Жданов С.К Цветков И.В - Основы физических процессов в плазме и в плазменных установках (2000)
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ɫɥɟɞɭɟɬ, ɱɬɨ ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ, ɩɪɨɧɢɡɵɜɚɸɳɢɣ ɥɚɪɦɨɪɨɜɫɤɢɣ ɤɪɭɠɨɤ, ɚɞɢɚɛɚɬɢɱɟɫɤɢ ɩɨɫɬɨɹɧɟɧ. ɗɬɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ ɩɪɢɜɨɞɢɬ ɤ ɜɵɜɨɞɭ, ɱɬɨ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ ɢɡɦɟɧɹɟɬɫɹ ɩɨ ɡɚɤɨɧɭ:
ρ ~ |
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ɬɨ ɟɫɬɶ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɞɥɟɧɧɟɟ, ɱɟɦ ɜ ɫɥɭɱɚɟ ɩɨɫɬɨɹɧɧɨɣ ɩɨɩɟɪɟɱɧɨɣ ɫɤɨɪɨɫɬɢ. |
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Ⱥɧɚɥɨɝɢɱɧɨ ɩɨɥɭɱɢɦ: |
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mv ρ = const , |
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ɬɨ ɟɫɬɶ ɦɨɦɟɧɬ ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ ɬɚɤɠɟ ɨɫɬɚɟɬɫɹ ɚɞɢɚɛɚɬɢɱɟɫɤɢ ɩɨɫɬɨɹɧɧɵɦ.
ɂɧɜɚɪɢɚɧɬɧɨɫɬɶ ɜɟɥɢɱɢɧɵ v|| l
Ɋɚɫɫɦɨɬɪɢɦ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰɵ ɜ ɹɳɢɤɟ ɫ ɭɩɪɭɝɢɦɢ ɫɬɟɧɤɚɦɢ (ɪɢɫ.2.12). ɉɭɫɬɶ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰɵ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɜɞɨɥɶ ɞɧɚ ɹɳɢɤɚ, ɪɚɜɧɚ v||, ɚ ɨɞɧɚ ɢɡ ɫɬɟɧɨɤ ɹɳɢɤɚ ɞɜɢɠɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ U<<v||. Ⱦɥɹ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ «ɫɬɟɧɤɨɣ ɹɳɢɤɚ» ɦɨɠɟɬ ɛɵɬɶ ɨɛɥɚɫɬɶ ɭɫɢɥɟɧɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɨɬ ɤɨɬɨɪɨɣ ɱɚɫɬɢɰɚ ɨɬɪɚɠɚɟɬɫɹ.
ɉɪɢ ɭɩɪɭɝɨɦ ɨɬɪɚɠɟɧɢɢ ɨɬ ɞɜɢɠɭɳɟɣɫɹ ɫɬɟɧɤɢ ɱɚɫɬɢɰɚ ɢɡɦɟɧɢɬ ɫɤɨɪɨɫɬɶ ɧɚ
ɜɟɥɢɱɢɧɭ δv = 2U (ɫɱɢɬɚɟɦ ɦɚɫɫɭ |
ɫɬɟɧɤɢ ɛɟɫɤɨɧɟɱɧɨɣ). |
Ɍɨɝɞɚ ɢɡɦɟɧɟɧɢɟ |
ɫɤɨɪɨɫɬɢ |
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ɱɚɫɬɢɰɵ ɡɚ ɨɞɧɨ ɩɨɥɧɨɟ ɤɨɥɟɛɚɧɢɟ |
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δ t = |
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ɛɭɞɟɬ ɪɚɜɧɨ |
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dv|| |
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δv |
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2U |
v . |
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dt |
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δt |
2l |
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Ɍɚɤ ɤɚɤ U = − |
dl |
, ɬɨ ɩɨɥɭɱɚɟɦ |
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Ɋɢɫ.2.12. ɑɚɫɬɢɰɚ ɜ ɹɳɢɤɟ ɫ |
dt |
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dv|| |
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ɞɜɢɠɭɳɟɣɫɹ ɫɬɟɧɤɨɣ. |
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ɢɥɢ |
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v||l = const . |
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(2.65) |
ɋɛɥɢɠɚɸɳɢɟɫɹ ɫɬɟɧɤɢ ɭɜɟɥɢɱɢɜɚɸɬ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰɵ.
§ 19. ɉɪɢɦɟɧɟɧɢɟ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢ ɞɪɟɣɮɨɜɨɝɨ ɩɪɢɛɥɢɠɟɧɢɣ
Ɂɟɪɤɚɥɶɧɵɟ ɥɨɜɭɲɤɢ (ɩɪɨɛɤɨɬɪɨɧɵ)
ɇɚ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɚɞɢɚɛɚɬɢɱɟɫɤɨɣ ɢɧɜɚɪɢɚɧɬɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɨɫɧɨɜɚɧɵ ɨɬɤɪɵɬɵɟ ɦɚɝɧɢɬɧɵɟ ɥɨɜɭɲɤɢ.
Ɋɚɫɫɦɨɬɪɢɦ ɞɜɢɠɟɧɢɟ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɩɨɫɬɨɹɧɧɨɦ ɜɨ ɜɪɟɦɟɧɢ ɚɤɫɢɚɥɶɧɨ-
ɫɢɦɦɟɬɪɢɱɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɫɨɥɟɧɨɢɞɚ, ɭɫɢɥɟɧɧɨɦ ɧɚ ɨɛɨɢɯ ɤɨɧɰɚɯ. Ɏɨɪɦɚ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɞɥɹ ɷɬɨɝɨ ɫɥɭɱɚɹ ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫ.2.13,ɚ.
ɉɭɫɬɶ ɜ ɧɟɤɨɬɨɪɨɣ ɬɨɱɤɟ Ⱥ ɪɨɞɢɥɚɫɶ ɡɚɪɹɠɟɧɧɚɹ ɱɚɫɬɢɰɚ, ɞɜɢɠɭɳɚɹɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ v&, ɧɚɩɪɚɜɥɟɧɧɨɣ ɩɨɞ ɭɝɥɨɦ α ɤ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (0≤α≤π).
ɂɫɩɨɥɶɡɭɹ |
ɨɩɪɟɞɟɥɟɧɢɟ ɩɨɩɟɪɟɱɧɨɝɨ |
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ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ |
ɢɧɜɚɪɢɚɧɬɚ |
(2.53), ɢ |
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ɱɬɨ |
v = v sinα , |
ɦɨɠɧɨ |
ɩɨɥɭɱɢɬɶ ɫɨɨɬɧɨɲɟɧɢɟ: |
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sin2 α |
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µ |
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(2.66) |
B |
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mv2 |
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ɝɞɟ ȼ - ɜɟɥɢɱɢɧɚ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɬɨɱɤɟ «ɪɨɠɞɟɧɢɹ» ɱɚɫɬɢɰɵ.
Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɨɫɤɨɥɶɤɭ ɩɪɚɜɚɹ ɱɚɫɬɶ (2.66) ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ
ɨɬɧɨɲɟɧɢɟ ɞɜɭɯ ɫɨɯɪɚɧɹɸɳɢɯɫɹ ɜɟɥɢɱɢɧ – ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢɧɜɚɪɢɚɧɬɚ µ ɢ ɩɨɥɧɨɣ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ mv2/2, ɬɨ ɷɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɫɩɪɚɜɟɞɥɢɜɨ ɧɟ ɬɨɥɶɤɨ ɜ ɧɚɱɚɥɶɧɨɣ ɬɨɱɤɟ, ɧɨ ɢ ɜ ɥɸɛɨɣ ɞɪɭɝɨɣ ɬɨɱɤɟ ɜɞɨɥɶ ɬɪɚɟɤɬɨɪɢɢ ɱɚɫɬɢɰɵ, ɟɫɥɢ ɩɨɞ ɜɟɥɢɱɢɧɚɦɢ α ɢ ȼ ɩɨɧɢɦɚɬɶ ɬɟɤɭɳɢɟ ɡɧɚɱɟɧɢɹ ɭɝɥɚ ɧɚɤɥɨɧɚ ɢ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ. ɂɧɵɦɢ ɫɥɨɜɚɦɢ, ɫɨɝɥɚɫɧɨ (2.66) ɩɪɢ ɫɦɟɳɟɧɢɢ ɱɚɫɬɢɰɵ ɜɞɨɥɶ ɬɪɚɟɤɬɨɪɢɢ ɢɡɦɟɧɟɧɢɟ ɨɞɧɨɣ ɢɡ ɜɟɥɢɱɢɧ sin2α ɢɥɢ ȼ ɜɵɡɵɜɚɟɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɟ ɢɡɦɟɧɟɧɢɟ ɞɪɭɝɨɣ ɢɡ ɧɢɯ. ɇɨ ɬɨɝɞɚ ɦɵ ɜɢɞɢɦ, ɱɬɨ ɩɪɢ ɞɜɢɠɟɧɢɢ ɜ ɨɛɥɚɫɬɶ ɫ ɭɜɟɥɢɱɢɜɚɸɳɢɦɫɹ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɩɨ ɦɟɪɟ ɪɨɫɬɚ ɜɟɥɢɱɢɧɵ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɭɝɨɥ ɧɚɤɥɨɧɚ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɫɢɥɨɜɨɣ ɥɢɧɢɢ, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɩɨɩɟɪɟɱɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ v ɞɨɥɠɧɵ ɭɜɟɥɢɱɢɜɚɬɶɫɹ. ȿɫɥɢ ɫɢɧɭɫ ɷɬɨɝɨ ɭɝɥɚ ɞɨɫɬɢɝɧɟɬ ɩɪɟɞɟɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ, ɪɚɜɧɨɝɨ ɟɞɢɧɢɰɟ, ɬɨ ɛɭɞɟɬ v =v, ɚ ɩɪɨɞɨɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰɵ ɨɛɪɚɬɢɬɫɹ ɜ ɧɨɥɶ, v||=0. ɑɚɫɬɢɰɚ ɩɟɪɟɫɬɚɧɟɬ ɫɦɟɳɚɬɶɫɹ ɜɞɨɥɶ ɫɢɥɨɜɨɣ
ɥɢɧɢɢ - ɨɧɚ ɨɬɪɚɡɢɬɫɹ ɢ ɫɬɚɧɟɬ ɞɜɢɝɚɬɶɫɹ ɧɚɡɚɞ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɤ ɰɟɧɬɪɭ ɫɢɫɬɟɦɵ (ɪɢɫ.2.13,a), ɡɚɬɟɦ, ɩɪɨɣɞɹ ɨɛɥɚɫɬɶ ɫ ɦɢɧɢɦɚɥɶɧɵɦ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ, ɞɨɫɬɢɝɧɟɬ
ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɝɨ ɤɨɧɰɚ, ɝɞɟ ɩɨɥɟ ɜɧɨɜɶ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɜɧɨɜɶ ɨɬɪɚɡɢɬɫɹ ɬɟɩɟɪɶ ɡɞɟɫɶ, ɢ ɬɚɤ ɞɚɥɟɟ. Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɱɚɫɬɢɰɚ ɨɤɚɠɟɬɫɹ “ɡɚɩɟɪɬɨɣ” ɦɟɠɞɭ ɦɚɝɧɢɬɧɵɦɢ ɩɪɨɛɤɚɦɢ (ɜ ɚɧɝɥɨɹɡɵɱɧɨɣ ɥɢɬɟɪɚɬɭɪɟ - mirrors, ɚ ɩɪɨɛɤɨɬɪɨɧ ɧɚɡɵɜɚɸɬ mirror machine). Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɜ ɩɨɥɟ ɞɚɧɧɨɣ ɫɢɫɬɟɦɵ ɦɨɝɭɬ ɭɞɟɪɠɢɜɚɬɶɫɹ ɧɟ ɜɫɟ ɱɚɫɬɢɰɵ, ɚ ɬɨɥɶɤɨ ɬɟ, ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɜ ɬɨɱɤɟ ɪɨɠɞɟɧɢɹ ɢɦɟɟɬ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ ɭɝɨɥ ɧɚɤɥɨɧɚ ɤ ɫɢɥɨɜɨɣ ɥɢɧɢɢ, ɫ ɬɟɦ, ɱɬɨɛɵ ɜ ɫɟɱɟɧɢɢ ɫ ɧɚɢɛɨɥɶɲɢɦ ɡɧɚɱɟɧɢɟɦ ȼ (ɢɥɢ ɪɚɧɶɲɟ) ɱɚɫɬɢɰɚ ɨɬɪɚɡɢɥɚɫɶ.
Ɉɬɧɨɲɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɩɨɥɹ ȼm ɤ ɦɢɧɢɦɚɥɶɧɨɦɭ ȼ0 ɜɞɨɥɶ ɨɫɢ ɫɢɫɬɟɦɵ (ɫɦ.
ɪɢɫ.2.13,ɚ),
R = Bm / B0 > 1 ,
ɧɚɡɵɜɚɸɬ ɩɪɨɛɨɱɧɵɦ ɨɬɧɨɲɟɧɢɟɦ, ɢ ɞɥɹ ɭɞɟɪɠɚɧɢɹ ɱɚɫɬɢɰ, ɪɨɞɢɜɲɢɯɫɹ ɜ ɰɟɧɬɪɟ, ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ ɛɵɥɨ ɜɵɩɨɥɧɟɧɨ ɧɟɪɚɜɟɧɫɬɜɨ
sin α ≥ 1 / R . |
(2.67) |
Ⱦɥɹ ɜɫɟɯ ɨɫɬɚɥɶɧɵɯ ɱɚɫɬɢɰ ɜɟɥɢɱɢɧɚ sin α ɞɨɥɠɧɚ ɛɵɬɶ ɟɳɟ ɛɨɥɶɲɟ, ɱɬɨɛɵ ɨɧɢ ɨɫɬɚɜɚɥɢɫɶ ɜ ɥɨɜɭɲɤɟ. Ⱥ ɬɟ ɱɚɫɬɢɰɵ, ɞɥɹ ɤɨɬɨɪɵɯ ɜɵɩɨɥɧɟɧɨ ɨɛɪɚɬɧɨɟ ɧɟɪɚɜɟɧɫɬɜɨ
sin α < 1 / R , |
(2.68) |
ɭɣɞɭɬ ɢɡ ɥɨɜɭɲɤɢ ɜɞɨɥɶ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ.
ɗɬɢ ɧɟɪɚɜɟɧɫɬɜɚ ɧɟɫɥɨɠɧɨ ɨɛɨɫɧɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. Ɉɛɨɡɧɚɱɢɦ ɩɨɫɪɟɞɫɬɜɨɦ αm ɭɝɨɥ ɧɚɤɥɨɧɚ ɫɤɨɪɨɫɬɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɨɛɥɚɫɬɢ, ɝɞɟ ɢɧɞɭɤɰɢɹ ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ȼ=ȼm. ɗɬɢ ɜɟɥɢɱɢɧɵ ɞɨɥɠɧɵ ɛɵɬɶ ɫɜɹɡɚɧɵ ɫɨɨɬɧɨɲɟɧɢɟɦ, ɤɨɬɨɪɨɟ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ, ɩɪɨɫɬɨ ɡɚɦɟɧɢɜ ɜ (2.66) α ɧɚ αm ɢ ȼ ɧɚ ȼm:
sin2 α |
m |
= |
2µ |
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mv2 |
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ɉɭɫɬɶ, ɞɚɥɟɟ, ȼ0 ɜɟɥɢɱɢɧɚ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɰɟɧɬɪɟ ɫɢɫɬɟɦɵ, ɝɞɟ ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɪɚɫɩɨɥɨɠɟɧɚ ɱɚɫɬɢɰɚ. Ɍɨɝɞɚ ɫɨɨɬɧɨɲɟɧɢɟ (2.66) ɜ ɷɬɨɦ ɩɨɥɨɠɟɧɢɢ ɞɨɥɠɧɨ ɛɵɬɶ ɡɚɩɢɫɚɧɨ ɜ ɜɢɞɟ:
sin2 α |
2µ |
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= |
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B |
mv2 |
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ɉɪɚɜɵɟ ɱɚɫɬɢ ɜ ɷɬɢɯ ɮɨɪɦɭɥɚɯ ɫɨɜɩɚɞɚɸɬ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɨɥɭɱɚɟɦ
sin2 αm = sin2 α , Bm B0
ɢɥɢ
sin2 αm = BBm sin2 α ≡ R sin2 α .
0
ɉɨɫɤɨɥɶɤɭ ɥɟɜɚɹ ɱɚɫɬɶ ɷɬɨɝɨ ɪɚɜɟɧɫɬɜɚ ɧɟ ɩɪɟɜɨɫɯɨɞɢɬ ɟɞɢɧɢɰɭ, ɬɨ ɜɨ ɜɫɟɯ «ɪɚɡɪɟɲɟɧɧɵɯ» ɞɥɹ ɞɜɢɠɟɧɢɹ
ɱɚɫɬɢɰɵ ɨɛɥɚɫɬɹɯ ɞɨɥɠɧɨ ɛɵɬɶ R sin2 α ≤ 1, ɬ. ɟ. ɱɚɫɬɢɰɵ ɧɚɜɟɪɧɹɤɚ ɩɨɤɢɧɭɬ ɥɨɜɭɲɤɭ, ɟɫɥɢ ɜɵɩɨɥɧɟɧɨ ɭɫɥɨɜɢɟ (2.68). ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɜɵɩɨɥɧɟɧɨ ɭɫɥɨɜɢɟ (2.67), ɨɛɥɚɫɬɶ ɫ ɦɚɤɫɢɦɚɥɶɧɵɦ ɩɨɥɟɦ ɞɥɹ ɱɚɫɬɢɰɵ ɨɤɚɡɵɜɚɟɬɫɹ ɧɟɞɨɫɬɢɠɢɦɨɣ, ɢ ɨɧɚ ɧɟ ɦɨɠɟɬ ɩɨɤɢɧɭɬɶ ɥɨɜɭɲɤɭ.
Ʉɨɧɭɫ ɧɚɩɪɚɜɥɟɧɢɣ, ɜ ɩɪɟɞɟɥɚɯ ɤɨɬɨɪɨɝɨ ɱɚɫɬɢɰɵ ɩɨɤɢɞɚɸɬ ɥɨɜɭɲɤɭ, ɧɨɫɢɬ ɧɚɡɜɚɧɢɟ ɨɩɚɫɧɨɝɨ ɤɨɧɭɫɚ ɩɨɬɟɪɶ. ɋɢɫɬɟɦɵ, ɜ ɤɨɬɨɪɵɯ ɜɫɟ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɜɵɯɨɞɹɬ ɡɚ ɩɪɟɞɟɥɵ ɪɚɛɨɱɟɣ ɤɚɦɟɪɵ, ɧɚɡɵɜɚɸɬ ɨɬɤɪɵɬɵɦɢ, ɤ ɧɢɦ ɨɬɧɨɫɹɬɫɹ ɜɫɟ ɩɪɨɛɤɨɬɪɨɧɵ. ɂɡ-ɡɚ ɫɢɦɦɟɬɪɢɢ ɝɟɨɦɟɬɪɢɢ ɭɞɟɪɠɢɜɚɸɳɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɬɚɤɢɟ ɥɨɜɭɲɤɢ ɟɳɟ ɧɚɡɵɜɚɸɬ
ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɵɦɢ ɥɨɜɭɲɤɚɦɢ. sin2 α
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɭɫɥɨɜɢɟ ɭɞɟɪɠɚɧɢɹ (2.67) ɜ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɣ ɥɨɜɭɲɤɟ ɹɜɥɹɟɬɫɹ ɭɧɢɜɟɪɫɚɥɶɧɵɦ − ɨɧɨ ɧɟ ɡɚɜɢɫɢɬ ɧɢ ɨɬ ɡɚɪɹɞɚ, ɧɢ ɨɬ ɦɚɫɫɵ, ɧɢ ɨɬ ɜɟɥɢɱɢɧɵ ɦɨɞɭɥɹ ɫɤɨɪɨɫɬɢ, ɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɥɢɲɶ ɨɬɧɨɲɟɧɢɟɦ ɩɪɨɞɨɥɶɧɨɣ ɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ (ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ) ɤɨɦɩɨɧɟɧɬ ɫɤɨɪɨɫɬɢ. ɉɪɚɜɞɚ, ɷɬɨ ɫɩɪɚɜɟɞɥɢɜɨ ɞɥɹ ɨɬɞɟɥɶɧɨɣ ɱɚɫɬɢɰɵ: ɪɟɚɥɶɧɨ ɜ ɩɥɚɡɦɟ ɱɚɫɬɢɰɵ ɪɚɫɫɟɢɜɚɸɬɫɹ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɹɯ, ɧɚɩɪɚɜɥɟɧɢɟ ɜɟɤɬɨɪɚ ɫɤɨɪɨɫɬɢ ɩɪɢ ɷɬɨɦ ɢɡɦɟɧɹɟɬɫɹ, ɦɨɠɟɬ ɩɨɩɚɫɬɶ ɜ ɨɩɚɫɧɵɣ ɤɨɧɭɫ ɢ ɱɚɫɬɢɰɚ ɩɨɤɢɧɟɬ ɥɨɜɭɲɤɭ. Ɇɟɞɥɟɧɧɵɟ ɱɚɫɬɢɰɵ ɪɚɫɫɟɢɜɚɸɬɫɹ ɛɵɫɬɪɟɟ
1
(ɬɚɤ ɤɚɤ ɞɥɹ ɧɢɯ ɫɟɱɟɧɢɟ ɤɭɥɨɧɨɜɫɤɨɝɨ ɪɚɫɫɟɹɧɢɹ ɛɨɥɶɲɟ, σc E2 , ɫɦ. § 6), ɩɨɷɬɨɦɭ ɨɧɢ
ɛɵɫɬɪɟɟ ɭɯɨɞɹɬ, ɢ ɜ ɫɩɟɤɬɪɟ ɱɚɫɬɢɰ ɜɨɡɧɢɤɚɟɬ “ɩɪɨɜɚɥ” ɜ ɨɛɥɚɫɬɢ ɦɚɥɵɯ ɫɤɨɪɨɫɬɟɣ. Ʉɪɨɦɟ ɬɨɝɨ, ɫ ɩɨɜɵɲɟɧɢɟɦ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ ɜ ɢɝɪɭ ɜɫɬɭɩɚɸɬ ɫɨɛɫɬɜɟɧɧɵɟ ɩɨɥɹ ɩɥɚɡɦɵ. ɗɬɨ − ɩɪɢɱɢɧɚ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɨ ɧɟɣ ɛɭɞɟɦ ɝɨɜɨɪɢɬɶ ɩɨɡɠɟ.
ȿɫɥɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɜ ɩɪɨɛɤɟ ɧɚɪɚɫɬɚɟɬ ɜɨ ɜɪɟɦɟɧɢ, ɬɨ, ɜɫɥɟɞɫɬɜɢɟ ɫɨɯɪɚɧɟɧɢɹ ɩɨɩɟɪɟɱɧɨɝɨ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢɧɜɚɪɢɚɧɬɚ, ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɦɨɞɭɥɶ ɩɨɩɟɪɟɱɧɨɣ ɤɨɦɩɨɧɟɧɬɵ ɫɤɨɪɨɫɬɢ v ɢ ɭɥɭɱɲɚɟɬɫɹ ɭɞɟɪɠɚɧɢɟ − ɩɪɢ ɷɬɨɦ ɢɡɦɟɧɢɬɫɹ ɩɪɨɛɨɱɧɨɟ ɨɬɧɨɲɟɧɢɟ ȼm/ȼ0, ɢ ɨɬɪɚɠɟɧɢɟ ɱɚɫɬɢɰ ɩɪɨɢɡɨɣɞɟɬ ɛɥɢɠɟ ɤ ɰɟɧɬɪɭ ɩɪɨɛɤɨɬɪɨɧɚ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɨɛɥɚɫɬɶ ɩɪɨɞɨɥɶɧɵɯ ɨɫɰɢɥɥɹɰɢɣ ɱɚɫɬɢɰ ɫɨɤɪɚɳɚɟɬɫɹ ɢ, ɫɨɝɥɚɫɧɨ (2.65), ɞɨɥɠɧɚ ɭɜɟɥɢɱɢɬɶɫɹ ɢ ɩɪɨɞɨɥɶɧɚɹ ɤɨɦɩɨɧɟɧɬɚ ɫɤɨɪɨɫɬɢ v|| ɡɚ ɫɱɟɬ ɫɛɥɢɠɟɧɢɹ ɨɬɪɚɠɚɸɳɢɯ ɱɚɫɬɢɰɭ ɭɩɪɭɝɢɯ ɫɬɟɧɨɤ. Ɍɨɱɧɨɟ ɪɟɲɟɧɢɟ ɩɨɞɨɛɧɨɣ ɡɚɞɚɱɢ ɨ ɞɜɢɠɟɧɢɢ ɱɚɫɬɢɰɵ ɜ ɩɟɪɟɦɟɧɧɨɦ ɢ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɨɣ ɩɪɨɛɥɟɦɨɣ.
