɤɨɣ ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ ɗɣɧɲɬɟɣɧɚ, ɫɨɛɵɬɢɹ, ɩɪɨɢɫɯɨɞɹɳɢɟ ɧɚ ɚɧɨɞɧɨɦ ɡɚɡɟɦ-
ɥɟɧɢɢ, ɢɫɨɛɵɬɢɹ, ɩɪɨɢɫɯɨɞɹɳɢɟ ɧɚ ɤɚɬɨɞɧɨɦ ɡɚɳɢɳɚɟɦɨɦ ɫɨɨɪɭɠɟɧɢɢ, ɧɟ ɦɨ-
ɝɭɬ ɛɵɬɶ ɜɪɟɦɟɧɢɩɨɞɨɛɧɵɦɢ. Ɉɛɴɹɫɧɟɧɢɟɦ ɷɬɨɝɨ ɹɜɥɹɟɬɫɹ ɦɧɨɝɨɜɟɤɨɜɨɣ ɨɩɵɬ:
1.
ɉɨɥɹɪɢɡɚɰɢɹ ɷɥɟɤɬɪɨɞɨɜ ɜ ɫɢɫɬɟɦɟ ɤɚɬɨɞɧɨɣ ɡɚɳɢɬɵ ɹɜɥɹɟɬɫɹ ɫɥɟɞɫɬɜɢ-
ɟɦ ɨɬɫɬɚɜɚɧɢɹ ɷɥɟɤɬɪɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɨɬ ɬɨɤɚ ɷɥɟɤɬɪɨɧɨɜ ɜ ɝɚɥɶɜɚɧɢɱɟɫɤɨɦ
ɷɥɟɦɟɧɬɟ
ɷɥɟɤɬɪɨɧɨɜ ɨɬ ɚɧɨɞɚ ɤ ɤɚɬɨɞɭ
. Ⱥɧɨɞɧɵɣ ɩɪɨɰɟɫɫ ɜɵɯɨɞɚ ɢɨɧɨɜ ɦɟɬɚɥɥɚ ɜ ɷɥɟɤɬɪɨɥɢɬ ɨɬɫɬɚɺɬ ɨɬ ɬɨɤɚ
. Ʉɚɬɨɞɧɵɣ ɩɪɨɰɟɫɫ ɚɫɫɢɦɢɥɹɰɢɢ ɷɥɟɤɬɪɨɧɨɜ ɨɬ-
ɫɬɚɺɬ ɨɬ ɩɨɫɬɭɩɥɟɧɢɹ ɧɚ ɤɚɬɨɞ ɷɥɟɤɬɪɨɧɨɜ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɨɬɪɢɰɚ-
ɬɟɥɶɧɨɝɨ ɡɚɪɹɞɚ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɷɥɟɤɬɪɨɞɚ ɢ ɞɟɥɚɟɬ ɩɨɬɟɧɰɢɚɥ ɤɚɬɨɞɚ ɛɨɥɟɟ ɨɬ-
ɪɢɰɚɬɟɥɶɧɵɦ. [16]
2.
ɉɨɥɹɪɢɡɚɰɢɨɧɧɚɹ ɤɪɢɜɚɹ ɹɜɥɹɟɬɫɹ ɡɚɜɢɫɢɦɨɫɬɶɸ ɧɚɩɪɹɠɟɧɢɹ (ɨɬɤɥɨɧɟ-
ɧɢɹ ɩɨɬɟɧɰɢɚɥɚ ɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɞɚ ɨɬ ɩɨɬɟɧɰɢɚɥɚ ɧɟɩɨɥɹɪɢɡɨɜɚɧɧɨɝɨ)
93
ɨɬ ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ JS. ɋɬɪɨɝɨ ɝɨɜɨɪɹ, ɩɨɥɹɪɢɡɚɰɢɨɧɧɵɟ ɤɪɢɜɵɟ ɨɛɪɚɡɭɸɬ ɫɭɦ-
ɦɚɪɧɭɸ ɩɨɥɹɪɢɡɚɰɢɨɧɧɭɸ ɤɪɢɜɭɸ, ɩɨɷɬɨɦɭ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɟ ɢɡɦɟɪɟɧɢɟ ɩɨɥɹ-
ɪɢɡɚɰɢɢ ɧɟɜɨɡɦɨɠɧɨ.
3.
Ⱦɜɨɣɧɨɣ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɫɥɨɣ ɧɟ ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɚɦɢ ɨɛɵɱɧɨɝɨ ɤɨɧɞɟɧ-
ɫɚɬɨɪɚ – ɺɦɤɨɫɬɶ ɞɜɨɣɧɨɝɨ ɫɥɨɹ ɡɚɜɢɫɢɬ ɨɬ ɭɪɨɜɧɹ ɧɚɩɪɹɠɟɧɢɹ, ɩɪɢɥɨɠɟɧɧɨɝɨ ɤ
ɷɥɟɤɬɪɨɞɚɦ ɢɫɬɨɱɧɢɤɚ ɩɨɫɬɨɹɧɧɨɝɨ ɢ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɬɨɤɚ
4.
