Жданов С.К Цветков И.В - Основы физических процессов в плазме и в плазменных установках (2000)
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ȽɅȺȼȺ 5
ɗɅȿɄɌɊɈɇɇȺə ɂ ɂɈɇɇȺə ɈɉɌɂɄȺ
§38. Ⱥɧɚɥɨɝɢɹ ɫɜɟɬɨɜɨɣ ɢ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ
Ɏɢɡɢɱɟɫɤɢɦ ɨɛɨɫɧɨɜɚɧɢɟɦ ɜɨɡɦɨɠɧɨɫɬɢ ɩɨɫɬɪɨɟɧɢɹ ɚɧɚɥɨɝɢɢ ɩɪɨɯɨɠɞɟɧɢɹ ɷɥɟɤɬɪɨɧɧɨɝɨ ɥɭɱɚ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɫ ɩɨɫɬɟɩɟɧɧɨ ɢɡɦɟɧɹɸɳɢɦɫɹ ɩɨɬɟɧɰɢɚɥɨɦ ɢ ɩɪɨɯɨɠɞɟɧɢɹ ɫɜɟɬɨɜɨɝɨ ɥɭɱɚ ɱɟɪɟɡ ɫɪɟɞɭ ɫ ɢɡɦɟɧɹɸɳɢɦɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɪɟɥɨɦɥɟɧɢɹ (ɨɩɬɢɤɨ-ɦɟɯɚɧɢɱɟɫɤɚɹ ɚɧɚɥɨɝɢɹ) ɹɜɥɹɟɬɫɹ ɨɛɳɟɟ ɫɯɨɞɫɬɜɨ ɦɟɠɞɭ ɨɛɵɱɧɨɣ ɦɟɯɚɧɢɤɨɣ ɢ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɩɬɢɤɨɣ. ɂ ɞɥɹ ɞɜɢɠɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɢ ɞɥɹ ɫɜɟɬɨɜɨɝɨ ɥɭɱɚ ɢɡɜɟɫɬɟɧ ɜɚɪɢɚɰɢɨɧɧɵɣ
t1
ɩɪɢɧɰɢɩ Ƚɚɦɢɥɶɬɨɧɚ: δ ³Ldt = 0 , ɝɞɟ t0 ɢ t1 ɜɪɟɦɹ ɜ ɧɚɱɚɥɶɧɨɣ ɢ ɤɨɧɟɱɧɨɣ
t0
ɬɨɱɤɚɯ ɬɪɚɟɤɬɨɪɢɢ, L(q, q ,t) – ɮɭɧɤɰɢɹ Ʌɚɝɪɚɧɠɚ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɨɛɨɛɳɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬ, ɫɤɨɪɨɫɬɟɣ ɢ ɜɪɟɦɟɧɢ.
Ɋɚɜɟɧɫɬɜɨ ɧɭɥɸ ɜɚɪɢɚɰɢɢ ɢɧɬɟɝɪɚɥɚ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɷɬɨɬ ɢɧɬɟɝɪɚɥ, ɜɡɹɬɵɣ ɜɞɨɥɶ ɞɟɣɫɬɜɢɬɟɥɶɧɨɣ ɬɪɚɟɤɬɨɪɢɢ, ɢɦɟɟɬ ɷɤɫɬɪɟɦɭɦ (ɦɢɧɢɦɭɦ) ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɞɪɭɝɢɦɢ ɜɨɡɦɨɠɧɵɦɢ ɜɢɪɬɭɚɥɶɧɵɦɢ ɬɪɚɟɤɬɨɪɢɹɦɢ (ɪɢɫ. 5.1). Ɏɭɧɤɰɢɹ Ʌɚɝɪɚɧɠɚ ɞɥɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɱɚɫɬɢɰɵ ɪɚɜɧɚ ɪɚɡɧɨɫɬɢ ɦɟɠɞɭ ɤɢɧɟɬɢɱɟɫɤɨɣ ɢ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɟɣ L = T – U, ɞɥɹ ɷɥɟɤɬɪɨɧɚ, ɞɜɢɠɭɳɟɝɨɫɹ ɜ ɱɢɫɬɨ
ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɦ ɩɨɥɟ L = mv2/2 |
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(-eϕ). ȼ |
Ɋɢɫ. 5.1. Ⱦɟɣɫɬɜɢɬɟɥɶɧɚɹ ɢ |
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ɩɪɢɫɭɬɫɬɜɢɢ |
ɦɚɝɧɢɬɧɨɝɨ |
ɩɨɥɹ |
B |
ɮɭɧɤɰɢɹ |
ɜɢɪɬɭɚɥɶɧɚɹ ɬɪɚɟɤɬɨɪɢɹ |
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Ʌɚɝɪɚɧɠɚ L = mv2/2 – (-eϕ) + (-e |
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ɝɞɟ A - |
ɱɚɫɬɢɰɵ |
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Av /c), |
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ɜɟɤɬɨɪɧɵɣ ɩɨɬɟɧɰɢɚɥ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ: |
B = rot A . ȿɫɥɢ ɜɜɟɫɬɢ ɨɛɨɛɳɟɧɧɵɣ |
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ɢɦɩɭɥɶɫ P = p − |
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Al , ɝɞɟ l - ɟɞɢɧɢɱɧɵɣ ɜɟɤɬɨɪ, ɧɚɩɪɚɜɥɟɧɧɵɣ ɩɨ ɤɚɫɚɬɟɥɶɧɨɣ |
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c |
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ɤ ɬɪɚɟɤɬɨɪɢɢ, ɬɨ ɜɚɪɢɚɰɢɨɧɧɵɣ ɩɪɢɧɰɢɩ Ƚɚɦɢɥɶɬɨɧɚ δS = 0, ɧɚɡɵɜɚɟɦɵɣ |
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ɩɪɢɧɰɢɩɨɦ |
ɧɚɢɦɟɧɶɲɟɝɨ |
ɞɟɣɫɬɜɢɹ |
ɢɥɢ ɩɪɢɧɰɢɩɨɦ Ɇɨɩɟɪɬɸɢ (ɢɧɬɟɝɪɚɥ |
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t1 |
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S = ³Ldt ɧɚɡɵɜɚɟɬɫɹ ɢɧɬɟɝɪɚɥɨɦ ɞɟɣɫɬɜɢɟɦ, ɢɥɢ ɩɪɨɫɬɨ ɞɟɣɫɬɜɢɟɦ) ɦɨɠɧɨ
t0 |
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B & |
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ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ: δ ³Pdl |
= 0 . ɗɬɨɬ ɩɪɢɧɰɢɩ ɚɧɚɥɨɝɢɱɟɧ ɩɪɢɧɰɢɩɭ Ɏɟɪɦɚ |
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B |
ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɩɬɢɤɢ: |
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δ ³ndl = 0 , ɤɨɬɨɪɵɣ ɨɡɧɚɱɚɟɬ ɦɢɧɢɦɚɥɶɧɨɫɬɶ |
A
B
ɨɩɬɢɱɟɫɤɨɣ ɞɥɢɧɵ ɧɚ ɪɟɚɥɶɧɨɦ ɩɭɬɢ ɫɜɟɬɚ. Ɍɨ ɟɫɬɶ ɨɩɬɢɱɟɫɤɢɣ ɩɭɬɶ ³ndl ɞɥɹ
A
ɫɜɟɬɨɜɨɝɨ ɥɭɱɚ – ɫɚɦɵɣ ɤɨɪɨɬɤɢɣ, ɝɞɟ n – ɩɨɤɚɡɚɬɟɥɶ ɩɪɟɥɨɦɥɟɧɢɹ ɫɪɟɞɵ, dl – ɷɥɟɦɟɧɬ ɬɪɚɟɤɬɨɪɢɢ ɥɭɱɚ. ȿɫɥɢ n = const, ɬɨ ɩɪɟɥɨɦɥɟɧɢɟ ɥɭɱɚ ɨɬɫɭɬɫɬɜɭɟɬ ɢ ɫɜɟɬ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɩɪɹɦɨɥɢɧɟɣɧɨ. ɂɡ ɩɪɢɧɰɢɩɚ Ɏɟɪɦɚ ɜɵɬɟɤɚɟɬ ɢɡɜɟɫɬɧɵɣ ɡɚɤɨɧ ɩɪɟɥɨɦɥɟɧɢɹ ɋɧɟɥɥɢɭɫɚ, ɤɨɬɨɪɵɣ ɡɚɞɚɟɬ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɭɝɥɨɦ
ɩɚɞɟɧɢɹ α ɢ ɭɝɥɨɦ ɩɪɟɥɨɦɥɟɧɢɹ β (ɭɝɥɵ ɦɟɠɞɭ ɥɭɱɨɦ ɢ ɧɨɪɦɚɥɶɸ ɤ ɝɪɚɧɢɰɟ
ɪɚɡɞɟɥɚ): |
sinα |
= |
n2 |
, ɝɞɟ n1 ɢ n2 – ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɪɟɥɨɦɥɟɧɢɹ ɫɪɟɞ [27]. |
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sin β |