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ ɫɠɚɬɢɢ ɪɚɫɬɟɬ ɢ ɩɥɨɬɧɨɫɬɶ ɱɢɫɥɚ ɱɚɫɬɢɰ, ɬɚɤ ɤɚɤ ɩɪɢ ɪɨɫɬɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɨɡɧɢɤɚɟɬ ɜɢɯɪɟɜɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɢ ɩɨɹɜɥɹɟɬɫɹ ɞɪɟɣɮɨɜɚɹ ɫɤɨɪɨɫɬɶ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɬɚɤ, ɱɬɨ ɱɚɫɬɢɰɵ ɫɨɛɢɪɚɸɬɫɹ ɤ ɰɟɧɬɪɭ ɫɢɫɬɟɦɵ.
ȼɟɥɢɱɢɧɭ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɟɣ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. Ɉɛɨɡɧɚɱɢɦ ɪɚɞɢɭɫ ɨɛɥɚɫɬɢ, ɡɚɧɹɬɨɣ ɩɥɚɡɦɨɣ, R(t), ɬɨɝɞɚ ɢɡ ɬɟɨɪɟɦɵ ɨ ɰɢɪɤɭɥɹɰɢɢ,
2π |
E R dϕ = − |
1 R( t ) ∂ B |
z |
2π rdr , |
(2.69) |
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ɩɨɥɭɱɚɟɦ
E = − |
R |
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dBz |
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(2.70) |
ϕ |
2c dt |
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ɉɪɢɛɥɢɠɟɧɧɨ ɫɱɢɬɚɟɦ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɨɞɧɨɪɨɞɧɵɦ ɜ ɩɪɟɞɟɥɚɯ ɨɤɪɭɠɧɨɫɬɢ ɫ ɪɚɞɢɭɫɨɦ R(t). Ɉɩɪɟɞɟɥɹɹ
ɞɚɥɟɟ ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ |
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v& |
= c |
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e& , |
(2.71) |
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r |
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ɩɪɢɯɨɞɢɦ ɤ ɫɨɨɬɧɨɲɟɧɢɸ |
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dR |
= − |
1 |
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dBz |
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R |
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ɢɥɢ |
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R2 B = const . |
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ɗɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɜɵɪɚɠɚɟɬ ɫɨɯɪɚɧɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɬɨɤɚ, ɩɪɨɧɢɡɵɜɚɸɳɟɝɨ ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ ɩɨɜɟɪɯɧɨɫɬɢ (ɱɚɫɬɨ ɧɚɡɵɜɚɟɦɨɣ ɞɪɟɣɮɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ), ɩɨ ɤɨɬɨɪɨɣ ɞɜɢɠɟɬɫɹ ɱɚɫɬɢɰɚ ɩɪɢ ɟɺ ɞɪɟɣɮɟ ɜ ɧɟɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ (ɫɦ. ɪɢɫ.2.13,ɚ,ɛ) - ɟɳɟ ɨɞɧɨɝɨ, ɬɚɤ ɧɚɡɵɜɚɟɦɨɝɨ ɬɪɟɬɶɟɝɨ ɚɞɢɚɛɚɬɢɱɟɫɤɨɝɨ ɢɧɜɚɪɢɚɧɬɚ, ɩɨɫɥɟ ɩɨɩɟɪɟɱɧɨɝɨ, ɨɬɜɟɱɚɸɳɟɝɨ ɛɵɫɬɪɨɦɭ ɜɪɚɳɟɧɢɸ ɩɨ ɥɚɪɦɨɪɨɜɫɤɨɣ ɨɤɪɭɠɧɨɫɬɢ, ɢ ɩɪɨɞɨɥɶɧɨɝɨ, ɨɬɜɟɱɚɸɳɟɝɨ ɛɨɥɟɟ ɦɟɞɥɟɧɧɵɦ ɩɪɨɞɨɥɶɧɵɦ ɨɫɰɢɥɥɹɰɢɹɦ ɱɚɫɬɢɰɵ ɦɟɠɞɭ ɩɪɨɛɤɚɦɢ.
ɇɟɫɦɨɬɪɹ ɧɚ ɜɧɟɲɧɟɟ ɫɯɨɞɫɬɜɨ ɮɨɪɦɭɥ (2.59) ɢ (2.73), ɨɧɢ ɨɬɪɚɠɚɸɬ ɪɚɡɥɢɱɧɵɟ ɹɜɥɟɧɢɹ. ɋɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ (2.59) ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ, ɩɪɨɧɢɡɵɜɚɸɳɢɣ ɥɚɪɦɨɪɨɜɫɤɭɸ ɨɤɪɭɠɧɨɫɬɶ, ɨɩɢɫɵɜɚɟɦɭɸ ɱɚɫɬɢɰɟɣ, ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ, ɚ ɜɵɪɚɠɟɧɢɟ (2.73) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɪɚɞɢɭɫ ɨɛɥɚɫɬɢ, ɡɚɧɹɬɨɣ ɩɥɚɡɦɨɣ, ɦɟɧɹɟɬɫɹ ɬɚɤ, ɱɬɨɛɵ ɩɨɬɨɤ ɱɟɪɟɡ ɷɬɭ ɨɛɥɚɫɬɶ ɛɵɥ ɩɨɫɬɨɹɧɧɵɦ. ɑɚɫɬɢɰɵ ɞɨɥɠɧɵ ɧɟ ɬɨɥɶɤɨ ɢɡɦɟɧɢɬɶ ɪɚɞɢɭɫ ɜɪɚɳɟɧɢɹ, ɧɨ ɢ ɩɟɪɟɦɟɫɬɢɬɶɫɹ ɩɨɩɟɪɟɤ ɩɨɥɹ.
ȿɫɥɢ ɩɨɥɧɨɟ ɱɢɫɥɨ ɱɚɫɬɢɰ N=nΩ (ɝɞɟ Ω - ɨɛɴɟɦ ɩɥɚɡɦɵ) ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ, ɬɨ, ɝɪɭɛɨ ɨɩɪɟɞɟɥɹɹ ɨɛɴɟɦ ɩɥɚɡɦɵ ɤɚɤ Ω ~ R2l, ɩɨɥɭɱɚɟɦ
N = n R2l |
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ɢɥɢ |
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nl = n l |
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¸ |
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(2.74) |
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ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɱɢɫɥɨ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɜ ɪɚɫɱɟɬɟ ɧɚ ɟɞɢɧɢɰɭ ɩɥɨɳɚɞɢ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ (ɩɨɝɨɧɧɚɹ ɩɥɨɬɧɨɫɬɶ) ɦɟɧɹɟɬɫɹ ɜɨ ɜɪɟɦɟɧɢ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ.
ɉɪɢɧɰɢɩ “ɦɢɧɢɦɭɦɚ B”
ȼ ɰɟɧɬɪɚɥɶɧɨɣ ɱɚɫɬɢ ɩɪɨɛɤɨɬɪɨɧɚ (ɪɢɫ.2.13) ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɭɛɵɜɚɟɬ ɩɨ ɪɚɞɢɭɫɭ ɨɬ ɰɟɧɬɪɚ, ɩɨɷɬɨɦɭ B ɧɚɩɪɚɜɥɟɧ ɤ ɰɟɧɬɪɭ. Ⱦɥɹ ɨɞɢɧɨɱɧɨɣ ɱɚɫɬɢɰɵ − ɷɬɨ ɩɪɢɱɢɧɚ ɞɪɟɣɮɚ
ɩɨ ɚɡɢɦɭɬɭ ɜɨɤɪɭɝ ɨɫɢ ɫɢɫɬɟɦɵ, ɧɨ ɱɚɫɬɢɰɵ ɪɚɡɧɵɯ ɡɧɚɤɨɜ ɞɪɟɣɮɭɸɬ ɧɚɜɫɬɪɟɱɭ ɞɪɭɝ ɞɪɭɝɭ (ɫɦ. ɪɢɫ.2.13,ɛ), ɜɨɡɧɢɤɚɟɬ ɞɪɟɣɮɨɜɵɣ ɬɨɤ, ɤɨɬɨɪɵɣ, ɨɱɟɜɢɞɧɨ, ɧɚɩɪɚɜɥɟɧ ɬɚɤ, ɱɬɨ
ɜɵɡɵɜɚɟɬ ɭɦɟɧɶɲɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫɨɥɟɧɨɢɞɚ. ɉɥɚɡɦɚ ɤɚɤ ɛɵ «ɜɵɬɚɥɤɢɜɚɟɬ» ɭɞɟɪɠɢɜɚɸɳɟɟ ɟɺ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. ȿɫɥɢ ɩɥɨɬɧɨɫɬɶ ɩɥɚɡɦɵ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɚ, ɬɨ ɷɮɮɟɤɬ ɛɭɞɟɬ ɫɭɳɟɫɬɜɟɧɧɵɦ. Ɉɧ ɪɟɚɥɶɧɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɢɡɦɟɪɟɧɢɹ ɞɚɜɥɟɧɢɹ ɩɥɚɡɦɵ ɩɨ ɜɟɥɢɱɢɧɟ ɜɵɬɟɫɧɹɟɦɨɝɨ ɩɨɥɹ - ɢɡɦɟɪɟɧɢɹ ɬɚɤ ɧɚɡɵɜɚɟɦɨɝɨ ɞɢɚɦɚɝɧɢɬɧɨɝɨ ɫɢɝɧɚɥɚ. ȿɫɥɢ ɫɢɫɬɟɦɚ ɢɞɟɚɥɶɧɨ ɫɢɦɦɟɬɪɢɱɧɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ, ɬɨ ɞɪɟɣɮɨɜɵɟ ɩɨɬɨɤɢ ɡɚɦɤɧɭɬɵ, ɢ ɧɚɤɨɩɥɟɧɢɹ ɡɚɪɹɞɚ ɧɟ ɩɪɨɢɫɯɨɞɢɬ. ɉɪɢ ɧɚɪɭɲɟɧɢɢ ɫɢɦɦɟɬɪɢɢ ɫɰɟɧɚɪɢɣ ɩɨɫɥɟɞɭɸɳɢɯ
ɫɨɛɵɬɢɣ ɩɪɢɨɛɪɟɬɚɟɬ ɞɪɚɦɚɬɢɱɟɫɤɢɣ ɯɚɪɚɤɬɟɪ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɧɚ ɛɨɤɨɜɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɩɥɚɡɦɵ ɜɨɡɧɢɤɚɟɬ ɜɵɫɬɭɩ (ɫɦ. ɪɢɫ.2.13,ɛ) – «ɩɥɚɡɦɟɧɧɵɣ ɹɡɵɤ». ɗɬɨ ɜɨɡɦɭɳɟɧɢɟ ɫɜɨɛɨɞɧɨ «ɪɚɫɬɟɤɚɟɬɫɹ» ɜɞɨɥɶ ɫɢɥɨɜɵɯ ɥɢɧɢɣ, ɜɜɢɞɭ ɨɬɫɭɬɫɬɜɢɹ ɩɪɨɬɢɜɨɞɟɣɫɬɜɢɹ ɬɚɤɨɦɭ ɪɚɫɬɟɤɚɧɢɸ, ɚ ɩɨɬɨɦɭ ɛɵɫɬɪɨ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɜɵɬɹɧɭɬɵɣ ɜɞɨɥɶ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɠɟɥɨɛɨɤ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɨɛɫɭɠɞɚɟɦɭɸ ɧɚɦɢ ɫɟɣɱɚɫ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ ɨɛɵɱɧɨ ɧɚɡɵɜɚɸɬ ɠɟɥɨɛɤɨɜɨɣ. ȼ ɨɛɥɚɫɬɢ ɠɟɥɨɛɤɚ ɞɪɟɣɮɨɜɵɟ ɩɨɬɨɤɢ ɧɟ ɡɚɦɤɧɭɬɵ, ɤɚɤ ɷɬɨ ɫɯɟɦɚɬɢɱɧɨ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 2.13,ɛ. ɉɨɷɬɨɦɭ ɡɞɟɫɶ ɩɪɨɢɡɨɣɞɟɬ ɪɚɡɞɟɥɟɧɢɟ ɡɚɪɹɞɨɜ ɢ ɜɨɡɧɢɤɧɟɬ ɩɨɥɹɪɢɡɚɰɢɨɧɧɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ& &ȿ, ɧɚɩɪɚɜɥɟɧɧɨɟ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨ ɪɟɡɭɥɶɬɢɪɭɸɳɢɣ ɞɪɟɣɮ ɜ ɫɤɪɟɳɟɧɧɵɯ E × B ɩɨɥɹɯ ɛɭɞɟɬ ɫɩɨɫɨɛɫɬɜɨɜɚɬɶ ɪɨɫɬɭ ɩɟɪɜɨɧɚɱɚɥɶɧɨɝɨ ɜɨɡɦɭɳɟɧɢɹ, ɡɚɜɟɪɲɚɸɳɟɝɨɫɹ ɜɵɛɪɨɫɨɦ ɩɥɚɡɦɵ ɧɚ ɫɬɟɧɤɭ ɤɚɦɟɪɵ.