ɉɨɬɟɧɰɢɚɥɶɧɚɹ ɫɢɫɬɟɦɚ ɡɚɳɢɳɚɟɦɨɝɨ ɫɨɨɪɭɠɟɧɢɹ ɢɡɧɚɱɚɥɶɧɨ ɹɜɥɹɟɬɫɹ
ɝɚɥɶɜɚɧɢɱɟɫɤɢɦ ɷɥɟɦɟɧɬɨɦ
ɢɫɬɨɱɧɢɤɨɦ ɬɨɤɚ
[14].
(ɢɫɬɨɱɧɢɤɨɦ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ) ɧɟ ɗȾɋ, ɚ
.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɥɹ ɨɩɢɫɚɧɢɹ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɢɫɯɨɞɹɳɢɯ ɜ ɫɢɫɬɟɦɟ ɤɚɬɨɞ-
ɧɨɣ ɡɚɳɢɬɵ, ɧɟɨɛɯɨɞɢɦɨ ɢɦɟɬɶ ɱɟɬɵɪɺɯɦɟɪɧɭɸ ɫɢɫɬɟɦɭ ɨɬɫɱɺɬɨɜ ɏ, Y, Z ɢ t ɫ
ɰɟɥɶɸ ɨɩɪɟɞɟɥɟɧɢɹ
«ɢɧɬɟɪɜɚɥɨɜ» ɦɟɠɞɭ ɫɨɛɵɬɢɹɦɢ ɧɚ ɚɧɨɞɟ ɢ ɤɚɬɨɞɟ:
222222
dzdydxdtCds
−−−=
ɩɨɫɤɨɥɶɤɭ ɩɨɥɭɱɢɬɶ ɞɨɫɬɨɜɟɪɧɵɟ ɪɟɡɭɥɶɬɚɬɵ
,
ɩɪɨɢɫɯɨɞɹɳɢɯ ɩɪɨɰɟɫɫɨɜ ɜ ɫɢɫɬɟɦɟ ɤɚɬɨɞɧɨɣ ɡɚɳɢɬɵ ɩɨ ɤɥɚɫɫɢɱɟɫɤɢɦ ɯɢɦɢɤɨ
ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɦ ɮɨɪɦɭɥɚɦ, ɩɨ-ɜɢɞɢɦɨɦɭ, ɧɟɜɨɡɦɨɠɧɨ.
ɉɪɢ ɷɬɨɦ ɧɚɩɨɦɧɢɦ [4], ɱɬɨ ɩɟɪɟɞɚɱɚ ɥɸɛɨɣ ɷɧɟɪɝɢɢ ɩɪɨɢɡɜɨɞɢɬɫɹ ɜ ɪɟ-
ɡɭɥɶɬɚɬɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ ɬɟɥ, ɢ ɬɨɥɶɤɨ ɜ ɞɜɭɯ ɮɨɪɦɚɯ: ɜ ɮɨɪɦɟ ɪɚɛɨɬɵ ɢ ɬɟɩɥɨ-
-
ɬɵ. ɉɟɪɟɞɚɱɚ ɷɧɟɪɝɢɢ ɜ ɮɨɪɦɟ ɪɚɛɨɬɵ ɩɪɨɢɡɜɨɞɢɬɫɹ ɜ ɩɪɨɰɟɫɫɟ ɫɢɥɨɜɨɝɨ ɜɡɚɢ-
ɦɨɞɟɣɫɬɜɢɹ ɬɟɥ, ɚ ɩɟɪɟɞɚɱɚ ɷɧɟɪɝɢɢ ɩɭɬɺɦ ɬɟɩɥɨɨɛɦɟɧɚ ɨɛɭɫɥɨɜɥɟɧɚ ɪɚɡɥɢɱɢɟɦ
ɬɟɦɩɟɪɚɬɭɪ ɢ ɦɨɠɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɤɚɤ ɩɪɢ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɦ ɤɨɧɬɚɤɬɟ ɬɟɥ
–
ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ ɢ ɤɨɧɜɟɤɬɢɜɧɵɣ ɬɟɩɥɨɨɛɦɟɧ, ɬɚɤ ɢ ɱɟɪɟɡ ɩɨɫɪɟɞɫɬɜɨ ɢɫɩɭɫ-
ɤɚɧɢɹ ɱɚɫɬɢɰ ɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ – ɥɭɱɢɫɬɵɣ ɬɟɩɥɨɨɛɦɟɧ. ɉɪɢ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɦɟɠɞɭ ɦɢɤɪɨɱɚɫɬɢɰɚɦɢ
–
ɝɨɜɨɪɹɬ ɥɢɲɶ ɨ ɩɪɨɰɟɫɫɚɯ ɫɨɜɟɪɲɟɧɢɹ ɪɚɛɨɬɵ. Ⱥɷɧɟɪɝɢɹ, ɩɨɥɭɱɚɟɦɚɹ ɬɟɥɨɦ ɜ
ɮɨɪɦɟ ɬɟɩɥɨɬɵ
, ɦɨɠɟɬ ɩɨɣɬɢ ɬɨɥɶɤɨ ɧɚ ɭɜɟɥɢɱɟɧɢɟ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɬɟɥɚ.
– ɚɬɨɦɚɦɢ, ɷɥɟɤɬɪɨɧɚɦɢ, ɢɨɧɚɦɢ ɢ ɬ.ɩ.