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ȼɫɥɭɱɚɟ ɷɥɟɤɬɪɨɧɨɜ ɢɯ ɤɨɦɩɨɧɟɧɬɚ ɫɤɨɪɨɫɬɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚɹ
ɷɥɟɤɬɪɢɱɟɫɤɨɦɭ ɩɨɥɸ, ɧɟ ɦɟɧɹɟɬɫɹ, ɚ ɦɨɞɭɥɶ ɫɤɨɪɨɫɬɢ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ |
U , |
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ɝɞɟ U – ɩɨɬɟɧɰɢɚɥ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ, ɜ ɤɨɬɨɪɨɣ ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɚ ɪɚɜɧɚ |
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ɧɭɥɸ. ɉɨɷɬɨɦɭ ɜ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɟ |
U ɢɝɪɚɟɬ ɪɨɥɶ ɩɨɤɚɡɚɬɟɥɹ ɩɪɟɥɨɦɥɟɧɢɹ |
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ɫɪɟɞɵ, ɚ ɡɚɤɨɧ ɩɪɟɥɨɦɥɟɧɢɹ ɢɦɟɟɬ ɜɢɞ: |
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sinα |
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U 2 |
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(5.1) |
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sin β |
U1 |
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ɟɫɥɢ ɫɱɢɬɚɬɶ, ɱɬɨ ɧɚ ɝɪɚɧɢɰɟ ɪɚɡɞɟɥɚ ɩɨɬɟɧɰɢɚɥ ɫɤɚɱɤɨɦ ɦɟɧɹɟɬɫɹ ɨɬ U1 ɞɨ U2. |
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Ɋɟɡɤɢɣ ɫɤɚɱɨɤ ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɩɭɬɢ |
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ɷɥɟɤɬɪɨɧɧɨɝɨ |
ɩɭɱɤɚ |
ɦɨɠɧɨ |
ɫɨɡɞɚɬɶ |
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ɦɟɠɞɭ ɞɜɭɯ ɦɟɬɚɥɥɢɱɟɫɤɢɯ ɫɟɬɨɤ ɫ |
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ɦɟɥɤɢɦɢ |
ɹɱɟɣɤɚɦɢ |
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ɧɚ |
ɛɥɢɡɤɨɦ |
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ɪɚɫɫɬɨɹɧɢɢ ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɧɚ ɤɨɬɨɪɵɟ |
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ɩɨɞɚɧɵ ɧɚɩɪɹɠɟɧɢɹ U1 ɢ U2 (ɪɢɫ. 5.2). |
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Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɩɨ ɚɧɚɥɨɝɢɢ ɫɨ |
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ɫɜɟɬɨɜɨɣ ɨɩɬɢɤɨɣ ɦɨɠɧɨ ɝɨɜɨɪɢɬɶ ɨɛ |
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ɷɥɟɤɬɪɨɧɧɵɯ |
ɥɭɱɚɯ, |
ɚ |
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ɬɚɤɠɟ |
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Ɋɢɫ. 5.2. ɉɪɟɥɨɦɥɟɧɢɟ ɩɭɱɤɚ ɡɚɪɹɠɟɧɧɵɯ |
ɨɩɪɟɞɟɥɢɬɶ |
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ɭɫɥɨɜɢɟ |
ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ |
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ɱɚɫɬɢɰ ɧɚ ɝɪɚɧɢɰɟ ɩɨɬɟɧɰɢɚɥɨɜ (a) ɢ ɫɜɟɬɚ |
ɨɩɬɢɤɢ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ: |
ɞɥɢɧɚ ɜɨɥɧɵ |
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ɧɚ ɝɪɚɧɢɰɟ ɞɜɭɯ ɫɪɟɞ (ɛ) |
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h |
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12.25 |
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ɷɥɟɤɬɪɨɧɚ |
λ[A] = mv |
≈ |
U[ɷȼ] |
ɦɚɥɚ |
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ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɯɚɪɚɤɬɟɪɧɵɦ ɪɚɡɦɟɪɨɦ ɧɟɨɞɧɨɪɨɞɧɨɫɬɟɣ ɫɢɫɬɟɦɵ, ɬ. ɟ. ɷɥɟɤɬɪɨɧ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɱɚɫɬɢɰɭ. ɇɨ ɭ ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ ɟɫɬɶ ɢ ɫɭɳɟɫɬɜɟɧɧɵɟ ɨɬɥɢɱɢɹ ɨɬ ɫɜɟɬɨɜɨɣ, ɨɧɢ ɜ ɨɫɧɨɜɧɨɦ ɫɨɫɬɨɹɬ ɜ ɫɥɟɞɭɸɳɟɦ:
1.Ɉɬɞɟɥɶɧɵɟ ɥɭɱɢ ɜ ɫɜɟɬɨɜɨɣ ɨɩɬɢɤɟ ɧɟɡɚɜɢɫɢɦɵ – ɷɥɟɤɬɪɨɧɧɵɟ ɥɭɱɢ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɞɪɭɝ ɫ ɞɪɭɝɨɦ.
2.ɉɨɤɚɡɚɬɟɥɶ ɩɪɟɥɨɦɥɟɧɢɹ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɜɫɟɝɞɚ ɧɟɩɪɟɪɵɜɟɧ, ɞɥɹ ɫɜɟɬɚ ɨɧ, ɤɚɤ ɩɪɚɜɢɥɨ, ɦɟɧɹɟɬɫɹ ɫɤɚɱɤɨɦ.
3.Ⱦɢɚɩɚɡɨɧ ɢɡɦɟɧɟɧɢɹ ɩɨɤɚɡɚɬɟɥɹ ɩɪɟɥɨɦɥɟɧɢɹ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɧɟ ɨɝɪɚɧɢɱɟɧ, ɜ ɨɩɬɢɤɟ n ≤ 2.5.
4.ɋɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɬɟɦ ɛɨɥɶɲɟ, ɱɟɦ ɛɨɥɶɲɟ ɩɨɤɚɡɚɬɟɥɶ ɩɪɟɥɨɦɥɟɧɢɹ, ɚ ɫɤɨɪɨɫɬɶ ɫɜɟɬɚ ɧɚɨɛɨɪɨɬ.
5.ɉɪɟɥɨɦɥɹɸɳɢɟ ɩɨɜɟɪɯɧɨɫɬɢ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɫɜɟɬɨɜɵɯ ɥɭɱɟɣ, ɧɟ ɦɨɝɭɬ ɛɵɬɶ ɩɪɨɢɡɜɨɥɶɧɵɦɢ – ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɨɜ ɜɫɟɝɞɚ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɪɚɜɧɟɧɢɸ Ʌɚɩɥɚɫɚ (ɥɢɧɟɣɧɚɹ ɷɥɟɤɬɪɨɧɧɚɹ ɨɩɬɢɤɚ) ɢɥɢ ɉɭɚɫɫɨɧɚ (ɧɟɥɢɧɟɣɧɚɹ ɷɥɟɤɬɪɨɧɧɚɹ ɨɩɬɢɤɚ).