ɗɬɨ ɩɪɨɹɜɥɟɧɢɟ ɞɢɚɦɚɝɧɟɬɢɡɦɚ ɩɥɚɡɦɵ: ɨɧɚ ɜɫɟɝɞɚ ɫɬɪɟɦɢɬɫɹ ɩɟɪɟɣɬɢ ɜ ɨɛɥɚɫɬɶ ɛɨɥɟɟ ɫɥɚɛɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɉɨɷɬɨɦɭ ɩɪɢ ɫɨɡɞɚɧɢɢ ɫɢɫɬɟɦ ɞɥɹ ɭɞɟɪɠɚɧɢɹ ɩɥɚɡɦɵ ɧɭɠɧɨ ɪɚɫɩɨɥɚɝɚɬɶ ɩɥɚɡɦɟɧɧɵɣ ɫɝɭɫɬɨɤ ɩɨ ɜɨɡɦɨɠɧɨɫɬɢ ɬɚɤ, ɱɬɨɛɵ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɜɨɡɪɚɫɬɚɥɨ ɨɬ ɧɟɝɨ ɜɨ ɜɫɟɯ ɧɚɩɪɚɜɥɟɧɢɹɯ, ɬ.ɟ. ɪɚɫɩɨɥɚɝɚɬɶ ɩɥɚɡɦɭ ɜ ɨɛɥɚɫɬɢ ɦɢɧɢɦɚɥɶɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɂɦɟɧɧɨ ɩɨ ɜɨɡɦɨɠɧɨɫɬɢ, ɩɨɫɤɨɥɶɤɭ ɫɨɡɞɚɧɢɟ ɤɨɧɮɢɝɭɪɚɰɢɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɜ ɤɨɬɨɪɵɯ ɩɨɥɟ ɧɚɪɚɫɬɚɥɨ ɛɵ ɜɨ ɜɫɟɯ ɧɚɩɪɚɜɥɟɧɢɹɯ, ɨɱɟɜɢɞɧɨ, ɧɟɜɨɡɦɨɠɧɨ. Ɋɟɱɶ ɦɨɠɟɬ ɢɞɬɢ ɥɢɲɶ ɨ ɧɚɪɚɫɬɚɧɢɢ ɧɚɪɭɠɭ ɜ ɫɪɟɞɧɟɦ, ɤɨɝɞɚ ɜɤɥɚɞ ɭɱɚɫɬɤɨɜ ɫ ɛɥɚɝɨɩɪɢɹɬɧɨɣ ɞɥɹ ɭɞɟɪɠɚɧɢɹ ɤɪɢɜɢɡɧɨɣ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɩɪɟɜɚɥɢɪɭɟɬ ɧɚɞ ɜɤɥɚɞɨɦ ɭɱɚɫɬɤɨɜ ɫ ɧɟɛɥɚɝɨɩɪɢɹɬɧɨɣ ɤɪɢɜɢɡɧɨɣ, ɝɞɟ ɩɨɥɟ ɭɛɵɜɚɟɬ. ɗɬɨ, ɩɨ ɫɭɬɢ ɞɟɥɚ, ɢ ɜɵɪɚɠɚɟɬ ɫɨɞɟɪɠɚɧɢɟ ɩɪɢɧɰɢɩɚ «ɦɢɧɢɦɭɦɚ ȼ». ɍɩɪɨɳɟɧɧɨ (ɜ ɞɟɬɚɥɹɯ ɫɦ. [11]) ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɷɬɨɦɭ ɩɪɢɧɰɢɩɭ ɭɫɥɨɜɢɟ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ȼɵɞɟɥɢɦ ɦɵɫɥɟɧɧɨ ɜ ɩɪɟɞɟɥɚɯ ɨɛɴɺɦɚ, ɡɚɧɢɦɚɟɦɨɝɨ ɩɥɚɡɦɨɣ, ɫɢɥɨɜɭɸ ɬɪɭɛɤɭ ɞɥɢɧɨɣ l ɢ ɫɟɱɟɧɢɟɦ S, ɜɵɬɹɧɭɬɭɸ ɜɞɨɥɶ ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɢ ɧɚɩɨɥɧɟɧɧɭɸ ɩɥɚɡɦɨɣ. ȼ ɪɚɜɧɨɜɟɫɢɢ ɬɚɤɚɹ ɬɪɭɛɤɚ ɡɚɧɢɦɚɟɬ ɩɨɥɨɠɟɧɢɟ, ɨɬɜɟɱɚɸɳɟɟ ɦɢɧɢɦɚɥɶɧɨɣ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ. ɋɚɦɚ ɩɨ ɫɟɛɟ ɬɚɤɚɹ ɬɪɭɛɤɚ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥ ɞɚɜɥɟɧɢɹ ɫɬɪɟɦɢɬɫɹ ɪɚɫɲɢɪɢɬɶɫɹ. ɉɭɫɬɶ ɞɥɹ ɩɪɨɫɬɨɬɵ ɞɚɜɥɟɧɢɟ ɩɥɚɡɦɵ ɜ ɩɪɟɞɟɥɚɯ ɷɬɨɣ ɬɪɭɛɤɢ ɩɨɫɬɨɹɧɧɨ − ɦɵ ɩɨɫɬɭɩɚɟɦɫɹ ɡɞɟɫɶ ɫɬɪɨɝɨɫɬɶɸ ɪɚɞɢ ɧɚɝɥɹɞɧɨɫɬɢ. ɂɬɚɤ, ɩɥɚɡɦɚ ɫɬɪɟɦɢɬɫɹ ɭɜɟɥɢɱɢɬɶ ɫɜɨɣ ɨɛɴɟɦ
Ω = ³dSdl . |
(2.75) |
ɉɨɞɟɥɢɜ ɢ ɞɨɦɧɨɠɢɜ ɩɨɞɵɧɬɟɝɪɚɥɶɧɨɟ ɜɵɪɚɠɟɧɢɟ ɧɚ ɜɟɥɢɱɢɧɭ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɡɚɩɢɲɟɦ ɷɬɭ ɮɨɪɦɭɥɭ ɜ ɜɢɞɟ
Ω = ³( BdS ) |
dl |
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(2.76) |
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ɉɨɫɤɨɥɶɤɭ ɩɪɨɧɢɡɵɜɚɸɳɢɣ ɷɬɭ ɬɪɭɛɤɭ ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ |
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Φ = ³BdS |
(2.77) |
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ɩɨɫɬɨɹɧɧɵɣ, ɬɨ ɷɬɭ (ɩɨɥɨɠɢɬɟɥɶɧɭɸ!) ɩɨɫɬɨɹɧɧɭɸ ɦɨɠɧɨ ɜɵɧɟɫɬɢ ɡɚ ɡɧɚɤ ɢɧɬɟɝɪɚɥɚ, ɢ ɦɵ ɩɨɥɭɱɚɟɦ
Ω = Φ ³ |
dl |
. |
(2.78) |
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B |
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ɂɧɬɟɝɪɚɥ ɡɞɟɫɶ ɛɟɪɟɬɫɹ ɜɞɨɥɶ ɫɢɥɨɜɨɣ ɥɢɧɢɢ. ɑɬɨɛɵ ɪɚɜɧɨɜɟɫɧɨɟ ɩɨɥɨɠɟɧɢɟ ɜɵɞɟɥɟɧɧɨɣ ɩɥɚɡɦɟɧɧɨɣ ɬɪɭɛɤɢ ɛɵɥɨ ɭɫɬɨɣɱɢɜɵɦ, ɨɧɚ ɞɨɥɠɧɚ ɢɦɟɬɶ ɜ ɷɬɨɦ ɩɨɥɨɠɟɧɢɢ ɦɚɤɫɢɦɚɥɶɧɵɣ ɨɛɴɟɦ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɢ ɥɸɛɨɦ «ɜɢɪɬɭɚɥɶɧɨɦ» ɫɦɟɳɟɧɢɢ ɬɪɭɛɤɢ ɜɚɪɢɚɰɢɹ
δ ³ |
dl |
< 0 |
(2.79) |
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B |
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ɞɨɥɠɧɚ ɛɵɬɶ ɨɬɪɢɰɚɬɟɥɶɧɚ. ɗɬɨ ɢ ɟɫɬɶ (ɜ ɭɩɪɨɳɟɧɧɨɣ ɮɨɪɦɟ) ɫɨɞɟɪɠɚɧɢɟ ɩɪɢɧɰɢɩɚ
«ɦɢɧɢɦɭɦɚ ȼ».
ɉɪɟɞɥɨɠɟɧɵ ɪɚɡɥɢɱɧɵɟ ɫɩɨɫɨɛɵ ɫɨɡɞɚɧɢɹ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɯ ɷɬɨɦɭ ɩɪɢɧɰɢɩɭ: ɧɚɥɨɠɟɧɢɟ ɧɚ ɩɨɥɟ ɩɪɨɫɬɨɝɨ ɩɪɨɛɤɨɬɪɨɧɚ “ɫɬɟɪɠɧɟɣ ɂɨɮɮɟ” (ɪɢɫ.2.14)
(ɧɚɡɜɚɧɧɵɯ ɬɚɤ ɩɨ ɮɚɦɢɥɢɢ ɚɜɬɨɪɚ, ɜɩɟɪɜɵɟ ɩɪɟɞɥɨɠɢɜɲɟɝɨ ɢ ɪɟɚɥɢɡɨɜɚɜɲɟɝɨ ɢɞɟɸ
ɬɚɤɨɣ ɫɬɚɛɢɥɢɡɚɰɢɢ), ɩɪɢɦɟɧɟɧɢɟ ɫɩɟɰɢɚɥɶɧɵɯ ɤɚɬɭɲɟɤ ɬɢɩɚ “ɛɟɣɫɛɨɥ” (ɪɢɫ.2.15) ɢ ɞɪ. ɋɨɛɥɸɞɟɧɢɟ ɩɪɢɧɰɢɩɚ “ɦɢɧɢɦɭɦɚ ȼ” ɨɛɹɡɚɬɟɥɶɧɨ, ɢɧɚɱɟ ɜ ɨɬɤɪɵɬɵɯ ɥɨɜɭɲɤɚɯ ɩɥɚɡɦɚ ɭɫɬɨɣɱɢɜɨ ɧɟ ɭɞɟɪɠɢɜɚɟɬɫɹ.