ȼɫɟ ɢɡɜɟɫɬɧɵɟ ɞɨ ɫɢɯ ɩɨɪ ɩɨɩɵɬɤɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɨɰɟɧɢɬɶ ɢɡɦɟɧɟɧɢɹ ɷɧɟɪ-
ɝɢɢ ɢɥɢ ɷɧɬɚɥɶɩɢɢ ɩɪɢ ɫɨɥɶɜɚɬɚɰɢɢ ɤɚɬɢɨɧɚ ɢɥɢ ɚɧɢɨɧɚ ɧɚɬɚɥɤɢɜɚɸɬɫɹ ɧɚ ɧɟ-
94
ɩɪɟɨɞɨɥɢɦɨɟ ɭɫɥɨɜɢɟ ɷɥɟɤɬɪɨɧɟɣɬɪɚɥɶɧɨɫɬɢ [18]. Ɋɚɛɨɬɚ, ɤɨɬɨɪɭɸ ɧɟɨɛɯɨɞɢɦɨ
ϕ
ɡɚɬɪɚɬɢɬɶ ɞɥɹ ɩɟɪɟɯɨɞɚ ɨɞɧɨɝɨ ɝɪɚɦɦɚ
ɮɚɡ
, ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ,
⋅⋅
FZ
i
, ɝɞɟ: Z
ij – ɩɨɜɟɪɯɧɨɫɬɧɵɣ ɩɨɬɟɧɰɢɚɥ. ɏɢɦɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɫɨɥɶɜɚɬɚɰɢɢ ɢɨɧɨɜ
-ɢɨɧɚ ɢɨɧɨɜ ɱɟɪɟɡ ɝɪɚɧɢɰɭ ɪɚɡɞɟɥɚ ɞɜɭɯ
– ɡɚɪɹɞ ɢɨɧɚ; F – ɱɢɫɥɨ Ɏɚɪɚɞɟɹ;
i
X
G
Δ
ɫɨɥɶɜ
ɧɟ ɭɱɢɬɵɜɚɟɬ ɪɚɛɨɬɵ ɜ ɮɚɡɨɜɨɦ ɩɟɪɟɯɨɞɟ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɭɳɟɫɬɜɭɟɬ ɫɥɟɞɭɸ-
ɳɟɟ ɫɨɨɬɧɨɲɟɧɢɟ ,
P
ɫɨɥɶɜ
i
X
..
iɫɨɥɶɜ
ϕ⋅⋅+=Δ
FZGG
i
ɝɞɟ ɡɚɪɹɞ ɢɨɧɚ Z
ɛɟɪɺɬɫɹ ɫ ɭɱɺ-
i
ɬɨɦ ɟɝɨ ɡɧɚɤɚ. Ʉɚɤ ɜɢɞɢɦ, ɞɥɹ ɤɨɥɢɱɟɫɬɜɟɧɧɨɝɨ ɧɚɯɨɠɞɟɧɢɹ ɡɧɚɱɟɧɢɹ ij ɧɟɨɛ-
ɯɨɞɢɦɨ ɡɧɚɬɶ ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ ɜ ɪɚɡɧɵɯ ɮɚɡɚɯ, ɢɡɦɟɪɢɬɶ ɷɬɭ ɪɚɡɧɨɫɬɶ ɧɟ
ɭɞɚɺɬɫɹ
ɫɦɵɫɥɚ
, ɚ ɧɟɤɨɬɨɪɵɟ ɢɫɫɥɟɞɨɜɚɬɟɥɢ ɫɱɢɬɚɸɬ, ɱɬɨ ɨɧɚ ɧɟ ɢɦɟɟɬ ɮɢɡɢɱɟɫɤɨɝɨ
. Ɉɱɟɜɢɞɧɨ, ɩɪɚɜɢɥɶɧɨ ɛɭɞɟɬ, «ɟɫɥɢ ɛɭɞɟɦ ɝɨɜɨɪɢɬɶ ɨɛ ɢɡɦɟɧɟɧɢɢ ɪɟ-
ɚɥɶɧɨɣ ɢɨɧɧɨɣ ɫɨɥɶɜɚɬɚɰɢɢ, ɚ ɧɟ ɞɟɥɢɬɶ ɢɡɦɟɧɟɧɢɟ ɷɧɟɪɝɢɢ ɩɪɢ ɫɨɥɶɜɚɬɚɰɢɢ
ɢɨɧɨɜ ɧɚ ɢɨɧɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ
» [18].
ɉɨɷɬɨɦɭ, ɱɬɨɛɵ ɧɚɣɬɢ ɫɢɫɬɟɦɭ ɨɬɫɱɺɬɚ ɫ ɬɪɟɛɭɟɦɵɦɢ ɫɜɨɣɫɬɜɚɦɢ, ɧɟɨɛɯɨ-
.