§39. ɗɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɢɟ ɥɢɧɡɵ
Ⱦɜɢɠɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ, ɡɚɜɢɫɹɳɟɟ ɨɬ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ, ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɜɨɡɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɥɢɲɶ ɱɢɫɥɟɧɧɵɦɢ ɦɟɬɨɞɚɦɢ. Ɉɞɧɚɤɨ ɜ ɨɬɞɟɥɶɧɵɯ ɫɥɭɱɚɹɯ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɚ ɜɨɡɦɨɠɧɨ ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɪɟɲɟɧɢɟ, ɧɚɩɪɢɦɟɪ, ɜ ɫɥɭɱɚɟ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɝɨ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥ U(z,r) ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɚɡɢɦɭɬɚɥɶɧɨɝɨ ɭɝɥɚ θ. Ɍɚɤ ɤɚɤ U(z,-r) = U(z,r), ɬɨ ɜ ɪɚɡɥɨɠɟɧɢɢ U ɩɨ ɫɬɟɩɟɧɹɦ r ɛɭɞɭɬ ɬɨɥɶɤɨ ɱɟɬɧɵɟ ɫɬɟɩɟɧɢ:
U(z,r) = b0(z) + b2(z)r2 + b4(z)r4 + … + b2k(z)r2k + … |
(5.2) |
ɉɨɞɫɬɚɜɥɹɹ ɷɬɨ ɜɵɪɚɠɟɧɢɟ ɜ ɭɪɚɜɧɟɧɢɟ Ʌɚɩɥɚɫɚ (ɧɟɬ ɡɚɪɹɞɨɜ ɜ ɩɪɨɦɟɠɭɬɤɟ) ɜ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ:
∂ 2U |
+ |
1 ∂U |
+ |
∂ 2U |
= 0 |
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(5.3) |
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∂r 2 |
r ∂r |
∂z 2 |
∂ 2U |
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(ɭɪɚɜɧɟɧɢɟ |
ɭɩɪɨɳɟɧɨ ɫ |
ɭɱɟɬɨɦ |
= 0 ), ɦɨɠɧɨ ɧɚɣɬɢ ɤɨɷɮɮɢɰɢɟɧɬɵ |
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∂θ 2 |
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ɪɚɡɥɨɠɟɧɢɹ, ɩɨɥɭɱɢɜ ɜ ɢɬɨɝɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨɬɟɧɰɢɚɥɚ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɜ ɜɢɞɟ:
U (z, r) = U (z) − ( |
r |
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2 |
U |
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(z) + |
1 |
( |
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4 |
U |
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(z) + ... + (−1) |
k U (2k ) (z) |
+ ... , (5.4) |
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(k!)2 |
22k |
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ɤɨɬɨɪɨɟ ɩɨɥɧɨɫɬɶɸ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɨɫɢ ɫɢɫɬɟɦɵ U(z) = U(0,z). ɗɬɨ ɫɢɥɶɧɨ ɭɩɪɨɳɚɟɬ ɪɚɫɱɟɬ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɥɹ ɩɪɢɨɫɟɜɵɯ ɷɥɟɤɬɪɨɧɨɜ (r2/L2ɯɚɪ<< r/Lɯɚɪ, ɝɞɟ Lɯɚɪ – ɯɚɪɚɤɬɟɪɧɚɹ ɞɥɢɧɚ ɫɢɫɬɟɦɵ), ɤɨɬɨɪɵɟ ɟɳɟ ɧɚɡɵɜɚɸɬ ɩɚɪɚɤɫɢɚɥɶɧɵɦɢ, ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɭɪɚɜɧɟɧɢɟ ɬɪɚɟɤɬɨɪɢɢ. Ⱦɥɹ ɷɬɨɝɨ ɜ ɪɚɫɩɪɟɞɟɥɟɧɢɢ ɩɨɬɟɧɰɢɚɥɚ ɩɪɟɧɟɛɪɟɝɚɟɦ ɫɥɚɝɚɟɦɵɦɢ ɫɨ ɫɬɟɩɟɧɹɦɢ r, ɬɨɝɞɚ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɧɚ:
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= -eEz = eU´(z) |
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= -eEr = -erU |
´´ |
(5.5) |
m z |
ɢ m r |
(z). |
ɉɨɫɥɟɞɧɟɟ ɭɪɚɜɧɟɧɢɟ ɡɚɦɟɱɚɬɟɥɶɧɨ ɬɟɦ, ɱɬɨ ɜ ɩɨɥɹɯ ɫ ɚɤɫɢɚɥɶɧɨɣ ɫɢɦɦɟɬɪɢɟɣ ɪɚɞɢɚɥɶɧɚɹ ɮɨɤɭɫɢɪɭɸɳɚɹ ɢɥɢ ɪɚɫɮɨɤɭɫɢɪɭɸɳɚɹ ɫɢɥɚ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɭɞɚɥɟɧɢɸ ɱɚɫɬɢɰɵ ɨɬ ɨɫɢ. ɍɱɢɬɵɜɚɹ, ɱɬɨ ɥɟɜɵɟ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ ɫɨɞɟɪɠɚɬ ɩɪɨɢɡɜɨɞɧɵɟ ɩɨ ɜɪɟɦɟɧɢ, ɚ ɩɪɚɜɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɩɨ z, ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ
ɩɟɪɟɯɨɞ ɤ ɩɪɨɢɡɜɨɞɧɨɣ ɩɨ ɩɟɪɟɦɟɧɧɨɣ z: |
d 2 z |
= |
1 d |
( |
dz |
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. Ɍɨɝɞɚ, ɢɧɬɟɝɪɢɪɭɹ |
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dt 2 |
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ɩɟɪɜɨɟ ɭɪɚɜɧɟɧɢɟ ɫ ɭɱɟɬɨɦ ɝɪɚɧɢɱɧɨɝɨ ɭɫɥɨɜɢɹ ɩɪɢ z = 0 U(z) = 0 ɢ dz/dt 0 = 0 (ɩɪɟɧɟɛɪɟɝɚɟɦ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɱɚɫɬɢɰ), ɩɨɥɭɱɢɦ dz/dt = 2eU (z) / m . ɂɫɩɨɥɶɡɭɹ ɷɬɨ ɫɨɨɬɧɨɲɟɧɢɟ ɞɥɹ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɜɬɨɪɨɝɨ ɭɪɚɜɧɟɧɢɹ ɢ ɩɟɪɟɯɨɞɹ
ɤ ɩɪɨɢɡɜɨɞɧɨɣ ɩɨ z: |
d 2 r |
= |
dz d |
( |
dr dz |
) , ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɬɪɚɟɤɬɨɪɢɢ r(z) |
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dt 2 |
dt dz |
dz dt |
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ɩɚɪɚɤɫɢɚɥɶɧɨɝɨ |
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ɩɭɱɤɚ: |
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d 2 r |
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U ' (z) dr |
+ |
U '' (z) |
r = 0 |
(5.6), |
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dz 2 |
2U (z) dz |
4U (z) |
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ɨɫɧɨɜɧɵɦ |
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ɤɨɬɨɪɨɟ |
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ɧɚɡɵɜɚɟɬɫɹ |
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ɭɪɚɜɧɟɧɢɟɦ |
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ɷɥɟɤɬɪɨɧɧɨɣ |
ɨɩɬɢɤɢ. |
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ɉɨɥɭɱɟɧɧɨɟ |
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ɥɢɧɟɣɧɨɟ ɨɞɧɨɪɨɞɧɨɟ |
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ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ 2-ɝɨ |
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ɩɨɪɹɞɤɚ ɨɬɧɨɫɢɬɟɥɶɧɨ U(z) ɢ r(z) |
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ɩɨɤɚɡɵɜɚɟɬ, |
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ɱɬɨ |
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Ɋɢɫ. 5.3. ɂɡɨɛɪɚɠɟɧɢɟ ɬɨɱɤɢ ɜ ɥɢɧɡɟ. |
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ɦɚɫɲɬɚɛɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ, |
ɬ. ɟ. ɟɫɥɢ |
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ɩɨɬɟɧɰɢɚɥ ɜɨ ɜɫɟɯ ɬɨɱɤɚɯ ɩɪɨɫɬɪɚɧɫɬɜɚ ɭɜɟɥɢɱɢɬɶ ɜ k ɪɚɡ (ɭɜɟɥɢɱɢɬɶ ɩɨɬɟɧɰɢɚɥ ɧɚ ɜɫɟɯ ɷɥɟɤɬɪɨɞɚɯ ɫɢɫɬɟɦɵ ɜ ɨɞɢɧɚɤɨɜɨɟ ɱɢɫɥɨ ɪɚɡ), ɬɨ ɭɪɚɜɧɟɧɢɟ, ɚ
ɫɥɟɞɨɜɚɬɟɥɶɧɨ |
ɢ |
ɬɪɚɟɤɬɨɪɢɹ |
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ɷɥɟɤɬɪɨɧɚ ɧɟ ɢɡɦɟɧɢɬɫɹ. Ʉɪɨɦɟ |
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ɬɨɝɨ, |
ɭɪɚɜɧɟɧɢɟ ɧɟ |
ɫɨɞɟɪɠɢɬ |
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ɨɬɧɨɲɟɧɢɹ e/m, ɩɨɷɬɨɦɭ ɬɪɚɟɤɬɨɪɢɢ |