Ɋɢɫ.2.14. ɋɯɟɦɚ |
ɫɨɡɞɚɧɢɹ |
ɩɨɥɹ |
ɫ |
Ɋɢɫ.2.15. Ɉɛɦɨɬɤɚ “ɛɟɣɫɛɨɥ” |
“ɦɢɧɢɦɭɦɨɦ B” |
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ɉɥɚɡɦɟɧɧɵɟ ɰɟɧɬɪɢɮɭɝɢ |
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ȼ ɰɢɥɢɧɞɪɢɱɟɫɤɢɯ ɫɢɫɬɟɦɚɯ ɫ ɚɤɫɢɚɥɶɧɵɦ ɩɨɥɟɦ E& ɢ ɪɚɞɢɚɥɶɧɵɦ ɩɨɥɟɦ B& (ɢɥɢ ɫ |
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ɚɤɫɢɚɥɶɧɵɦ ɩɨɥɟɦ B& |
ɢ ɪɚɞɢɚɥɶɧɵɦ ɩɨɥɟɦ |
E&) ɩɥɚɡɦɚ ɛɭɞɟɬ ɜɪɚɳɚɬɶɫɹ ɩɨ ɚɡɢɦɭɬɭ ɫ |
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ɞɪɟɣɮɨɜɨɣ ɫɤɨɪɨɫɬɶɸ |
vE = c |
E |
. ȼɬɨɪɨɣ |
ɜɚɪɢɚɧɬ ɤɨɧɫɬɪɭɤɬɢɜɧɨ |
ɩɪɨɳɟ, |
ɟɝɨ |
ɞɥɹ |
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B |
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F = mvE2 |
/ r , |
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ɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɢ ɛɭɞɟɦ ɨɛɫɭɠɞɚɬɶ. ȼɨɡɧɢɤɚɟɬ ɰɟɧɬɪɨɛɟɠɧɚɹ ɫɢɥɚ |
ɬɟɦ |
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ɛɨɥɶɲɚɹ, ɱɟɦ ɛɨɥɶɲɟ ɦɚɫɫɚ ɱɚɫɬɢɰɵ. ɗɬɚ ɰɟɧɬɪɨɛɟɠɧɚɹ ɫɢɥɚ ɧɚɩɪɚɜɥɟɧɚ ɩɨ ɪɚɞɢɭɫɭ ɢ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɫɨɡɞɚɟɬ ɞɪɟɣɮɨɜɭɸ ɫɤɨɪɨɫɬɶ (ɪɚɡɧɨɝɨ ɡɧɚɤɚ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ, ɧɨ ɜ ɭɩɪɨɳɟɧɧɨɦ ɪɚɫɫɦɨɬɪɟɧɢɢ ɡɚɛɭɞɟɦ ɨɛ ɷɥɟɤɬɪɨɧɚɯ), ɫɤɥɚɞɵɜɚɸɳɭɸɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ vE. Ɍɚɤ ɤɚɤ ɩɪɢ ɡɚɞɚɧɧɨɦ ɪɚɞɢɭɫɟ ɷɬɚ ɞɨɛɚɜɤɚ ɪɚɡɧɚɹ ɞɥɹ ɱɚɫɬɢɰ ɫ ɪɚɡɧɨɣ ɦɚɫɫɨɣ, ɬɨ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɜɨɡɧɢɤɚɟɬ ɫɢɥɚ ɬɪɟɧɢɹ Fmɪ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɩɨ ɤɚɫɚɬɟɥɶɧɨɣ ɤ ɨɤɪɭɠɧɨɫɬɢ, ɬɨɪɦɨɡɹɳɚɹ ɬɹɠɟɥɵɟ ɢ ɭɫɤɨɪɹɸɳɚɹ ɥɟɝɤɢɟ ɢɨɧɵ. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɬɨɣ ɫɢɥɵ ɬɪɟɧɢɹ ɩɨɹɜɢɬɫɹ ɞɪɟɣɮ ɬɹɠɟɥɵɯ ɱɚɫɬɢɰ ɨɬ ɰɟɧɬɪɚ, ɚ ɥɟɝɤɢɯ - ɤ ɰɟɧɬɪɭ ɫɢɫɬɟɦɵ. ɂɨɧɵ ɛɭɞɭɬ ɪɚɡɞɟɥɹɬɶɫɹ ɩɨ ɦɚɫɫɚɦ, ɤɚɤ ɢ ɜ ɨɛɵɱɧɨɣ ɰɟɧɬɪɢɮɭɝɟ, ɧɨ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɛɨɥɶɲɢɦɢ, ɡɧɚɱɢɬ, ɦɨɠɟɬ ɛɵɬɶ ɛɨɥɶɲɢɦ ɢ ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɡɞɟɥɟɧɢɹ. Ɋɟɚɥɶɧɨ ɜɫɟ ɫɥɨɠɧɟɟ ɢ ɧɚɞɨ ɭɱɢɬɵɜɚɬɶ ɬɪɟɧɢɟ ɡɚ ɫɱɟɬ ɫɬɨɥɤɧɨɜɟɧɢɣ ɫ ɷɥɟɤɬɪɨɧɚɦɢ, ɬɟɪɦɨɞɢɮɮɭɡɢɸ, ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɫɨ ɫɬɟɧɤɚɦɢ ɢ ɬ.ɞ. ȼɟɞɟɬɫɹ ɦɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɣ ɩɨ ɩɪɢɦɟɧɟɧɢɸ ɩɨɞɨɛɧɵɯ ɰɟɧɬɪɢɮɭɝ ɞɥɹ ɪɚɡɞɟɥɟɧɢɹ ɷɥɟɦɟɧɬɨɜ (ɢɥɢ ɯɢɦɢɱɟɫɤɢɯ ɫɨɟɞɢɧɟɧɢɣ) ɢ ɞɚɠɟ ɢɡɨɬɨɩɨɜ.
§ 20. əɜɥɟɧɢɹ ɩɟɪɟɧɨɫɚ ɜ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ
ɉɥɚɡɦɚ, ɩɨɦɟɳɟɧɧɚɹ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɫɬɚɧɨɜɢɬɫɹ ɚɧɢɡɨɬɪɨɩɧɨɣ: ɧɚɩɪɚɜɥɟɧɢɹ ɜɞɨɥɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɨɤɚɡɵɜɚɸɬɫɹ ɧɟɪɚɜɧɨɩɪɚɜɧɵɦɢ. ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɯɚɪɚɤɬɟɪ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜɞɨɥɶ ɩɨɥɹ ɢ ɩɨɩɟɪɟɤ ɩɨɥɹ ɪɟɡɤɨ ɨɬɥɢɱɚɟɬɫɹ. ȼ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɪɨɞɨɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɜ ɨɬɫɭɬɫɬɜɢɢ ɞɪɭɝɢɯ ɫɢɥ ɨɫɬɚɟɬɫɹ ɫɜɨɛɨɞɧɵɦ, ɚ ɜ ɩɨɩɟɪɟɱɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɱɚɫɬɢɰɚ ɜɪɚɳɚɟɬɫɹ ɩɨ ɥɚɪɦɨɪɨɜɫɤɨɣ ɨɤɪɭɠɧɨɫɬɢ, ɪɚɞɢɭɫ ɤɨɬɨɪɨɣ ɬɟɦ ɦɟɧɶɲɟ, ɱɟɦ ɛɨɥɶɲɟ ɜɟɥɢɱɢɧɚ ɩɨɥɹ.
Ɋɚɡɥɢɱɢɟ ɜ ɯɚɪɚɤɬɟɪɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɧɚɯɨɞɢɬ ɫɜɨɟ ɨɬɪɚɠɟɧɢɟ ɜ ɢɡɦɟɧɟɧɢɢ ɫɜɨɣɫɬɜ ɩɥɚɡɦɵ, ɜ ɱɚɫɬɧɨɫɬɢ, ɦɨɠɧɨ ɨɠɢɞɚɬɶ ɫɭɳɟɫɬɜɟɧɧɨɟ ɨɬɥɢɱɢɟ ɜ ɜɟɥɢɱɢɧɟ «ɩɪɨɞɨɥɶɧɵɯ» ɢ «ɩɨɩɟɪɟɱɧɵɯ» ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɟɪɟɧɨɫɚ. ɋɜɨɟɨɛɪɚɡɢɟ ɩɥɚɡɦɟɧɧɨɣ ɫɪɟɞɵ, ɨɞɧɚɤɨ, ɜ ɬɨɦ, ɱɬɨ ɨɧɚ ɡɚɱɚɫɬɭɸ ɧɟ ɫɥɟɞɭɟɬ ɩɪɨɫɬɵɦ, ɧɚ ɩɟɪɜɵɣ ɜɡɝɥɹɞ ɨɱɟɜɢɞɧɵɦ, ɫɯɟɦɚɦ. Ɍɚɤɨɜɚ, ɧɚɩɪɢɦɟɪ, ɫɢɬɭɚɰɢɹ ɫ ɩɪɨɜɨɞɢɦɨɫɬɶɸ - ɩɪɨɞɨɥɶɧɚɹ ɢ ɩɨɩɟɪɟɱɧɚɹ ɩɪɨɜɨɞɢɦɨɫɬɢ ɨɬɥɢɱɚɸɬɫɹ ɥɢɲɶ ɩɪɢɦɟɪɧɨ ɜɞɜɨɟ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ ɨ ɧɚɥɢɱɢɢ ɧɟɤɨɬɨɪɨɝɨ «ɦɟɯɚɧɢɡɦɚ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ», ɜɵɪɚɜɧɢɜɚɸɳɟɝɨ ɚɧɢɡɨɬɪɨɩɢɸ. Ɉɛɫɭɠɞɟɧɢɟ ɩɪɨɰɟɫɫɨɜ ɩɟɪɟɧɨɫɚ ɜ «ɡɚɦɚɝɧɢɱɟɧɧɨɣ» ɩɥɚɡɦɟ ɧɚɱɧɟɦ ɫ ɞɢɮɮɭɡɢɢ.
Ⱦɢɮɮɭɡɢɹ
ɋɬɨɥɤɧɨɜɟɧɢɹ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɨɞɧɨɝɨ ɫɨɪɬɚ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɧɟ ɩɪɢɜɨɞɹɬ ɤ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɢɦ ɢɡɦɟɧɟɧɢɹɦ ɢɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ [12], ɧɟ ɩɪɢɜɨɞɹɬ, ɬɟɦ ɫɚɦɵɦ, ɤ ɞɢɮɮɭɡɢɢ. Ⱦɢɮɮɭɡɢɹ ɜɨɡɦɨɠɧɚ ɥɢɲɶ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɪɚɡɧɨɪɨɞɧɵɯ ɱɚɫɬɢɰ, ɧɚɩɪɢɦɟɪ ɢɨɧɨɜ ɢ ɷɥɟɤɬɪɨɧɨɜ ɩɥɚɡɦɵ. ɇɚɩɨɦɧɢɦ, ɱɬɨ ɞɢɮɮɭɡɢɨɧɧɵɣ ɩɨɬɨɤ (ɟɫɥɢ ɨɬɜɥɟɱɶɫɹ ɨɬ ɷɮɮɟɤɬɨɜ ɬɟɪɦɨɞɢɮɮɭɡɢɢ ɢ ɛɚɪɨɞɢɮɮɭɡɢɢ) ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɝɪɚɞɢɟɧɬɭ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɥɚɡɦɵ, ɩɪɢ ɷɬɨɦ ɧɚɩɪɚɜɥɟɧɢɟ ɩɨɬɨɤɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɝɪɚɞɢɟɧɬɭ ɤɨɧɰɟɧɬɪɚɰɢɢ, ɚ ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɢ ɟɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ.