i
ɞɢɦɨ ɩɪɢɧɹɬɶ ɜɨ ɜɧɢɦɚɧɢɟ ɜɜɟɞɺɧɧɵɟ ɜ ɫɜɹɡɢ ɫ ɩɪɢɧɰɢɩɨɦ ɗɣɧɲɬɟɣɧɚ ɩɨɧɹ-
ɬɢɹ: ɜɪɟɦɹ ɧɟ ɹɜɥɹɟɬɫɹ ɚɛɫɨɥɸɬɧɵɦ; ɫɨɛɵɬɢɹ ɨɩɪɟɞɟɥɹɸɬɫɹ ɬɪɟɦɹ ɤɨɨɪɞɢɧɚɬɚ-
ɦɢ ɢ ɦɨɦɟɧɬɨɦ ɜɪɟɦɟɧɢ; ɜɫɹɤɨɣ ɱɚɫɬɢɰɟ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬɚɯ ɫɨ-
ɨɬɜɟɬɫɬɜɭɟɬ ɦɢɪɨɜɚɹ ɥɢɧɢɹ. ɉɨɧɹɬɢɟ ɢɧɬɟɪɜɚɥɚ ɦɟɠɞɭ ɞɜɭɦɹ ɫɨɛɵɬɢɹɦɢ: ɜɪɟ-
ɦɟɧɢɩɨɞɨɛɧɵɟ ɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɩɨɞɨɛɧɵɟ – ɚɛɫɨɥɸɬɧɨɟ.
Ȼɭɞɟɦ ɭɱɢɬɵɜɚɬɶ, ɱɬɨ ɜ ɥɸɛɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɰɟɩɢ, ɜ ɬɨɦ ɱɢɫɥɟ ɢ ɷɥɟɤ-
ɬɪɨɞɧɨɣ, ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ ɧɟɪɚɡɪɵɜɧɨ ɫɜɹɡɚɧ ɫ ɦɚɝɧɢɬɧɵɦɢ ɢ ɷɥɟɤɬɪɢɱɟɫɤɢ-
ɦɢ ɩɨɥɹɦɢ, ɚ «ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɦɟɠɞɭ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɢ ɫɪɟɞɨɣ ɨɛɭ-
ɫɥɨɜɥɢɜɚɟɬɫɹ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɦɢ ɱɚɫɬɢɰɚɦɢ, ɧɟɡɚɜɢɫɢɦɨ ɪɚɫɩɪɟɞɟ-
ɥɺɧɧɵɦɢ ɜ ɬɟɥɟ ɢɥɢ ɫɜɹɡɚɧɧɵɦɢ ɜ ɞɢɩɨɥɢ». ɂɫɯɨɞɹ ɢɡ ɬɨɝɨ, ɱɬɨ ɬɨɤ ɜ ɷɥɟɤɬɪɨ-
ɥɢɬɟ ɹɜɥɹɟɬɫɹ ɫɭɦɦɚɪɧɨɣ ɜɟɥɢɱɢɧɨɣ, ɨɛɪɚɡɨɜɚɧɧɨɣ ɜɫɬɪɟɱɧɵɦ ɢ ɨɞɧɨɜɪɟɦɟɧ-
ɧɵɦ ɞɜɢɠɟɧɢɟɦ ɚɧɢɨɧɨɜ ɢ ɤɚɬɢɨɧɨɜ, ɢ 1ȼ = 1,6·10
1Ⱥ = 6,25·10
18
ɷɥ. ɡɚɪɹɞ / ɫ, ɨɱɟɜɢɞɧɨ, ɜɷɬɨɦɫɥɭɱɚɟP = 6,25·10
–19
Ⱦɠ / ɷɥ. ɡɚɪɹɞ, ɚ
18
·I·1,6×10
–19
·U.
ɉɪɢ ɷɬɨɦ ɞɥɹ ɤɚɠɞɨɝɨ ɭɪɨɜɧɹ ɧɟɨɛɯɨɞɢɦɨ ɨɬɥɢɱɚɬɶ ɬɨɤ ɷɥɟɤɬɪɨɧɧɵɣ, ɢɡɦɟɪɹɟ-
95
ɦɵɣ ɚɦɩɟɪɦɟɬɪɨɦ ɜ ɰɟɩɢ, ɨɬ ɬɨɤɚ ɦɟɠɞɭ ɚɧɨɞɨɦ ɢ ɤɚɬɨɞɨɦ; U – ɩɚɞɟɧɢɟ ɧɚɩɪɹ-
ɠɟɧɢɹ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɬɨɤɚ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɢɫɬɨɱɧɢɤɚ ɩɢɬɚɧɢɹ.
ɉɨɥɧɚɹ ɦɨɳɧɨɫɬɶ, ɩɨɞɜɟɞɺɧɧɚɹ ɤ ɷɥɟɤɬɪɨɥɢɬɢɱɟɫɤɨɣ «ɜɚɧɧɟ», ɫɨɫɬɚɜɥɹɟɬ
[5]
+ Q,
ɝɞɟ W
ɷɥ.ɦɚɝɧ
P = W
ɷɥ.ɦɚɝɧ.
– ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɷɧɟɪɝɢɹ ɧɚ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɯɢɦɢɱɟɫɤɨɣ ɷɧɟɪ-
ɝɢɢ; Q – ɦɨɳɧɨɫɬɶ, ɩɪɟɨɛɪɚɡɨɜɚɧɧɚɹ ɜ ɬɟɩɥɨɬɭ.