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ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɧɟ ɨɬɥɢɱɚɸɬɫɹ. |
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ȿɫɥɢ |
ɩɪɟɞɦɟɬɧɚɹ |
ɩɥɨɫɤɨɫɬɶ |
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ɧɚɯɨɞɢɬɫɹ ɩɪɢ z = a, ɚ ɩɥɨɫɤɨɫɬɶ |
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ɢɡɨɛɪɚɠɟɧɢɹ ɩɪɢ z = b (ɪɢɫ. 5.3), ɬɨ |
Ɋɢɫ. 5.4. ɍɝɥɵ, ɨɛɪɚɡɭɟɦɵɟ ɬɪɚɟɤɬɨɪɢɟɣ ɫ |
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ɥɢɧɟɣɧɨɟ |
ɭɜɟɥɢɱɟɧɢɟ |
ɥɢɧɡɵ: |
ɨɫɶɸ ɜ ɩɪɟɞɦɟɬɧɨɣ ɩɥɨɫɤɨɫɬɢ ɢ ɬɨɱɤɟ |
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M = |
r(b) |
, ɝɞɟ r(a) ɢ r(b) ɪɚɫɫɬɨɹɧɢɟ ɞɨ ɬɪɚɟɤɬɨɪɢɢ ɨɬ ɨɫɢ ɫɢɫɬɟɦɵ. ɍɝɥɨɜɨɟ |
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ɭɜɟɥɢɱɟɧɢɟ ɥɢɧɡɵ, ɨɩɪɟɞɟɥɹɟɦɨɟ ɤɚɤ ɨɬɧɨɲɟɧɢɟ ɬɚɧɝɟɧɫɨɜ ɭɝɥɨɜ ɧɚɤɥɨɧɚ
ɬɪɚɟɤɬɨɪɢɢ ɤ ɨɫɢ G = |
tgγ 2 |
= |
r ' (b) |
(ɪɢɫ. 5.4). ɂɡ ɨɫɧɨɜɧɨɝɨ ɭɪɚɜɧɟɧɢɹ |
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tgγ 1 |
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ɷɥɟɤɬɪɨɧɧɨɣ ɨɩɬɢɤɢ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɥɢɧɟɣɧɵɦ ɢ ɭɝɥɨɜɵɦ ɭɜɟɥɢɱɟɧɢɟɦ ɥɢɧɡɵ[28]:
M G = U (a) , |
(5.7) |
U (b) |
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ɤɨɬɨɪɨɟ ɹɜɥɹɟɬɫɹ ɚɧɚɥɨɝɨɦ ɬɟɨɪɟɦɵ Ʌɚɝɪɚɧɠɚ-Ƚɟɥɶɦɝɨɥɶɰɚ ɞɥɹ ɫɜɟɬɨɜɨɣ
ɨɩɬɢɤɢ: |
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M G |
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n1 |
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Ɏɨɤɭɫɧɵɟ |
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ɫɥɟɜɚ f1 ɢ ɫɩɪɚɜɚ f2 ɨɬ |
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ɝɥɚɜɧɵɯ ɩɥɨɫɤɨɫɬɟɣ h1 ɢ |
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h2 |
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ɥɢɧɡɵ |
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ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ |
ɱɟɪɟɡ |
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ɬɪɚɟɤɬɨɪɢɢ, |
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ɱɟɪɟɡ ɮɨɤɭɫ ɥɢɧɡɵ r1 ɢ |
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ɩɚɪɚɥɥɟɥɶɧɨ |
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ɨɫɢ |
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r2 |
Ɋɢɫ. 5.5. ɏɨɞ ɝɥɚɜɧɵɯ ɥɭɱɟɣ ɜ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɣ |
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ɫɢɫɬɟɦɵ |
(ɪɢɫ. |
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5.5): |
ɥɢɧɡɟ |
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f |
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r1 (b) |
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2 |
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r2 (a) |
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r ' (a) |
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r ' |
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Ɍɨɧɤɢɟ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɢɟ ɥɢɧɡɵ
Ɋɚɫɫɦɨɬɪɢɦ ɬɨɧɤɢɟ ɥɢɧɡɵ, ɝɥɚɜɧɵɟ ɩɥɨɫɤɨɫɬɢ ɤɨɬɨɪɵɯ ɧɚɯɨɞɹɬɫɹ ɩɪɢ z = a ɢ ɩɪɢ z = b. Ⱦɥɹ ɬɨɧɤɢɯ ɥɢɧɡ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɝɥɚɜɧɵɦɢ ɩɥɨɫɤɨɫɬɹɦɢ ɦɧɨɝɨ ɦɟɧɶɲɟ ɮɨɤɭɫɧɵɯ ɪɚɫɫɬɨɹɧɢɣ (b - a) << f1, f2 , ɬ. ɟ. ɝɥɚɜɧɵɟ ɩɥɨɫɤɨɫɬɢ ɫɥɢɜɚɸɬɫɹ, ɮɨɤɭɫɧɵɟ ɪɚɫɫɬɨɹɧɢɹ ɫɥɟɜɚ ɢ ɫɩɪɚɜɚ ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫɨɨɬɧɨɲɟɧɢɹɦɢ:
1 |
= 4 |
1 |
b |
U '' (z) |
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1 |
= 4 |
1 |
b |
U '' (z) |
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f1 |
U (a) |
³a |
U (z) |
dz ɢ |
f2 |
U (b) |
³a |
U (z) |
dz . |
(5.8) |
Ɉɬɧɨɲɟɧɢɟ ɮɨɤɭɫɧɵɯ ɪɚɫɫɬɨɹɧɢɣ: |
f1 = − |
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f2 |
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U (b) |
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Ɉɩɬɢɱɟɫɤɚɹ ɫɢɥɚ: |
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1 |
1 |
U ' (b) |
U ' (a) |
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b (U ' (z))2 |
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D = f2 |
= 4 U (b) |
( U (b) − |
U (a) ) |
+ |
8 U (b) |
³a U 3 / 2 (z) dz . |
(5.9) |
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ȿɫɥɢ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɫɩɪɚɜɚ ɢ ɫɥɟɜɚ ɨɬ ɥɢɧɡɵ ɪɚɜɧɨ, ɬɨ D > 0, ɬ. ɟ. ɥɢɧɡɚ |
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ɜɫɟɝɞɚ ɫɨɛɢɪɚɸɳɚɹ. |
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Ⱦɥɹ ɨɞɢɧɨɱɧɨɣ ɞɢɚɮɪɚɝɦɵ ɫ ɤɪɭɝɥɵɦ ɨɬɜɟɪɫɬɢɟɦ: |
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D = |
1 |
= |
E1 − E2 |
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(5.10) |
fd |
4U d |
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ɝɞɟ E1 ɢ E2 – ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɨɥɟɣ ɫɥɟɜɚ ɢ ɫɩɪɚɜɚ ɨɬ ɞɢɚɮɪɚɝɦɵ, Ud – ɩɨɬɟɧɰɢɚɥ ɞɢɚɮɪɚɝɦɵ.
Ⱦɥɹ ɫɢɫɬɟɦɵ ɢɡ ɞɜɭɯ ɥɢɧɡ – ɞɢɚɮɪɚɝɦ ɫ ɮɨɤɭɫɚɦɢ f1 ɢ f2 ɢ ɪɚɫɫɬɨɹɧɢɟɦ ɦɟɠɞɭ ɥɢɧɡɚɦɢ l ɨɩɬɢɱɟɫɤɚɹ ɫɢɥɚ ɡɚɞɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ:
1 |
= |
1 |
+ |
1 |
+ |
l |
. |
(5.11) |
f |
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f2 |
f1 f2 |
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ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɝɨ ɩɨɥɹ ɬɪɚɟɤɬɨɪɢɹ ɷɥɟɤɬɪɨɧɚ ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɹɦɢ:
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m r |
= −eE |
r |
≈ − |
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(5.12) |
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¯m z = −eEz ≈ eU |
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ɬ.ɟ. ɮɨɤɭɫɢɪɭɸɳɚɹ ɫɢɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɧɚɤɨɦ ɜɬɨɪɨɣ ɩɪɨɢɡɜɨɞɧɨɣ ɨɬ
ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɨɫɢ ɫɢɫɬɟɦɵ. ȿɫɥɢ U′′(z) > 0, ɬɨ ɫɢɫɬɟɦɚ ɮɨɤɭɫɢɪɭɸɳɚɹ, ɟɫɥɢ U′′(z) < 0, ɬɨ ɪɚɫɮɨɤɭɫɢɪɭɸɳɚɹ.