Ʉɨɷɮɮɢɰɢɟɧɬ ɩɪɨɞɨɥɶɧɨɣ ɞɢɮɮɭɡɢɢ ɩɥɚɡɦɵ, ɩɨɦɟɳɟɧɧɨɣ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɢɦɟɟɬ ɬɚɤɭɸ ɠɟ ɜɟɥɢɱɢɧɭ, ɤɚɤ ɢ ɤɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ ɩɥɚɡɦɵ ɜ ɨɬɫɭɬɫɬɜɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ:
D |
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= |
1 |
λ v |
Te |
= |
Te |
τ |
ei |
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3 |
m |
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ɉɨɫɤɨɥɶɤɭ ɩɟɪɟɦɟɳɟɧɢɟ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɨɫɥɟ ɫɬɨɥɤɧɨɜɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɟɥɢɱɢɧɨɣ ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɪɚɞɢɭɫɚ ρ, ɚ ɬɚɤɠɟ ɜɪɟɦɟɧɟɦ ɦɟɠɞɭ ɷɥɟɤɬɪɨɧɢɨɧɧɵɦɢ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ, τei, ɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɩɟɪɟɱɧɨɣ ɞɢɮɮɭɡɢɢ, ɤɚɤ ɷɬɨ ɫɥɟɞɭɟɬ ɢɡ ɨɛɳɟɝɨ ɨɩɪɟɞɟɥɟɧɢɹ D ~< ( ∆x )2 > /τ (ɫɦ. §10), ɞɨɥɠɟɧ ɨɩɪɟɞɟɥɹɬɶɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ:
D ~ |
ρ 2 |
(2.81) |
. |
||
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τei |
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ɉɨɫɤɨɥɶɤɭ ɞɢɮɮɭɡɢɹ ɩɥɚɡɦɵ ɧɨɫɢɬ ɚɦɛɢɩɨɥɹɪɧɵɣ ɯɚɪɚɤɬɟɪ, ɬɨ ɜ ɤɚɱɟɫɬɜɟ ɯɚɪɚɤɬɟɪɧɨɝɨ ɪɚɡɦɟɪɚ ɜ ɮɨɪɦɭɥɭ (2.81) ɫɥɟɞɭɟɬ ɩɨɞɫɬɚɜɥɹɬɶ ɦɟɧɶɲɢɣ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ, ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ - ɷɥɟɤɬɪɨɧɧɵɣ. ɉɨɫɤɨɥɶɤɭ ɷɥɟɤɬɪɨɧɧɵɣ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɩɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ ɷɥɟɤɬɪɨɧɨɜ vTe ɢ ɷɥɟɤɬɪɨɧɧɨɣ ɰɢɤɥɨɬɪɨɧɧɨɣ ɱɚɫɬɨɬɨɣ ωȼɟ:
ρ ~ |
vTe |
, |
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||
e |
ωBe |
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ɬɨ, ɩɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɜ (2.81), ɥɟɝɤɨ ɩɨɥɭɱɢɬɶ
D |
D|| |
)2 . |
(2.82) |
(ωτei |
ȼɟɥɢɱɢɧɚ ɩɪɨɢɡɜɟɞɟɧɢɹ ωBeτei ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɡɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɱɚɫɬɢɰ (ɢɧɨɝɞɚ ɟɺ ɧɚɡɵɜɚɸɬ ɩɚɪɚɦɟɬɪɨɦ ɡɚɦɚɝɧɢɱɟɧɧɨɫɬɢ), ɬ.ɟ. ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɫɬɟɩɟɧɶ ɜɥɢɹɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɢɯ ɞɜɢɠɟɧɢɟ. ȿɫɥɢ ɷɬɨ ɩɪɨɢɡɜɟɞɟɧɢɟ ɜɟɥɢɤɨ, ɬɨ ɱɚɫɬɢɰɚ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɫɨɜɟɪɲɚɟɬ ɦɧɨɝɨ ɥɚɪɦɨɪɨɜɫɤɢɯ ɨɛɨɪɨɬɨɜ. ȼɵɪɚɠɟɧɢɟ (2.82) ɩɪɢɦɟɧɢɦɨ ɤ ɫɥɭɱɚɸ ɫɢɥɶɧɨ
ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ, ɧɨ ɟɝɨ ɧɟɬɪɭɞɧɨ ɨɛɨɛɳɢɬɶ. ȼ ɫɥɭɱɚɟ ɫɥɚɛɨɝɨ ɩɨɥɹ ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɪɨɞɨɥɶɧɨɣ ɢ ɩɨɩɟɪɟɱɧɨɣ ɞɢɮɮɭɡɢɢ ɞɨɥɠɧɵ ɫɨɜɩɚɞɚɬɶ D /D||~1, ɚ ɞɥɹ ɫɢɥɶɧɨɝɨ ɩɨɥɹ,
ɮɚɤɬɢɱɟɫɤɢ, |
D |
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D |
~ (ω |
Be |
τ |
ei |
)−2 . ɉɨɷɬɨɦɭ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɞɨɥɠɧɨ ɛɵɬɶ [13]: |
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1 |
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D ~ D|| |
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(2.83) |
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1 +(ωBeτei |
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)2 |
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ȿɫɥɢ ɭɱɟɫɬɶ ɪɚɡɥɢɱɢɟ ɢɨɧɧɨɣ ɢ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪ, ɬɨ ɜɵɪɚɠɟɧɢɟ ɞɥɹ |
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ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ ɩɨɩɟɪɟɤ ɩɨɥɹ ɩɪɢɧɢɦɚɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ [12]: |
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D |
Te |
+Ti |
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D0 |
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τ |
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)2 |
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T |
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1 +(ω |
Be |
ei |
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ȼ ɫɢɥɶɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ, ɤɨɝɞɚ ɩɚɪɚɦɟɬɪ ɡɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɜɟɥɢɤ, |
ɞɢɮɮɭɡɢɹ |
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ɩɨɩɟɪɟɤ ɩɨɥɹ ɞɨɥɠɧɚ ɩɪɨɢɫɯɨɞɢɬɶ ɨɱɟɧɶ ɦɟɞɥɟɧɧɨ. ɉɨɞɱɟɪɤɧɟɦ, ɱɬɨ ɫɭɳɟɫɬɜɟɧɧɨ ɨɬɥɢɱɚɟɬɫɹ ɢ ɯɚɪɚɤɬɟɪ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɞɢɮɮɭɡɢɢ ɨɬ ɩɚɪɚɦɟɬɪɨɜ ɩɥɚɡɦɵ. ɋɨɝɥɚɫɧɨ ɜɵɪɚɠɟɧɢɸ (1.54), ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɪɨɞɨɥɶɧɨɣ ɞɢɮɮɭɡɢɢ ɢɦɟɟɦ D0 Ɍ5/2/n, ɚ ɬɚɤ ɤɚɤ ωȼɟ ȼ, τei T3/2/n, ɬɨ ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɨɩɟɪɟɱɧɨɣ ɞɢɮɮɭɡɢɢ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɵ ɩɨɥɭɱɚɟɦ
D |
n |
T |
. |
(2.84) |
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B2 |
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Ɇɵ ɜɢɞɢɦ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɞɨɥɶɧɨɣ ɞɢɮɮɭɡɢɢ ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɪɨɫɬɨɦ ɩɥɨɬɧɨɫɬɢ ɩɥɚɡɦɵ ɢ ɪɚɫɬɟɬ ɫ ɪɨɫɬɨɦ ɟɺ ɬɟɦɩɟɪɚɬɭɪɵ, ɚ ɩɨɩɟɪɟɱɧɨɣ, ɧɚɩɪɨɬɢɜ, ɪɚɫɬɟɬ ɫ ɪɨɫɬɨɦ ɩɥɨɬɧɨɫɬɢ ɢ ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɪɨɫɬɨɦ ɬɟɦɩɟɪɚɬɭɪɵ!
Ɍɨɬ ɮɚɤɬ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɩɟɪɟɱɧɨɣ ɞɢɮɮɭɡɢɢ ɛɵɫɬɪɨ ɭɛɵɜɚɟɬ ɫ ɪɨɫɬɨɦ ɜɟɥɢɱɢɧɵ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɤ ɬɨɦɭ ɠɟ ɞɨɥɠɟɧ ɭɦɟɧɶɲɚɬɶɫɹ ɩɨ ɦɟɪɟ ɧɚɝɪɟɜɚ ɩɥɚɡɦɵ, ɢ ɨɩɪɟɞɟɥɢɥɨ ɧɚɞɟɠɞɭ ɨɛɟɫɩɟɱɢɬɶ ɬɟɪɦɨɢɡɨɥɹɰɢɸ ɩɥɚɡɦɵ ɫ ɩɨɦɨɳɶɸ ɫɢɥɶɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ʉ ɫɨɠɚɥɟɧɢɸ, ɫɭɳɟɫɬɜɭɸɬ ɢ ɞɪɭɝɢɟ ɩɪɢɱɢɧɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɜɨɡɧɢɤɧɨɜɟɧɢɸ ɩɨɬɨɤɨɜ ɩɥɚɡɦɵ ɩɨɩɟɪɟɤ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɸɳɢɯ ɩɨɬɨɤɢ, ɜɵɡɵɜɚɟɦɵɟ ɤɥɚɫɫɢɱɟɫɤɨɣ ɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɣ ɞɢɮɮɭɡɢɟɣ. ɇɚɢɛɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɵɦɢ ɢɡ ɧɢɯ ɹɜɥɹɸɬɫɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɢ, ɨ ɧɢɯ ɛɭɞɟɦ ɝɨɜɨɪɢɬɶ ɩɨɡɠɟ. ɇɨ ɢ ɜ ɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ, ɜ ɫɩɨɤɨɣɧɨɣ ɛɟɫɬɨɤɨɜɨɣ ɩɥɚɡɦɟ ɦɨɝɭɬ ɜɨɡɧɢɤɚɬɶ ɦɟɫɬɧɵɟ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɩɨɥɹ, ɩɨɹɜɥɟɧɢɟ ɤɨɬɨɪɵɯ ɬɚɤɠɟ ɩɪɢɜɨɞɢɬ ɤ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɸ ɤɨɧɰɟɧɬɪɚɰɢɢ, ɤ ɞɢɮɮɭɡɢɢ.