Ɉɞɧɨɜɪɟɦɟɧɧɨɟ ɢ ɩɪɨɬɢɜɨɩɨɥɹɪɧɨɟ ɞɜɢɠɟɧɢɟ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ (ɚɧɢɨɧɨɜ
ɢɤɚɬɢɨɧɨɜ
) ɜ ɷɥɟɤɬɪɨɥɢɬɢɱɟɫɤɨɣ «ɜɚɧɧɟ» ɩɨɡɜɨɥɹɟɬ ɫɞɟɥɚɬɶ ɜɵɜɨɞ, ɱɬɨ ɦɨɥɟ-
ɤɭɥɹɪɧɨ-ɤɢɧɟɬɢɱɟɫɤɢɟ ɫɤɨɪɨɫɬɢ ɪɚɡɥɢɱɚɸɬɫɹ ɦɟɠɞɭ ɫɨɛɨɣ ɢ ɫɤɥɚɞɵɜɚɸɬɫɹ. Ɍɚ-
ɤɢɦ ɨɛɪɚɡɨɦ, ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɜ ɫɢɫɬɟɦɟ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ
P
ɮɨɪɦɭɥɟ
ɧɢɹ ɨɬ U
I
min
=
U
ɞɨ U
max
101,6106,25
⋅⋅⋅⋅
.
ɩɨɫɬɨɹɧɧɨɝɨ ɢɥɢ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟ-
1918
−
ȼ ɫɜɹɡɢ ɫ ɜɵɲɟɢɡɥɨɠɟɧɧɵɦ ɩɪɟɞɫɬɚɜɢɦ ɱɟɬɵɪɺɯɦɟɪɧɭɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢ-
ɧɚɬ (ɪɢɫ. 15).
ȼ ɷɬɨɣ ɫɢɫɬɟɦɟ ɧɚ ɨɫɹɯ X, Y, Z, t ɨɬɤɥɚɞɵɜɚɸɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɡɧɚɱɟ-
ɧɢɹ, ɚ ɧɚɱɚɥɨɦ ɤɨɨɪɞɢɧɚɬ ɹɜɥɹɟɬɫɹ «ɦɢɪɨɜɚɹ» ɬɨɱɤɚ ɫɨɛɵɬɢɹ
ɧɨɟ ɪɚɜɧɨɦɟɪɧɨɟ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ, ɩɪɨɯɨɞɹɳɢɯ ɱɟɪɟɡ ɬɨɱɤɭ
ɢɡɨɛɪɚɠɚɟɬɫɹ ɩɪɹɦɨɣ ɩɨɞ ɭɝɥɨɦ, ɬɚɧɝɟɧɫ ɤɨɬɨɪɨɝɨ ɪɚɜɟɧ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰ
Ɉ
. ɉɪɹɦɨɥɢɧɟɣ-
Ɉ (ɏ
= 0 ɩɪɢ t = 0)
ɫ
t.
ɉɨɫɤɨɥɶɤɭ ɧɚɢɛɨɥɶɲɚɹ ɜɨɡɦɨɠɧɚɹ ɫɤɨɪɨɫɬɶ ɪɚɜɧɚ c, ɬɨ ɫɭɳɟɫɬɜɭɟɬ ɧɚɢɛɨɥɶɲɢɣ
, ɤɨɬɨɪɵɣ ɦɨɠɟɬ ɨɛɪɚɡɨɜɵɜɚɬɶ ɷɬɚ ɩɪɹɦɚɹ ɫ ɨɫɶɸ t. ɉɪɹɦɵɟ a
ɭɝɨɥ
ɜ
ɢ cd ɢɡɨ-
ɛɪɚɠɚɸɬ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ ɞɜɭɯ ɫɢɝɧɚɥɨɜ,
ɩɪɨɯɨɞɹɳɢɯ ɫɨ ɫɤɨɪɨɫɬɶɸ ɫ ɱɟɪɟɡ ɫɨɛɵɬɢɟ
ɩɪɹɦɵɯ
ab ɢ cdɯ = ±ct, ɚɜɫɟɥɢɧɢɢ, ɢɡɨɛɪɚɠɚɸɳɢɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ, ɦɨɝɭɬ
ɥɟɠɚɬɶ ɬɨɥɶɤɨ ɜɧɭɬɪɢ ɨɛɥɚɫɬɟɣ
ɬɨɱɤɢ ɩɨɞɱɢɧɹɸɬɫɹ ɭɫɥɨɜɢɸ
2t2
ɫ
2
–
ɯ
> 0, ɚɬɚɤɠɟt > 0, ɬ.ɟ. ɜɫɟ ɫɨɛɵɬɢɹ ɜ ɨɛɥɚɫ-
ɚɈɫ
Ɉ
, ɬ.ɟ.