§40. Ɇɚɝɧɢɬɧɵɟ ɥɢɧɡɵ
Ɏɨɤɭɫɢɪɨɜɤɭ ɩɭɱɤɨɜ ɜ ɚɤɫɢɚɥɶɧɨɫɢɦɦɟɬɪɢɱɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɪɨɳɟ ɜɫɟɝɨ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɬɶ ɧɚ ɩɪɢɦɟɪɟ ɩɚɪɚɤɫɢɚɥɶɧɨɝɨ ɩɭɱɤɚ ɷɥɟɤɬɪɨɧɨɜ, ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɵɯ ɜɞɨɥɶ ɨɫɢ ɫɢɫɬɟɦɵ ɦɧɨɝɨ ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ ɜ ɪɚɞɢɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ vz >> vr. ɇɚ ɷɥɟɤɬɪɨɧ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ Ʌɨɪɟɧɰɚ
& |
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e & |
& |
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F |
= − |
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v |
× B . Ɋɚɞɢɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ |
c |
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ɷɬɨɣ ɫɢɥɵ ɹɜɥɹɟɬɫɹ ɮɨɤɭɫɢɪɭɸɳɟɣ: Fr = - (e/c)vϕBz (ɪɢɫ.5.6). Ⱥɡɢɦɭɬɚɥɶɧɚɹ
Ɋɢɫ. 5.6. Ɏɨɤɭɫɢɪɨɜɤɚ ɜ ɚɤɫɢɚɥɶɧɨɫɢɦɦɟɬɪɢɱɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ
ɫɨɫɬɚɜɥɹɸɳɚɹ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɚ ɩɨɹɜɥɹɟɬɫɹ ɡɚ ɫɱɟɬ ɚɡɢɦɭɬɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɫɢɥɵ Ʌɨɪɟɧɰɚ: Fϕ = -(e/c)(vzBr + vrBz) ≈ -(e/c)vzBr , ɬɚɤ ɤɚɤ vz >> vr. ɋɨɫɬɚɜɥɹɸɳɚɹ ɫɤɨɪɨɫɬɢ vz ɧɟ ɦɟɧɹɟɬ ɡɧɚɤɚ, ɪɚɞɢɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ Br ɦɨɠɟɬ ɦɟɧɹɬɶ ɡɧɚɤ, ɩɪɢ ɷɬɨɦ ɚɡɢɦɭɬɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɚ vϕ ɛɭɞɟɬ ɭɦɟɧɶɲɚɬɶɫɹ (ɜɪɚɳɟɧɢɟ ɡɚɦɟɞɥɹɬɶɫɹ), ɧɨ ɧɚɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɟ ɧɢɤɨɝɞɚ ɧɟ ɦɟɧɹɟɬɫɹ, ɩɨɷɬɨɦɭ ɮɨɤɭɫɢɪɭɸɳɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɫɢɥɵ Ʌɨɪɟɧɰɚ Fr ɜɫɟɝɞɚ ɫɨɯɪɚɧɹɟɬ ɡɧɚɤ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɦɚɝɧɢɬɧɚɹ ɥɢɧɡɚ ɜɫɟɝɞɚ ɫɨɛɢɪɚɸɳɚɹ.
ɋ ɭɱɟɬɨɦ ɬɟɨɪɟɦɵ Ƚɚɭɫɫɚ, ɞɚɸɳɟɣ ɫɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɩɪɨɞɨɥɶɧɨɣ Bz ɢ ɪɚɞɢɚɥɶɧɨɣ ɤɨɦɩɨɧɟɧɬɚɦɢ Br ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
B (Bz,Br) Br = -(r/2)(dBz/dz), ɞɜɢɠɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɜɞɨɥɶ ɨɫɢ ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ:
d 2 z |
= − |
e2 |
r 2 Bz |
dB |
z |
. |
(5.13) |
dt 2 |
4m2 c2 |
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Ⱥɡɢɦɭɬɚɥɶɧɨɟ ɞɜɢɠɟɧɢɟ (ɩɨɜɨɪɨɬ) ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ:
dϕ |
= |
eBz |
(5.14) |
dt |
2mc |
(ɥɚɪɦɨɪɨɜɫɤɨɟ ɜɪɚɳɟɧɢɟ), ɬ. ɟ. ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɫɟɯ ɷɥɟɤɬɪɨɧɨɜ ɨɞɢɧɚɤɨɜɚ ɢ ɢɡɨɛɪɚɠɟɧɢɟ ɜɪɚɳɚɟɬɫɹ ɤɚɤ ɰɟɥɨɟ, ɩɪɢɱɟɦ, ɧɚɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɹ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȿɫɥɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɭɫɥɨɜɢɸ:
b
³Bz (z)dz = 0, ɬɨ ɜɪɚɳɟɧɢɟ ɢɡɨɛɪɚɠɟɧɢɹ ɛɭɞɟɬ ɨɬɫɭɬɫɬɜɨɜɚɬɶ. ɍɱɢɬɵɜɚɹ, ɱɬɨ ɞɥɹ
a
ɩɚɪɚɤɫɢɚɥɶɧɵɯ ɩɭɱɤɨɜ vz>>vr (ɜ ɩɪɢɛɥɢɠɟɧɢɢ |
mv2 |
≈ U0 ), ɞɜɢɠɟɧɢɟ ɩɨ ɪɚɞɢɭɫɭ |
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ɡɚɞɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ: |
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= − |
eBz2 |
r , |
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dz 2 |
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ɝɞɟ U0 – ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɚɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɨɩɢɫɵɜɚɟɬ ɬɪɚɟɤɬɨɪɢɸ ɜ ɩɥɨɫɤɨɫɬɢ, ɤɨɬɨɪɚɹ ɜɪɚɳɚɟɬɫɹ ɫ ɥɚɪɦɨɪɨɜɫɤɨɣ ɱɚɫɬɨɬɨɣ. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ, ɬɪɚɟɤɬɨɪɢɹ ɷɥɟɤɬɪɨɧɚ ɩɨɥɧɨɫɬɶɸ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɧɚɱɟɧɢɟɦ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɨɫɢ Bz. ȼ ɭɪɚɜɧɟɧɢɹ ɜɯɨɞɹɬ ɡɚɪɹɞ ɢ ɦɚɫɫɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɪɚɡɧɵɟ ɱɚɫɬɢɰɵ ɞɜɢɠɭɬɫɹ ɩɨ ɪɚɡɧɵɦ ɬɪɚɟɤɬɨɪɢɹɦ. ɍɪɚɜɧɟɧɢɹ ɥɢɧɟɣɧɵ ɢ ɨɞɧɨɪɨɞɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɨɫɢ r, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɥɸɛɨɟ ɚɤɫɢɚɥɶɧɨɫɢɦɦɟɬɪɢɱɧɨɟ ɩɨɥɟ ɫɩɨɫɨɛɧɨ ɫɨɡɞɚɬɶ ɢɡɨɛɪɚɠɟɧɢɟ ɢ ɹɜɥɹɟɬɫɹ ɥɢɧɡɨɣ.