Ɍɚɤɢɟ ɩɪɨɰɟɫɫɵ ɩɨɥɭɱɢɥɢ ɧɚɡɜɚɧɢɟ ɬɭɪɛɭɥɟɧɬɧɨɣ ɞɢɮɮɭɡɢɢ. Ʉɚɱɟɫɬɜɟɧɧɨ ɦɨɠɧɨ ɟɟ ɨɩɢɫɚɬɶ, ɩɪɟɞɩɨɥɨɠɢɜ, ɱɬɨ ɦɚɫɲɬɚɛ ɜɨɡɧɢɤɚɸɳɢɯ ɮɥɭɤɬɭɚɰɢɨɧɧɵɯ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ:
elE T. (2.85)
Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɯɚɪɚɤɬɟɪɧɚɹ ɷɧɟɪɝɢɹ, ɤɨɬɨɪɭɸ ɧɚɛɢɪɚɸɬ ɱɚɫɬɢɰɵ (ɫ ɡɚɪɹɞɨɦ ɟ) ɜ ɩɨɥɟ, ɨɤɚɡɵɜɚɟɬɫɹ ɩɨɪɹɞɤɚ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ ɩɥɚɡɦɵ. ȼ ɩɪɟɞɟɥɚɯ ɨɛɥɚɫɬɢ, ɩɪɨɬɹɠɟɧɧɨɫɬɶ ɤɨɬɨɪɨɣ ɩɨɪɹɞɤɚ l, ɩɥɚɡɦɚ ɞɪɟɣɮɭɟɬ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɤɪɟɳɟɧɧɵɯ ȿ×ȼ ɩɨɥɟɣ. ȿɫɥɢ ɧɚɩɪɚɜɥɟɧɢɟ ɩɨɥɹ ɦɟɧɹɟɬɫɹ ɯɚɨɬɢɱɟɫɤɢ, ɬɨ ɜ ɫɨɫɟɞɧɢɯ ɨɛɥɚɫɬɹɯ ɫ ɢɡɦɟɧɟɧɢɟɦ ɧɚɩɪɚɜɥɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɦɟɧɹɟɬɫɹ ɢ ɧɚɩɪɚɜɥɟɧɢɟ ɞɪɟɣɮɚ − ɩɥɚɡɦɚ ɞɜɢɠɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ
vE = c |
E |
, |
(2.86) |
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B |
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ɢ ɛɟɫɩɨɪɹɞɨɱɧɨ ɦɟɧɹɟɬ ɧɚɩɪɚɜɥɟɧɢɟ ɫɜɨɟɝɨ ɞɜɢɠɟɧɢɹ. Ɏɥɭɤɬɭɚɰɢɨɧɧɵɟ ɹɱɟɣɤɢ ɠɢɜɭɬ ɤɨɪɨɬɤɨɟ ɜɪɟɦɹ, ɩɨɪɹɞɤɚ ɜɪɟɦɟɧɢ ɩɪɨɥɟɬɚ τ ~ l/vE. ɂɡɭɱɟɧɢɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɜ ɩɨɞɨɛɧɵɯ ɬɭɪɛɭɥɟɧɬɧɵɯ ɩɨɥɹɯ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɨɣ, ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɡɚɞɚɱɟɣ. ɍɩɪɨɳɟɧɧɨ ɟɝɨ ɦɨɠɧɨ ɬɪɚɤɬɨɜɚɬɶ ɤɚɤ ɞɢɮɮɭɡɢɸ (ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɸɬ
ɬɟɪɦɢɧ ɬɭɪɛɭɥɟɧɬɧɚɹ ɞɢɮɮɭɡɢɹ) ɫ ɷɮɮɟɤɬɢɜɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɞɢɮɮɭɡɢɢ, ɨɩɪɟɞɟɥɹɟɦɨɦ ɜɟɥɢɱɢɧɨɣ l ɢɡ
(2.85) ɢ vE ɢɡ (2.86),
D |
~ |
<( ∆x )2 |
> |
~ |
l 2 |
~ v l ~ |
cT |
(2.87) |
τ |
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τ |
eB |
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Ɍɭ ɪɛ |
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E |
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ɗɬɚ ɩɨɥɭɱɟɧɧɚɹ ɢɡ ɧɟɫɬɪɨɝɢɯ ɤɚɱɟɫɬɜɟɧɧɵɯ ɫɨɨɛɪɚɠɟɧɢɣ ɮɨɪɦɭɥɚ ɮɚɤɬɢɱɟɫɤɢ ɫɨɜɩɚɞɚɟɬ ɫ ɷɦɩɢɪɢɱɟɫɤɨɣ ɮɨɪɦɭɥɨɣ Ȼɨɦɚ, ɩɨɥɭɱɟɧɧɨɣ ɢɡ ɚɧɚɥɢɡɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ:
DB = |
1 |
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c |
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T |
. |
(2.88) |
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16 e B |
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Ʉɨɷɮɮɢɰɢɟɧɬ ɞɢɮɮɭɡɢɢ, ɨɩɪɟɞɟɥɹɟɦɵɣ ɷɬɨɣ ɮɨɪɦɭɥɨɣ, ɧɨɫɢɬ ɧɚɡɜɚɧɢɟ ɛɨɦɨɜɫɤɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ. Ɂɚɜɢɫɢɦɨɫɬɢ ɜɟɥɢɱɢɧ DB ɢ D ɨɬ ɜɟɥɢɱɢɧɵ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɪɚɡɥɢɱɧɵ. ɋɪɚɜɧɢɜɚɹ ɜɵɪɚɠɟɧɢɹ (2.82) ɢ (2.88), ɧɚɯɨɞɢɦ ɞɥɹ ɨɬɧɨɲɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɞɢɮɮɭɡɢɢ
(2.89)
ɬ.ɟ. ɜ ɡɚɦɚɝɧɢɱɟɧɧɨɣ ɩɥɚɡɦɟ, ɤɨɝɞɚ ɡɚ ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ɷɥɟɤɬɪɨɧ ɭɫɩɟɜɚɟɬ ɫɨɜɟɪɲɢɬɶ ɦɧɨɝɨ ɥɚɪɦɨɪɨɜɫɤɢɯ ɨɛɨɪɨɬɨɜ, ɨɩɪɟɞɟɥɹɸɳɭɸ ɪɨɥɶ ɞɨɥɠɧɚ ɢɝɪɚɬɶ ɬɭɪɛɭɥɟɧɬɧɚɹ ɞɢɮɮɭɡɢɹ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ ɤɨɷɮɮɢɰɢɟɧɬ ɤɥɚɫɫɢɱɟɫɤɨɣ ɞɢɮɮɭɡɢɢ D ɭɦɟɧɶɲɚɟɬɫɹ, ɚ ɬɭɪɛɭɥɟɧɬɧɨɣ, DɌɭɪɛ, − ɪɚɫɬɟɬ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɞɢɮɮɭɡɢɹ «ɩɨ Ȼɨɦɭ» ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɨɫɬɚɜɥɹɟɬ ɧɚɞɟɠɞ ɧɚ ɞɥɢɬɟɥɶɧɨɟ ɭɞɟɪɠɚɧɢɟ ɝɨɪɹɱɟɣ ɩɥɚɡɦɵ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ.
ɇɟɨɤɥɚɫɫɢɱɟɫɤɚɹ ɞɢɮɮɭɡɢɹ
ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɪɹɞɟ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɫɨ ɫɩɨɤɨɣɧɨɣ, ɩɪɚɤɬɢɱɟɫɤɢ ɪɚɜɧɨɜɟɫɧɨɣ, ɯɨɥɨɞɧɨɣ ɩɥɚɡɦɨɣ (ɧɚ ɬɚɤ ɧɚɡɵɜɚɟɦɵɯ Q-ɦɚɲɢɧɚɯ) ɧɟɨɞɧɨɤɪɚɬɧɨ ɧɚɛɥɸɞɚɥɚɫɶ ɞɢɮɮɭɡɢɹ, ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɬɨɪɨɣ ɜɟɫɶɦɚ ɛɥɢɡɨɤ ɤ ɤɥɚɫɫɢɱɟɫɤɨɦɭ ɡɧɚɱɟɧɢɸ.
ɇɚ ɞɪɭɝɢɯ ɭɫɬɚɧɨɜɤɚɯ, ɜ ɱɚɫɬɧɨɫɬɢ, ɧɚ ɫɬɟɥɥɚɪɚɬɨɪɚɯ ɢɡɦɟɪɹɟɦɨɟ ɜɪɟɦɹ ɭɞɟɪɠɚɧɢɹ ɩɥɚɡɦɵ ɫɨɨɬɜɟɬɫɬɜɨɜɚɥɨ ɤɨɷɮɮɢɰɢɟɧɬɭ ɞɢɮɮɭɡɢɢ ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɸɳɟɦɭ ɤɥɚɫɫɢɱɟɫɤɢɣ ɢ ɛɥɢɡɤɨɦɭ ɩɨ ɜɟɥɢɱɢɧɟ ɤ ɨɩɪɟɞɟɥɹɟɦɨɦɭ ɮɨɪɦɭɥɨɣ Ȼɨɦɚ. ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɢɡɦɟɪɟɧɧɵɟ ɧɚ ɭɫɬɚɧɨɜɤɚɯ ɬɢɩɚ ɬɨɤɚɦɚɤɚ, ɫɨɡɞɚɧɧɵɯ ɨɬɟɱɟɫɬɜɟɧɧɵɦɢ ɭɱɟɧɵɦɢ, ɜɟɥɢɱɢɧɵ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ ɨɤɚɡɚɥɢɫɶ ɛɨɥɶɲɟ ɤɥɚɫɫɢɱɟɫɤɨɝɨ, ɧɨ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ ɛɨɦɨɜɫɤɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ.
ɉɪɟɜɵɲɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ ɜ ɫɬɨɥɤɧɨɜɢɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɧɚɞ ɟɝɨ ɤɥɚɫɫɢɱɟɫɤɢɦ ɡɧɚɱɟɧɢɟɦ, ɩɨɥɭɱɟɧɧɵɦ ɞɥɹ ɨɞɧɨɪɨɞɧɨɝɨ ɩɨɥɹ, ɧɚɯɨɞɢɬ ɨɛɴɹɫɧɟɧɢɟ, ɤɚɤ ɜɩɟɪɜɵɟ ɛɵɥɨ ɩɨɤɚɡɚɧɨ ɉɮɢɪɲɟɦ ɢ ɒɥɸɬɟɪɨɦ, ɜ ɢɡɦɟɧɟɧɢɢ ɝɟɨɦɟɬɪɢɢ ɩɨɥɹ. ȼ ɝɟɨɦɟɬɪɢɢ ɧɟɨɞɧɨɪɨɞɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɬɨɤɚɦɚɤɚ (ɪɢɫ. 2.16), ɫɭɳɟɫɬɜɟɧɧɭɸ ɪɨɥɶ ɢɝɪɚɸɬ ɞɪɟɣɮɵ. Ⱦɪɟɣɮɨɜɵɟ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬɥɢɱɚɸɬɫɹ ɨɬ ɦɚɝɧɢɬɧɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ. ɉɪɢ ɷɬɨɦ ɫɞɜɢɝ ɦɨɠɟɬ ɩɪɟɜɵɲɚɬɶ ɜɟɥɢɱɢɧɭ ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɪɚɞɢɭɫɚ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɪɢ ɫɬɨɥɤɧɨɜɟɧɢɢ ɱɚɫɬɢɰɚ ɫɦɟɳɚɟɬɫɹ ɩɨɩɟɪɟɤ ɩɨɥɹ ɧɚ ɪɚɫɫɬɨɹɧɢɟ, ɩɪɟɜɵɲɚɸɳɟɟ ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ, ɱɬɨ ɢ ɜɵɡɵɜɚɟɬ ɷɮɮɟɤɬɢɜɧɨɟ ɭɜɟɥɢɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɨɩɟɪɟɱɧɨɣ ɞɢɮɮɭɡɢɢ, ɤɨɬɨɪɵɣ ɨɤɚɡɵɜɚɟɬɫɹ ɪɚɜɧɵɦ:
D |
ɉɒ |
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ɝɞɟ q>1 - ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɩɚɫɚ ɭɫɬɨɣɱɢɜɨɫɬɢ, ɪɚɜɧɵɣ ɨɬɧɨɲɟɧɢɸ ɲɚɝɚ ɫɢɥɨɜɨɣ ɥɢɧɢɢ ɤ ɞɥɢɧɟ ɫɢɫɬɟɦɵ ɜɞɨɥɶ ɨɫɢ.
Ʉɚɱɟɫɬɜɟɧɧɨ ɷɬɨɬ ɪɟɡɭɥɶɬɚɬ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ȼ ɜɢɧɬɨɜɨɦ ɩɨɥɟ ɯɚɪɚɤɬɟɪɧɵɦ ɪɚɡɦɟɪɨɦ ɹɜɥɹɟɬɫɹ ɲɚɝ ɫɢɥɨɜɨɣ ɥɢɧɢɢ, ɩɭɫɬɶ h. ɑɚɫɬɢɰɚ, ɞɜɢɠɭɳɚɹɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ v, ɩɪɨɥɟɬɚɟɬ ɪɚɫɫɬɨɹɧɢɟ ɩɨɪɹɞɤɚ ɲɚɝɚ ɡɚ ɜɪɟɦɹ tɩɪɨɥ~h/v, ɢ ɡɚ ɷɬɨ ɜɪɟɦɹ ɫɞɪɟɣɮɨɜɵɜɚɟɬ ɩɨɩɟɪɟɤ ɩɨɥɹ ɧɚ ɪɚɫɫɬɨɹɧɢɟ
∆ɩɪɨɥ ~ vd tɩɪɨɥ .
Ɂɞɟɫɶ vd - ɫɤɨɪɨɫɬɶ ɞɪɟɣɮɚ ɩɨ ɛɢɧɨɪɦɚɥɢ, ɤɨɬɨɪɭɸ, ɝɪɭɛɨ ɫɱɢɬɚɹ v||~v ~vɌ, ɨɰɟɧɢɜɚɟɦ, ɫɨɝɥɚɫɧɨ (2.36), ɤɚɤ
vd = |
v2 |
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ɝɞɟ R – ɛɨɥɶɲɨɣ ɪɚɞɢɭɫ ɬɨɪɚ, ωȼ – ɰɢɤɥɨɬɪɨɧɧɚɹ ɱɚɫɬɨɬɚ, ɚ vɌ – ɬɟɩɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ. Ɍɨɝɞɚ
∆ |
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~ qρ |
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d v |
RωB |
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ɝɞɟ ρȼ -ɥɚɪɦɨɪɨɜɫɤɢɣ ɪɚɞɢɭɫ, ɚ q=h/2πR. – ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɩɚɫɚ ɭɫɬɨɣɱɢɜɨɫɬɢ.
ɍɜɟɥɢɱɟɧɢɟ ɜ q ɪɚɡ ɯɚɪɚɤɬɟɪɧɨɝɨ ɪɚɡɦɟɪɚ ɩɪɢɜɨɞɢɬ ɤ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦɭ ɭɜɟɥɢɱɟɧɢɸ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ, ɢ ɜ ɪɟɠɢɦɟ ɉɮɢɪɲɚ-ɒɥɸɬɟɪɚ ɞɨɥɠɧɨ ɛɵɬɶ:
D |
ɉɒ |
~ q2 D |
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Ɂɚɦɟɧɢɜ ɡɞɟɫɶ q2 ɧɚ 1+q2, ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ ɚɤɤɭɪɚɬɧɵɣ ɩɟɪɟɯɨɞ ɤ ɫɥɭɱɚɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫ ɩɪɹɦɵɦɢ ɫɢɥɨɜɵɦɢ ɥɢɧɢɹɦɢ, ɤɨɝɞɚ q→0, ɩɪɢɯɨɞɢɦ ɤ ɮɨɪɦɭɥɟ (2.90).