ɢ d
ɯ
= 0 ɢ t = 0. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɧɚ
Ɉ
b. ȼ ɨɛɥɚɫɬɢ
ɚɈɫ
ɜɫɟ
96
ɬɢ
ɚɈɫ
ɹɜɥɹɸɬɫɹ ɚɛɫɨɥɸɬɧɨ ɛɭɞɭɳɢɦɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤɈɜɨ ɜɫɟɯ ɫɢɫɬɟɦɚɯ ɨɬ-
ɫɱɺɬɚ. Ⱥɧɚɥɨɝɢɱɧɨ ɜɫɟ ɫɨɛɵɬɢɹ ɜ ɨɛɥɚɫɬɢ b
ɦɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ
ɯɨɞɹɬ ɞɨ ɫɨɛɵɬɢɹ
ɫɬɨ ɨɞɧɨɣ, ɦɵ ɢɦɟɥɢ ɛɵ ɤɨɧɭɫ x
Ɉ
. ɋɨɛɵɬɢɹ ɜ ɷɬɨɣ ɨɛɥɚɫɬɢ ɜɨ ɜɫɟɯ ɫɢɫɬɟɦɚɯ ɨɬɫɱɺɬɚ ɩɪɨɢɫ-
Ɉ
. Ɋɚɫɫɦɚɬɪɢɜɚɹ ɜɫɟ ɬɪɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɜɦɟ-
2
+ y2+ z2– c2t2= 0. ȼ 4-ɦɟɪɧɵɯ ɫɢɫɬɟɦɚɯ ɤɨɨɪ-
Ɉ
d ɹɜɥɹɸɬɫɹ ɚɛɫɨɥɸɬɧɨ ɩɪɨɲɟɞɲɢ-
ɞɢɧɚɬ ɏ, Y, Z, t, ɝɞɟ ɨɫɶ ɤɨɧɭɫɚ ɫɨɜɩɚɞɚɟɬ ɫ ɨɫɶɸ t, ɤɪɢɜɚɹ kd ɨɩɪɟɞɟɥɹɟɬ ɩɪɨɰɟɫɫɵ, ɩɪɨɢɫɯɨɞɹɳɢɟ ɜ ɞɚɧɧɨɣ ɷɥɟɤɬɪɨɞɧɨɣ ɫɢɫɬɟɦɟ. Ʉɪɢɜɚɹ k
ɞɚɧɧɵɦ ɷɤɫɩɟɪɢɦɟɧɬɚ
, ɩɪɢɜɟɞɺɧɧɵɦ ɜ ɬɚɛɥ. 1–3.
U
c
k
ɦ
ɩɨɫɬɪɨɟɧɚ ɩɨ
x
Ɋɢɫ
Ƚɥɚɜɚ 7
I
b
. 15.
Ⱦɜɟ ɩɪɹɦɵɟ, ɢɡɨɛɪɚɠɚɸɳɢɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɞɜɭɯ ɫɢɝɧɚɥɨɜ
ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ ɫɨ ɫɤɨɪɨɫɬɶɸ ɫɜɟɬɚ
ɩɪɨɯɨɞɹɳɢɯ ɱɟɪɟɡ ɫɨɛɵɬɢɟ Ɉ
97
,
ɊȺɁɊȺȻɈɌɄȺ ɆɈȾȿɅɂ ɂɋɋɅȿȾɈȼȺɇɂə ɁȺɄɈɇɈɆȿɊɇɈɋɌɂ
ɆȿɏȺɇɂɁɆȺ ɉɊɈȼɈȾɂɆɈɋɌȿɃ ȺɇɂɈɇɈȼ, ɄȺɌɂɈɇɈȼ,
ɈȻɓȿɃ ɉɊɈȼɈȾɂɆɈɋɌɂ. ȺɇȺɅɈȽɂə ɉȿɊȿȾȺɑɂ ɋȼȿɌɈȼɈɃ
ɂ ɗɅȿɄɌɊɈɆȺȽɇɂɌɇɈɃ ɗɇȿɊȽɂɃ ȼ ɉɊɈȼɈȾɇɂɄȺɏ ȼɌɈɊɈȽɈ
ɊɈȾȺ
ɂɫɫɥɟɞɨɜɚɧɢɟ ɤɨɥɢɱɟɫɬɜɟɧɧɨɣ ɫɬɨɪɨɧɵ ɹɜɥɟɧɢɣ
,
ɟɫɬɶ ɫɬɭɩɟɧɶ ɭɝɥɭɛɥɟɧɢɹ ɩɨɡɧɚɧɢɹ
ɜɭɸɳɚɹ ɪɚɫɤɪɵɬɢɸ ɢɯ ɡɚɤɨɧɨɜ. ȼɵɫɲɚɹ ɫɬɭɩɟɧɶ
ɫɩɨɫɨɛɫɬ
-
ɩɨɡɧɚɧɢɹ ɧɟɜɨɡɦɨɠɧɚ ɛɟɡ ɫɜɹɡɢ ɫɨ ɫɬɚɪɵɦɢ ɬɟɨ
ɪɢɹɦɢ, ɛɟɡ ɨɩɨɪɵ ɧɚ ɧɢɯ ɢ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɹ
ɉɨɡɧɚɧɢɟ
7.1. Ɋɚɡɪɚɛɨɬɤɚ ɦɨɞɟɥɢ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɢɫɬɟɦɵ ɤɚɬɨɞɧɨɣ ɡɚɳɢɬɵ
ȼɜɨɞɧɚɹ ɱɚɫɬɶ.