Ⱦɥɹ ɬɨɧɤɨɣ ɦɚɝɧɢɬɧɨɣ ɥɢɧɡɵ (ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɚ ɨɫɢ ɛɵɫɬɪɨ ɩɚɞɚɟɬ ɩɨ ɦɟɪɟ ɭɞɚɥɟɧɢɹ ɨɬ ɥɢɧɡɵ) ɨɩɬɢɱɟɫɤɚɹ ɫɢɥɚ:
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b |
2 |
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0.022 b |
2 |
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= |
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³a |
Bz |
dz ɢɥɢ |
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³a |
Bz |
[Ƚɫ]dz . |
(5.16) |
f |
8mc2U 0 |
f |
ɫɦ |
U 0 [ɷȼ] |
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ɍɝɨɥ ɩɨɜɨɪɨɬɚ ɜ ɦɚɝɧɢɬɧɨɣ ɥɢɧɡɟ
1 |
e |
b |
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0.15 |
b |
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³a |
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ϕ[ ɪɚɞ] = |
³a |
Bz [Ƚɫ]dz . |
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ϕ (z) = c |
8mU 0 |
Bz dz ɢɥɢ |
U0 [ɷȼ] |
(5.17) |
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Ⱦɥɹ ɦɚɝɧɢɬɧɨɝɨ ɜɢɬɤɚ ɫ ɬɨɤɨɦ I ɪɚɞɢɭɫɚ R |
ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ Bz= |
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z 2 |
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3 / 2 |
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ɝɞɟ Bm – ɩɨɥɟ ɜ ɰɟɧɬɪɟ ɜɢɬɤɚ (ɮɨɪɦɭɥɚ Ȼɢɨ-ɋɚɜɚɪɚ). ɂɧɬɟɝɪɢɪɭɹ (5.16), ɦɨɠɧɨ ɧɚɣɬɢ ɮɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɞɥɹ ɨɞɧɨɝɨ ɬɨɤɨɜɨɝɨ ɜɢɬɤɚ:
f [ɫɦ] ≈ 96.8 |
U 0 [ɷȼ]R[ɫɦ] |
. |
(5.18ɚ) |
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I 2 [A] |
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Ⱦɥɹ ɤɚɬɭɲɤɢ ɢɡ N ɜɢɬɤɨɜ: |
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f [ɫɦ] ≈ 96.8 |
U 0 [ɷȼ]R[ɫɦ] |
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(5.18ɛ) |
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(NI[A])2 |
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ɍɝɨɥ ɩɨɜɨɪɨɬɚ: |
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ϕ[ ɪɚɞ] ≈ 10.7 |
NI[A] . |
(5.19) |
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U0 [ɷȼ] |
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Ⱦɥɹ ɷɤɪɚɧɢɪɨɜɚɧɧɨɣ ɥɢɧɡɵ fɷ = kf, ɝɞɟ k – ɩɨɩɪɚɜɨɱɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ, k = 0.5÷0.7.
§41. Ɉɬɤɥɨɧɹɸɳɢɟ ɢ ɮɨɤɭɫɢɪɭɸɳɢɟ ɷɥɟɤɬɪɨɧɧɨ-ɨɩɬɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ
Ɉɬɤɥɨɧɟɧɢɟ ɢ ɮɨɤɭɫɢɪɨɜɤɚ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɢ ɦɚɝɧɢɬɧɨɦ ɩɨɥɹɯ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɫɨɡɞɚɧɢɹ ɢ ɞɢɚɝɧɨɫɬɢɤɢ ɩɥɚɡɦɵ, ɚ ɬɚɤɠɟ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɪɨɰɟɫɫɨɜ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɩɥɚɡɦɵ ɫ ɬɜɟɪɞɵɦ ɬɟɥɨɦ. Ɋɚɫɫɦɨɬɪɢɦ ɧɟɤɨɬɨɪɵɟ ɢɡ ɬɚɤɢɯ ɫɢɫɬɟɦ.
ɗɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɢɟ ɷɧɟɪɝɨɚɧɚɥɢɡɚɬɨɪɵ
ɇɚɢɛɨɥɟɟ ɩɪɨɫɬɨɣ ɹɜɥɹɟɬɫɹ ɫɢɫɬɟɦɚ ɜ ɜɢɞɟ ɩɥɨɫɤɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ. ȿɫɥɢ ɩɭɱɨɤ ɱɚɫɬɢɰ ɡɚɩɭɫɤɚɟɬɫɹ ɩɚɪɚɥɥɟɥɶɧɨ ɩɥɚɫɬɢɧɚɦ (ɪɢɫ. 5.7 ), ɬɨ ɭɝɨɥ ɨɬɤɥɨɧɟɧɢɹ
ɩɭɱɤɚ α ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɱɚɫɬɢɰ U0:
α(U0) = ∆UlE/(2U0d), |
(5.20) |
ɝɞɟ ∆U - ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ, ɩɪɢɥɨɠɟɧɧɚɹ ɤ ɩɥɚɫɬɢɧɚɦ, lE - ɞɥɢɧɚ ɩɥɚɫɬɢɧ ɜɞɨɥɶ ɞɜɢɠɟɧɢɹ ɩɭɱɤɚ, d - ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɩɥɚɫɬɢɧɚɦɢ. Ȼɥɚɝɨɞɚɪɹ ɪɚɡɥɢɱɧɵɦ ɡɧɚɱɟɧɢɹɦ ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɜɟɪɯɧɟɣ ɢ ɧɢɠɧɟɣ ɝɪɚɧɢɰɟ ɩɭɱɤɚ, ɚ
ɡɧɚɱɢɬ ɢ ɪɚɡɥɢɱɧɵɦ ɫɤɨɪɨɫɬɹɦ ɱɚɫɬɢɰ, ɩɪɨɢɫɯɨɞɢɬ ɮɨɤɭɫɢɪɨɜɤɚ ɩɭɱɤɚ. ɏɨɪɨɲɭɸ ɮɨɤɭɫɢɪɨɜɤɭ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɢɬɶ ɰɢɥɢɧɞɪɢɱɟɫɤɢɣ ɤɨɧɞɟɧɫɚɬɨɪ
(ɪɢɫ. 5.8). ɗɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ ɨɛɪɚɬɧɨ
ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɪɚɞɢɭɫɭ E(r) = a/r, ɢɧɬɟɝɪɢɪɭɹ ɭɪɚɜɧɟɧɢɟ dU(r)/dr = a/r, ɦɨɠɧɨ ɧɚɣɬɢ ɤɨɷɮɮɢɰɢɟɧɬ a = (U2 – U1)/ln(R2/R1), ɚ ɡɧɚɱɢɬ E(r) == (U2 – U1)/(rln(R2/R1)), ɝɞɟ U1, U2, R1, R2 – ɩɨɬɟɧɰɢɚɥɵ ɢ ɪɚɞɢɭɫɵ ɜɧɭɬɪɟɧɧɟɝɨ ɢ
ɜɧɟɲɧɟɝɨ ɰɢɥɢɧɞɪɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɑɟɪɟɡ ɭɡɤɭɸ ɜɵɯɨɞɧɭɸ ɳɟɥɶ ɛɭɞɭɬ «ɭɫɩɟɲɧɨ» ɩɪɨɯɨɞɢɬɶ ɬɨɥɶɤɨ ɱɚɫɬɢɰɵ, ɢɦɟɸɳɢɟ ɤɪɭɝɨɜɵɟ ɬɪɚɟɤɬɨɪɢɢ ɢ ɫɤɨɪɨɫɬɢ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɭɫɥɨɜɢɸ: mv2/r = qE (ɨɫɬɚɥɶɧɵɟ ɩɨɩɚɞɭɬ ɧɚ ɫɬɟɧɤɢ ɰɢɥɢɧɞɪɚ), ɬ. ɟ. ɱɚɫɬɢɰɵ, ɢɦɟɸɳɢɟ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ:
U0[ɷȼ]= q(U2 – U1)/(2ln(R2/R1)). |
(5.21) |
Ⱦɥɹ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɞɥɹ ɧɟɤɪɭɝɨɜɵɯ ɬɪɚɟɤɬɨɪɢɣ ɜ ɩɨɥɹɪɧɵɯ
Ɋɢɫ. 5.8. Ɏɨɤɭɫɬɪɨɜɤɚ ɜ ɰɢɥɢɧɞɪɢɱɟɫɤɨɦ ɤɨɧɞɟɧɫɚɬɨɪɟ
ɘɡɭ ɢ Ɋɨɠɚɧɫɤɨɦɭ).