ɉɨɞɱɟɪɤɧɟɦ ɟɳɟ ɪɚɡ, ɱɬɨ ɩɨɥɭɱɟɧɧɨɟ ɭɜɟɥɢɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɮɮɭɡɢɢ ɧɟ ɫɜɹɡɚɧɨ ɫ ɭɱɟɬɨɦ ɤɚɤɢɯ-ɥɢɛɨ ɬɭɪɛɭɥɟɧɬɧɵɯ ɩɭɥɶɫɚɰɢɣ, ɚ ɥɢɲɶ ɫ ɚɤɤɭɪɚɬɧɵɦ ɭɱɟɬɨɦ ɝɟɨɦɟɬɪɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȼ ɷɬɨɦ ɩɥɚɧɟ ɮɨɪɦɭɥɚ ɉɮɢɪɲɚ-ɒɥɸɬɟɪɚ ɬɚɤɠɟ ɨɩɢɫɵɜɚɟɬ ɤɥɚɫɫɢɱɟɫɤɭɸ ɫɬɨɥɤɧɨɜɢɬɟɥɶɧɭɸ ɞɢɮɮɭɡɢɸ ɩɨɩɟɪɟɤ ɩɨɥɹ, ɧɨ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɬɨɪɨɢɞɚɥɶɧɨɣ ɝɟɨɦɟɬɪɢɢ ɩɪɢ ɧɚɥɢɱɢɢ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ. ɉɪɢ ɷɬɨɦ ɫɬɨɥɤɧɨɜɟɧɢɹ ɫɱɢɬɚɸɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɱɚɫɬɵɦɢ. ɉɨɹɫɧɢɦ, ɤɚɤ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɨɬɜɟɱɚɸɳɭɸ ɷɬɨɦɭ ɬɪɟɛɨɜɚɧɢɸ ɝɪɚɧɢɱɧɭɸ ɱɚɫɬɨɬɭ ɫɬɨɥɤɧɨɜɟɧɢɣ. Ɉɱɟɜɢɞɧɨ, ɧɟɨɛɯɨɞɢɦɨ ɫɪɚɜɧɢɬɶ ɯɚɪɚɤɬɟɪɧɨɟ ɜɪɟɦɹ ɦɟɠɞɭ ɫɬɨɥɤɧɨɜɟɧɢɹɦɢ ~ν −1 ɢ ɯɚɪɚɤɬɟɪɧɨɟ ɩɪɨɥɟɬɧɨɟ ɜɪɟɦɹ ~h/v, ɫ ɬɟɦ, ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ ɞɥɹ ɪɟɠɢɦɚ ɉɮɢɪɲɚ-ɒɥɸɬɟɪɚ:
ν >νɉɒ ~ |
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ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɷɬɨɝɨ ɭɫɥɨɜɢɹ ɱɚɫɬɢɰɵ |
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ɭɫɩɟɜɚɸɬ ɫɬɨɥɤɧɭɬɶɫɹ ɪɚɧɶɲɟ, ɱɟɦ |
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ɩɪɨɥɟɬɹɬ |
ɯɚɪɚɤɬɟɪɧɵɣ |
ɪɚɡɦɟɪ |
ɩɨɪɹɞɤɚ |
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ɲɚɝɚ ɜɢɧɬɚ. |
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ɉɪɢ |
ɦɟɧɶɲɢɯ |
ɱɚɫɬɨɬɚɯ |
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ɫɬɨɥɤɧɨɜɟɧɢɣ, ɤɚɤ ɜɩɟɪɜɵɟ ɩɨɤɚɡɚɥɢ |
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Ƚɚɥɟɟɜ ɢ ɋɚɝɞɟɟɜ [14], ɨɤɚɡɵɜɚɟɬɫɹ |
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ɫɭɳɟɫɬɜɟɧɧɵɦ ɭɱɟɫɬɶ ɟɳɺ ɨɞɧɭ ɜɚɠɧɭɸ |
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ɨɫɨɛɟɧɧɨɫɬɶ ɜ ɯɚɪɚɤɬɟɪɟ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ |
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ɜ ɬɨɪɨɢɞɚɥɶɧɨɦ ɩɨɥɟ ɫ ɜɢɧɬɨɜɵɦɢ |
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ɫɢɥɨɜɵɦɢ ɥɢɧɢɹɦɢ. ȼɢɧɬɨɜɵɟ ɫɢɥɨɜɵɟ |
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ɥɢɧɢɢ, «ɧɚɦɨɬɚɧɧɵɟ ɧɚ ɬɨɪ», ɫɝɭɳɚɸɬɫɹ |
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ɧɚ ɜɧɭɬɪɟɧɧɟɦ ɨɛɜɨɞɟ ɬɨɪɚ ɢ ɪɚɡɪɟɠɚɸɬɫɹ |
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ɧɚ ɜɧɟɲɧɟɦ (ɪɢɫ. 2.16,ɚ). ɍɦɟɫɬɧɚɹ |
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ɚɧɚɥɨɝɢɹ: ɩɪɟɞɫɬɚɜɢɦ ɫɟɛɟ ɧɚɦɨɬɚɧɧɭɸ ɫ |
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ɩɨɫɬɨɹɧɧɵɦ ɲɚɝɨɦ ɢɡ ɝɢɛɤɨɣ ɩɪɨɜɨɥɨɤɢ |
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ɩɪɹɦɭɸ ɫɩɢɪɚɥɶ. ȿɫɥɢ ɟɺ ɢɡɨɝɧɭɬɶ ɜ |
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Ɋɢɫ.2.16. ɋɯɟɦɚ ɨɛɪɚɡɨɜɚɧɢɹ ɥɨɤɚɥɶɧɵɯ ɩɪɨɛɨɤ ɜ |
ɤɚɤɨɦ-ɥɢɛɨ ɦɟɫɬɟ, ɬɨ ɧɚ ɜɧɭɬɪɟɧɧɟɣ ɱɚɫɬɢ |
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ɜ ɦɟɫɬɟ ɢɡɝɢɛɚ ɜɢɬɤɢ ɫɝɭɳɚɸɬɫɹ, ɚ ɧɚ |
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ɬɨɤɚɦɚɤɚɯ (ɚ); ɫɯɟɦɚɬɢɱɟɫɤɨɟ ɢɡɨɛɪɚɠɟɧɢɟ |
ɜɧɟɲɧɟɣ - ɪɚɫɯɨɞɹɬɫɹ. ȼ ɦɟɫɬɚɯ ɫɝɭɳɟɧɢɹ |
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ɩɪɨɟɤɰɢɣ ɬɪɚɟɤɬɨɪɢɣ ɡɚɩɟɪɬɵɯ ɱɚɫɬɢɰ ɧɚ ɫɟɱɟɧɢɟ |
ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɛɨɥɶɲɟ ɢ |
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ɬɨɤɚɦɚɤɚ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ ɤ ɟɝɨ ɛɨɥɶɲɨɦɭ |
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ɞɢɚɦɟɬɪɭ (ɛ ɢ ɜ) |
ɩɨɷɬɨɦɭ |
ɡɞɟɫɶ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɥɨɤɚɥɶɧɵɟ |
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ɩɪɨɛɤɢ ɬɚɤ |
ɠɟ, ɤɚɤ ɢ |
ɜ ɩɪɨɛɤɨɬɪɨɧɚɯ, |
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ɫɩɨɫɨɛɧɵɟ ɨɬɪɚɠɚɬɶ ɱɚɫɬɢɰɵ, ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɢɦɟɟɬ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ ɭɝɨɥ ɧɚɤɥɨɧɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɣ ɫɢɥɨɜɨɣ ɥɢɧɢɢ. Ʉɨɧɟɱɧɨ, ɝɟɨɦɟɬɪɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɷɬɢɯ «ɩɪɨɛɤɨɬɪɨɧɚɯ» ɫɥɨɠɧɟɟ, ɱɟɦ ɜ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɵɯ ɥɨɜɭɲɤɚɯ, ɧɨ ɫɭɬɶ ɞɟɥɚ ɨɫɬɚɺɬɫɹ ɩɪɟɠɧɟɣ: ɱɚɫɬɶ ɱɚɫɬɢɰ ɩɥɚɡɦɵ ɫ ɦɚɥɨɣ ɩɪɨɞɨɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɨɬɪɚɠɚɟɬɫɹ ɜ ɩɪɨɛɤɚɯ ɢ ɨɤɚɡɵɜɚɟɬɫɹ ɡɚɯɜɚɱɟɧɧɨɣ. ɉɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɬɨɤɚɦɚɤɚɦ ɞɥɹ ɧɢɯ ɫɥɨɠɢɥɫɹ ɬɟɪɦɢɧ ɡɚɩɟɪɬɵɟ ɱɚɫɬɢɰɵ. Ɉɫɬɚɥɶɧɵɟ ɱɚɫɬɢɰɵ, ɢ ɢɯ ɩɨɞɚɜɥɹɸɳɟɟ ɛɨɥɶɲɢɧɫɬɜɨ, ɧɟ ɭɞɟɪɠɢɜɚɸɬɫɹ ɜ ɩɪɨɛɤɚɯ, ɚ ɩɨɬɨɦɭ ɧɚɡɵɜɚɸɬɫɹ ɩɪɨɥɟɬɧɵɦɢ ɱɚɫɬɢɰɚɦɢ. ȿɫɥɢ ɬɨɪ ɬɨɧɤɢɣ, ɬɚɤ ɱɬɨ ɨɬɧɨɲɟɧɢɟ ɪɚɞɢɭɫɚ ɫɟɱɟɧɢɹ ɬɨɪɚ ɤ ɪɚɞɢɭɫɭ ɬɨɪɚ ɹɜɥɹɟɬɫɹ ɦɚɥɨɣ ɜɟɥɢɱɢɧɨɣ, ε=r/R<<1, ɬɨ «ɩɪɨɛɨɱɧɨɟ ɨɬɧɨɲɟɧɢɟ» ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɟɞɢɧɢɰɵ ɥɢɲɶ ɧɚ
ɦɚɥɭɸ ɜɟɥɢɱɢɧɭ ~ε. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ, ɨɱɟɜɢɞɧɨ, ɡɚɩɟɪɬɵɦɢ ɛɭɞɭɬ ɥɢɲɶ ɬɟ ɱɚɫɬɢɰɵ (ɜɫɩɨɦɧɢɦ ɨɩɪɟɞɟɥɟɧɢɟ ɭɝɥɚ ɪɚɫɬɜɨɪɚ ɨɩɚɫɧɨɝɨ ɤɨɧɭɫɚ ɩɨɬɟɪɶ (2.67)), ɭ ɤɨɬɨɪɵɯ ɦɚɥɚ
ɩɪɨɞɨɥɶɧɚɹ |
ɫɤɨɪɨɫɬɶ |
v|| v < |
ε <<1 . |
ɂɯ |
ɨɬɧɨɫɢɬɟɥɶɧɨɟ |
ɱɢɫɥɨ ɩɨ ɩɥɨɬɧɨɫɬɢ (ɩɪɢ |
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ɪɚɜɧɨɪɚɫɩɪɟɞɟɥɟɧɢɢ |
ɩɨ ɭɝɥɚɦ) ɬɚɤɠɟ, |
ɨɱɟɜɢɞɧɨ, |
ɧɟɜɟɥɢɤɨ, |
ɢ |
ɫɨɫɬɚɜɥɹɟɬ |
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nɡɚɩ nɩɪɨɥ < |
ε <<1. ȼ |
ɷɬɨɦ |
ɦɨɠɧɨ |
ɥɟɝɤɨ |
ɭɛɟɞɢɬɶɫɹ, ɨɰɟɧɢɜ ɨɛɴɟɦ |
ɜ |
ɫɤɨɪɨɫɬɧɨɦ |
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ɩɪɨɫɬɪɚɧɫɬɜɟ, ɩɪɢɯɨɞɹɳɢɣɫɹ ɧɚ ɞɨɥɸ ɡɚɩɟɪɬɵɯ ɱɚɫɬɢɰ.