ɉɪɢ ɧɚɥɢɱɢɢ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɭɪɨɜɧɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ,
ɨɪɢɟɧɬɢɪɨɜɚɧɧɨɝɨ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ (H
(ɝɪɭɧɬ) ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɩɨɥɹ
ɝɞɟ
Ʉ
– ɩɨɥɹɪɢɡɭɟɦɨɫɬɶ ɞɢɷɥɟɤɬɪɢɤɚ. ɇɚɩɪɚɜɥɟɧɢɟ ɜɟɤɬɨɪɚ
–
ɫɢɧɬɟɡ ɜɫɟɝɨ ɩɪɟɞɲɟɫɬɜɭɸɳɟɝɨ
) Ɂɟɦɥɢ, ɩɨɥɹɪɢɡɚɰɢɹ ɞɢɷɥɟɤɬɪɢɤɚ
0
ȿ
Ɋ
ɜɢɡɨɬɪɨɩɧɵɯɞɢ-
.
: P = K·E,
ɷɥɟɤɬɪɢɤɚɯ ɨɩɪɟɞɟɥɟɧɨ ɢɡ ɫɨɨɛɪɚɠɟɧɢɣ ɫɢɦɦɟɬɪɢɢ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɩɨɥɹȿɢɥɢ
ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɷɬɨɦɭ ɩɨɥɸ
, ɩɨɷɬɨɦɭ ɜ ɜɟɤɬɨɪɧɨɣ ɮɨɪɦɟ
P = K·E
.
-
.
ȼ ɚɧɢɡɨɬɪɨɩɧɵɯ ɫɪɟɞɚɯ ɧɚɩɪɚɜɥɟɧɢɟ ɜɟɤɬɨɪɚ ɩɨɥɹɪɢɡɚɰɢɢ ɧɟ ɫɨɜɩɚɞɚɟɬ ɫ ɧɚ-
ɩɪɚɜɥɟɧɢɟɦ ɩɨɥɹ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɚɛɫɨɥɸɬɧɚɹ ɜɟɥɢɱɢɧɚ ɜɟɤɬɨɪɚɊɡɚɜɢɫɢɬ ɨɬ ɟɝɨ
ȿ
ɚɛɫɨɥɸɬɧɨɣ ɜɟɥɢɱɢɧɵ ɢ ɧɚɩɪɚɜɥɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɟɤɬɨɪɚ
ɬɪɨɩɧɵɯ ɞɢɷɥɟɤɬɪɢɤɚɯ ɫɥɟɞɭɟɬ ɭɱɢɬɵɜɚɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɪɨɟɤɰɢɣ ɩɨ ɨɫɹɦ:
++=
;
EKEKEKP
131211
zyxx
. ɉɨɷɬɨɦɭ ɜ ɚɧɢɡɨ-
°
®
°
¯
++=
++=
98
;
EKEKEKP
232221
zyxy
.
EKEKEKP
333231
zyxz
(92)
Ⱦɥɹ ɭɞɨɛɫɬɜɚ ɜɦɟɫɬɨ ɜɟɤɬɨɪɚ ɩɨɥɹɪɢɡɚɰɢɢ
Ɋ
ɜɜɨɞɢɬɫɹ ɜɟɤɬɨɪ ɷɥɟɤɬɪɢɱɟ-
ɫɤɨɣ ɢɧɞɭɤɰɢɢ D, ɬɨɝɞɚ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ [5]: D = E = 4ʌP, ɩɪɢ ɷɬɨɦ ɨɞɧɨ ɢɡ ɨɫ-
ɧɨɜɧɵɯ ɭɪɚɜɧɟɧɢɣ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɩɪɢɧɢɦɚɟɬ ɜɟɫɶɦɚ ɩɪɨɫɬɨɣ ɜɢɞ:
ɟɫɥɢ ɫɪɟɞɚ ɜɚɤɭɭɦ, ɬɨ
ȿ
, ɢ ɬɨɝɞɚ
divD = 4
Ɋ
= 0, ɜɟɤɬɨɪ ɢɧɞɭɤɰɢɢ D ɫɨɜɩɚɞɚɟɬ ɫ ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ
divE = 4ʌȡ.
ʌȡ
,
ɂɫɩɨɥɶɡɭɹ ɬɟɨɪɟɦɭ Ƚɚɭɫɫɚ ɞɥɹ ɥɸɛɨɣ ɢɡɨɬɪɨɩɧɨɣ ɫɪɟɞɵ ɢ ɜɜɨɞɹ ɷɥɟɦɟɧɬ
ɨɛɴɟɦɚ
, ɩɨɥɭɱɢɦ
D = (1 + 4ʌK)E = İE,
İ = 1 + 4ʌK,
ɝɞɟ İ
ʹ
ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɨɫɬɨɹɧɧɚɹ.
ɉɨ ɚɧɚɥɨɝɢɢ ɫ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɨɫɬɨɹɧɧɨɣ İ ɦɚɝɧɢɬɧɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ μ
ɫɪɟɞɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ
μ = 1 + 4ʌæ, B
=
μH.
Ɉɞɧɚɤɨ ɟɫɥɢ ɩɨɥɹɪɢɡɚɰɢɹ ɞɢɷɥɟɤɬɪɢɤɨɜɊɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɧɚɩɪɹɠɟɧɧɨ-
ɫɬɢ
ȿ
ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɬ.ɟ. P = K·E, ɬɨ ɦɚɝɧɟɬɢɤɢ ɩɨ ɯɚɪɚɤɬɟɪɭ ɡɚɜɢɫɢɦɨɫɬɢ
ɢɯ ɧɚɦɚɝɧɢɱɟɧɢɹ
I ɢ ɧɚɩɪɹɠɺɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
ɪɚɡɥɢɱɧɵɯ ɤɥɚɫɫɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ
ɇ
ɩɨɞɪɚɡɞɟɥɹɸɬɫɹ ɧɚ ɬɪɢ
ɦɚɝɧɢɬɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨ-
ɫɬɢ æ: I = æ·H.