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ɤɨɨɪɞɢɧɚɬɚɯ: |
= − mr |
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ɫ ɭɱɟɬɨɦ |
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r |
− rϕ |
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ɩɨɫɬɨɹɧɫɬɜɚ |
ɫɟɤɬɨɪɚɥɶɧɨɣ |
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ɫɤɨɪɨɫɬɢ |
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r |
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ɭɞɨɛɧɨ |
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ɪɚɫɫɦɨɬɪɟɬɶ |
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ϕ = const , |
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ɨɬɤɥɨɧɟɧɢɟ u ɬɪɚɟɤɬɨɪɢɢ ɨɬ ɤɪɭɝɨɜɨɣ: r = r0+u (u << r), ɝɞɟ r0 - ɪɚɞɢɭɫ, ɧɚ ɤɨɬɨɪɨɦ ɩɭɱɨɤ ɱɚɫɬɢɰ ɜɥɟɬɚɟɬ ɜ ɤɨɧɞɟɧɫɚɬɨɪ. Ɍɨɝɞɚ
ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ: u + 2ω 02 u = 0 , ɝɞɟ ω02 = (qa)/(mr02),
ɪɟɲɟɧɢɟ ɤɨɬɨɪɨɝɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɤɨɥɟɛɚɧɢɹ ɨɤɨɥɨ ɤɪɭɝɨɜɨɣ ɬɪɚɟɤɬɨɪɢɢ ɫ
ɩɟɪɢɨɞɨɦ 2π/ 
2 , ɬɨ ɟɫɬɶ ɩɨɫɥɟ ɩɨɜɨɪɨɬɚ ɧɚ ɭɝɨɥ π/ 
2 =127.3ɨ ɩɭɱɨɤ ɮɨɤɭɫɢɪɭɟɬɫɹ ɧɚ ɤɪɭɝɨɜɨɣ ɬɪɚɟɤɬɨɪɢɢ (ɮɨɤɭɫɢɪɨɜɤɚ ɩɨ
Ɇɚɝɧɢɬɧɵɟ ɦɚɫɫ-ɫɟɩɚɪɚɬɨɪɵ ɢ ɷɧɟɪɝɨɚɧɚɥɢɡɚɬɨɪɵ
Ȼɥɚɝɨɞɚɪɹ ɡɚɜɢɫɢɦɨɫɬɢ ɪɚɞɢɭɫɚ ɜɪɚɳɟɧɢɹ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ rɥ = vmceB (ɥɚɪɦɨɪɨɜɫɤɨɝɨ ɪɚɞɢɭɫɚ) ɨɬ ɫɤɨɪɨɫɬɢ
v ɢ ɦɚɫɫɵ m ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ, ɜɨɡɦɨɠɧɨ ɢɯ ɪɚɡɞɟɥɟɧɢɟ (ɫɟɩɚɪɚɰɢɹ) ɩɨ ɷɧɟɪɝɢɹɦ ɢ ɦɚɫɫɚɦ, ɚ ɬɚɤɠɟ ɮɨɤɭɫɢɪɨɜɤɚ ɤɚɤ ɜ ɩɨɩɟɪɟɱɧɨɦ, ɬɚɤ ɢ ɜ ɩɪɨɞɨɥɶɧɨɦ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ. ȼ ɩɨɩɟɪɟɱɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɧɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɨɣ ɹɜɥɹɟɬɫɹ ɫɯɟɦɚ ɫ ɩɨɥɭɤɪɭɝɨɜɨɣ ɮɨɤɭɫɢɪɨɜɤɨɣ (ɪɢɫ. 5.9). ȼɵɯɨɞɹɳɢɣ ɢɡ ɬɨɱɟɱɧɨɝɨ ɢɫɬɨɱɧɢɤɚ Ⱥ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɫɢɥɨɜɵɦ ɥɢɧɢɹɦ ɩɭɱɨɤ ɦɨɧɨɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɱɚɫɬɢɰ ɛɭɞɟɬ
ɮɨɤɭɫɢɪɨɜɚɬɶɫɹ ɩɨɫɥɟ ɩɨɥɭɨɛɨɪɨɬɚ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 2rɥ. Ɏɨɤɭɫɢɪɨɜɤɚ ɱɚɫɬɢɰ, ɜɵɥɟɬɟɜɲɢɯ ɩɨɞ ɨɞɢɧɚɤɨɜɵɦ ɭɝɥɨɦ α ɤ ɰɟɧɬɪɚɥɶɧɨɣ ɬɪɚɟɤɬɨɪɢɢ ɩɭɱɤɚ, ɩɪɨɢɫɯɨɞɢɬ ɛɥɚɝɨɞɚɪɹ ɬɨɦɭ, ɱɬɨ ɤɪɭɝɨɜɵɟ ɬɪɚɟɤɬɨɪɢɢ ɱɚɫɬɢɰ ɢɦɟɸɬ ɨɞɢɧɚɤɨɜɵɟ ɪɚɞɢɭɫɵ, ɢ ɢɯ ɬɪɚɟɤɬɨɪɢɢ ɨɩɢɪɚɸɬɫɹ ɧɚ ɞɢɚɦɟɬɪɵ, ɪɚɫɩɨɥɨɠɟɧɧɵɟ ɩɨɞ ɬɟɦ ɠɟ ɭɝɥɨɦ 2α, ɱɬɨ ɢ ɤɚɫɚɬɟɥɶɧɵɟ ɤ ɬɪɚɟɤɬɨɪɢɹɦ ɜ ɧɚɱɚɥɶɧɨɣ ɬɨɱɤɟ.
ɒɢɪɢɧɚ ɳɟɥɢ δ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɩɪɨɯɨɠɞɟɧɢɹ ɜɫɟɝɨ ɩɭɱɤɚ, ɡɚɜɢɫɢɬ ɨɬ ɪɚɫɯɨɞɢɦɨɫɬɢ 2α ɜɯɨɞɹɳɟɝɨ ɩɭɱɤɚ: δ =2rɥ(1-cosα). ȼ ɫɟɤɬɨɪɧɵɯ ɦɚɫɫ-ɫɩɟɤɬɪɨɦɟɬɪɚɯ ɫ ɨɞɧɨɪɨɞɧɵɦ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ (ɪɢɫ. 5.10) ɮɨɤɭɫɢɪɨɜɤɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɡɚ ɫɱɟɬ ɬɨɝɨ, ɱɬɨ ɞɥɢɧɚ ɬɪɚɟɤɬɨɪɢɢ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɞɥɹ ɱɚɫɬɢɰ, ɧɚɯɨɞɹɳɢɯɫɹ ɧɚ ɪɚɡɧɨɦ ɪɚɫɫɬɨɹɧɢɢ ɨɬ ɰɟɧɬɪɚ ɫɟɤɬɨɪɚ, ɪɚɡɥɢɱɧɚ. Ɏɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɬɚɤɨɣ ɫɢɫɬɟɦɵ
ɡɚɜɢɫɢɬ ɨɬ ɭɝɥɚ ɫɟɤɬɨɪɚ ϕ ɢ |
Ɋɢɫ. 5.10. ɋɟɤɬɨɪɧɵɣ ɦɚɝɧɢɬɧɵɣ |
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ɪɚɫɫɬɨɹɧɢɹ ɨɬ |
ɢɫɬɨɱɧɢɤɚ ɞɨ |
ɦɚɫɫ-ɫɟɩɚɪɚɬɨɪ |
ɝɪɚɧɢɰɵ ɩɨɥɹ. |
ȿɫɥɢ ɬɪɚɟɤɬɨɪɢɹ |
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ɨɫɟɜɵɯ ɱɚɫɬɢɰ ɩɭɱɤɚ ɧɚ ɜɯɨɞɟ ɢ ɜɵɯɨɞɟ ɢɡ ɫɟɤɬɨɪɚ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚ ɟɝɨ ɝɪɚɧɢɰɟ (ɰɟɧɬɪ ɜɪɚɳɟɧɢɹ ɨɫɟɜɵɯ ɱɚɫɬɢɰ ɫɨɜɩɚɞɚɟɬ ɫ ɰɟɧɬɪɨɦ ɫɟɤɬɨɪɚ), ɬɨ ɪɚɫɱɟɬɵ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɮɨɤɭɫɢɪɨɜɤɚ ɩɪɨɢɫɯɨɞɢɬ ɧɚ ɝɪɚɧɢɰɟ ɜɥɟɬɚ ɩɭɱɤɚ ɜ
ɫɢɫɬɟɦɭ, ɬ. ɟ. ε1 + ϕ + ε2 = 180ɨ (ɪɢɫ. 5.10).