ȼɨɫɩɪɢɢɦɱɢɜɨɫɬɶ æ ɩɚɪɚɦɚɝɧɢɬɧɵɯ ɬɟɥ μ > 1 (ɤɚɤ ɢ ɩɨɥɹɪɢɡɭɟɦɨɫɬɶ ɞɢ-
ɷɥɟɤɬɪɢɤɨɜ) ɢɦɟɟɬ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ æ > 0, ɬ.ɟ. ɧɚɩɪɚɜɥɟɧɢɟ ɧɚɦɚɝɧɢɱɟ-
ɧɢɹ I ɫɨɜɩɚɞɚɟɬ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɩɨɥɹ
ɇ
. Ⱦɢɚɦɚɝɧɟɬɢɤɢ μ < 1 ɨɬɥɢɱɚɸɬɫɹ ɨɬ ɩɚ-
ɪɚɦɚɝɧɟɬɢɤɨɜ ɬɟɦ, ɱɬɨ ɢɯ ɦɚɝɧɢɬɧɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ æ < 0 ɨɬɪɢɰɚɬɟɥɶɧɚ, ɬ.ɟ.
ɧɚɩɪɚɜɥɟɧɢɟ ɧɚɦɚɝɧɢɱɟɧɢɹ ɞɢɚɦɚɝɧɟɬɢɤɨɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɧɚɩɪɚɜɥɟɧɢɸ ɧɚ-
ɦɚɝɧɢɱɢɜɚɸɳɟɝɨ ɢɯ ɩɨɥɹ
ɇ
.
99
Ɏɟɪɪɨɦɚɝɧɟɬɢɤɢ ɧɟ ɬɨɥɶɤɨ ɧɟɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɩɨɥɹ
ɇ
, ɧɨ
ɢ ɜɨɜɫɟ ɧɟ ɫɜɹɡɚɧɵ ɩɪɨɫɬɨɣ ɮɭɧɤɰɢɨɧɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ
).
ɝɢɫɬɟɪɟɡɢɫ
(ɬɚɦ ɧɚɛɥɸɞɚɟɬɫɹ
Ʌɨɤɚɥɢɡɚɰɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ. Ɂɚɤɨɧ Ɇɚɤɫɜɟɥɥɚ, ɉɨɣɧɬɢɧɝɚ.
ȼ ɩɪɚɤɬɢɱɟɫɤɨɣ ɷɥɟɤɬɪɨɬɟɯɧɢɤɟ ɞɥɹ ɫɥɭɱɚɟɜ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬ-
ɧɨɣ ɷɧɟɪɝɢɢ ɜ ɪɚɡɥɢɱɧɵɯ ɫɪɟɞɚɯ İμ ɩɪɢɧɢɦɚɟɬɫɹ ɡɚ const. ȼɟɤɬɨɪɵ ȿɢ
ɇ
ɜɡɚ-
ɢɦɧɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵ ɢ ɨɛɪɚɡɭɸɬ ɩɪɚɜɨɜɢɧɬɨɜɭɸ ɫɢɫɬɟɦɭ (ɪɢɫ. 16), ɩɨɷɬɨɦɭ
.EH
ε=μ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɧɚɩɪɚɜɥɟɧɢɟ ɜɟɤɬɨɪɚ ɉɨɣɧɬɢɧɝɚ, ɧɚɩɪɚɜɥɟɧɢɟ ɩɨ-
ɬɨɤɚ ɷɧɟɪɝɢɢ, ɫɨɜɩɚɞɚɟɬ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ:
c
S
[]
=
EH
π
4
Ɋɢɫ
. 16.
ɇɚɩɪɚɜɥɟɧɢɟ ɩɨɬɨɤɚ ɷɧɟɪɝɢɢ ɜɟɤɬɨɪɚ ɉɨɣɧɬɢɧɝɚ
Ʉɨɥɢɱɟɫɬɜɨ ɷɧɟɪɝɢɢ Sdt, ɩɪɨɬɟɤɚɸɳɟɟ ɡɚ ɷɥɟɦɟɧɬ ɜɪɟɦɟɧɢ dt ɱɟɪɟɡ ɟɞɢ-
ɧɢɱɧɭɸ ɩɥɨɳɚɞɤɭ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɭɸ ɜɟɤɬɨɪɭ S, ɪɚɜɧɨ Wɋ
·dt, ɢɥɢ
1
C
.
εμ=
C
1
(93)
ɉɪɟɥɨɦɥɟɧɢɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ ɞɥɢɧɧɵɯ ɜɨɥɧ. ɗɮɮɟɤɬ Ɏɚɪɚɞɟɹ
Ɂɚɤɨɧɵ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɫɜɟɬɚ ɛɵɥɢ ɢɡɜɟɫɬɧɵ ɟɳɟ ɞɨ ɜɵɹɫɧɟɧɢɹ ɟɝɨ ɷɥɟɤɬɪɨ-
100
.
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