ȼ ɩɪɨɞɨɥɶɧɨɦ
Ɋɢɫ. 5.11. Ɏɨɤɭɫɢɪɨɜɤɚ ɜ ɨɞɧɨɪɨɞɧɨɦ ɩɪɨɞɨɥɶɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ
ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɮɨɤɭɫɢɪɨɜɤɚ ɩɪɨɢɫɯɨɞɢɬ ɜ ɫɢɥɭ ɬɨɝɨ, ɱɬɨ ɜɵɲɟɞɲɢɟ ɢɡ ɨɞɧɨɣ ɬɨɱɤɢ ɱɚɫɬɢɰɵ ɩɨɫɥɟ ɫɨɜɟɪɲɟɧɢɹ ɨɞɧɨɝɨ ɨɛɨɪɨɬɚ ɩɨ ɥɚɪɦɨɪɨɜɫɤɨɣ
ɨɤɪɭɠɧɨɫɬɢ ɜɨɡɜɪɚɳɚɸɬɫɹ ɧɚ ɢɫɯɨɞɧɭɸ ɫɢɥɨɜɭɸ ɥɢɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɪɢɫ. 5.11). ɉɪɨɟɤɰɢɹ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰ ɧɚ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɭɸ ɤ ɫɢɥɨɜɵɦ ɥɢɧɢɹɦ ɩɥɨɫɤɨɫɬɶ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɭɱɨɤ ɨɤɪɭɠɧɨɫɬɟɣ, ɢɦɟɸɳɢɯ ɨɛɳɭɸ ɬɨɱɤɭ. ȿɫɥɢ ɭɝɨɥ ɪɚɫɯɨɞɢɦɨɫɬɢ ɩɭɱɤɚ α ɧɟɜɟɥɢɤ, ɬɨ ɮɨɤɭɫɢɪɨɜɤɚ ɦɨɧɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɩɭɱɤɚ ɩɪɨɢɡɨɣɞɟɬ ɱɟɪɟɡ ɨɞɢɧ ɨɛɨɪɨɬ ɧɚ ɪɚɫɫɬɨɹɧɢɢ l = τɥvcosα ≈ 2πmvc/(eB), ɝɞɟ τɥ = 2πmc/(eB) – ɩɟɪɢɨɞ
ɜɪɚɳɟɧɢɹ ɩɨ ɥɚɪɦɨɪɨɜɫɤɨɣ ɨɤɪɭɠɧɨɫɬɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɫɫɬɨɹɧɢɟ ɞɨ ɦɟɫɬɚ ɮɨɤɭɫɢɪɨɜɤɢ ɩɭɱɤɚ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ ɢ ɦɚɫɫɵ ɱɚɫɬɢɰ, ɢ ɩɪɨɞɨɥɶɧɨɟ ɨɞɧɨɪɨɞɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɨ ɞɥɹ ɷɧɟɪɝɨ- ɢ ɦɚɫɫɫɟɩɚɪɚɰɢɢ ɱɚɫɬɢɰ.
ɗɥɟɤɬɪɨɧɧɵɟ ɢ ɢɨɧɧɵɟ ɩɭɲɤɢ
ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɷɥɟɤɬɪɨɧɧɵɯ ɩɭɲɟɤ ɢɫɬɨɱɧɢɤɨɦ ɷɥɟɤɬɪɨɧɨɜ
ɫɥɭɠɢɬ ɬɟɪɦɨɤɚɬɨɞ (ɜɨɥɶɮɪɚɦɨɜɵɣ, ɨɤɫɢɞɧɵɣ ɢ ɬ.ɩ.) (ɪɢɫ. 5.12).
Ɋɢɫ. 5.12. ɗɥɟɤɬɪɨɧɧɚɹ ɩɭɲɤɚ: 1 – ɧɢɬɶ ɧɚɤɚɥɚ, 2 – ɤɚɬɨɞ, ɩɨɞɨɝɪɟɜɚɟɦɵɣ ɧɢɬɶɸ ɧɚɤɚɥɚ, 3 – ɭɩɪɚɜɥɹɸɳɢɣ ɷɥɟɤɬɪɨɞ ɫ ɫɟɬɤɨɣ, 4 – ɚɧɨɞ ɫ ɫɟɬɤɨɣ.
Ɏɨɤɭɫɢɪɨɜɤɚ ɩɭɱɤɚ ɢ ɭɩɪɚɜɥɟɧɢɟ ɟɝɨ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɭɩɪɚɜɥɹɸɳɢɦ (ɢɥɢ ɮɨɤɭɫɢɪɭɸɳɢɦ) ɷɥɟɤɬɪɨɞɨɦ. Ⱥɧɨɞɨɦ ɹɜɥɹɟɬɫɹ ɞɢɚɮɪɚɝɦɚ, ɦɟɠɞɭ ɤɨɬɨɪɨɣ ɢ ɤɚɬɨɞɨɦ ɦɨɠɟɬ ɩɪɢɤɥɚɞɵɜɚɬɶɫɹ ɧɚɩɪɹɠɟɧɢɟ ɨɬ ɟɞɢɧɢɰ ɞɨ ɫɨɬɟɧ ɤɢɥɨɜɨɥɶɬ. ɇɚ ɭɩɪɚɜɥɹɸɳɢɣ ɷɥɟɤɬɪɨɞ ɩɨɞɚɟɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɨɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɚɬɨɞɚ ɧɚɩɪɹɠɟɧɢɟ ɞɨ 500 ȼ. ɍɩɪɚɜɥɟɧɢɟ ɭɠɟ ɫɮɨɪɦɢɪɨɜɚɧɧɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɭɱɤɚ ɦɨɠɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɫ ɩɨɦɨɳɶɸ ɨɬɤɥɨɧɹɸɳɟɣ ɫɢɫɬɟɦɵ, ɤɚɤ ɷɬɨ ɩɪɨɢɫɯɨɞɢɬ ɜ ɷɥɟɤɬɪɨɧɧɨ-ɥɭɱɟɜɵɯ ɬɪɭɛɤɚɯ ɬɟɥɟɜɢɡɨɪɨɜ ɢ ɦɨɧɢɬɨɪɨɜ.
ɉɪɢɧɰɢɩ ɪɚɛɨɬɵ ɢɨɧɧɨɣ ɩɭɲɤɢ ɩɨɞɨɛɟɧ ɷɥɟɤɬɪɨɧɧɨɣ. ɋɭɳɟɫɬɜɭɟɬ ɛɨɥɶɲɨɟ ɦɧɨɠɟɫɬɜɨ ɪɚɡɧɨɨɛɪɚɡɧɵɯ ɤɨɧɫɬɪɭɤɰɢɣ ɢɨɧɧɵɯ ɩɭɲɟɤ (ɢɨɧɧɵɯ ɢɫɬɨɱɧɢɤɨɜ). ȼ ɧɢɯ ɢɫɩɨɥɶɡɭɸɬɫɹ ɪɚɡɥɢɱɧɵɟ ɫɩɨɫɨɛɵ ɫɨɡɞɚɧɢɹ ɢɨɧɨɜ, ɧɚɩɪɢɦɟɪ, ɬɟɪɦɨɢɨɧɧɚɹ ɷɦɢɫɫɢɹ, ɢɨɧɢɡɚɰɢɹ ɝɚɡɚ ɢɥɢ ɩɚɪɨɜ ɜɟɳɟɫɬɜɚ ɷɥɟɤɬɪɨɧɧɵɦ ɭɞɚɪɨɦ. ɇɚɢɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɵɦɢ ɢɫɬɨɱɧɢɤɚɦɢ ɢɨɧɨɜ ɹɜɥɹɸɬɫɹ ɩɥɚɡɦɟɧɧɵɟ, ɜ ɤɨɬɨɪɵɯ ɫɨɡɞɚɟɬɫɹ ɝɚɡɨɪɚɡɪɹɞɧɚɹ ɩɥɚɡɦɚ, ɚ ɢɨɧɵ ɜɵɬɹɝɢɜɚɸɬɫɹ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɩɨɥɟɦ ɫ ɟɟ ɝɪɚɧɢɰɵ. ɉɪɢɦɟɪɨɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɜɟɫɶɦɚ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɣ ɢɫɬɨɱɧɢɤ ɢɨɧɨɜ ɬɢɩɚ ɞɭɨɩɥɚɡɦɚɬɪɨɧ (ɪɢɫ. 5.13), ɜ ɤɨɬɨɪɨɦ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɪɚɡɪɹɞ ɮɨɪɦɢɪɭɟɬɫɹ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɩɪɨɦɟɠɭɬɨɱɧɵɦ ɚɧɨɞɨɦ. Ʉɨɧɢɱɟɫɤɚɹ ɮɨɪɦɚ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɚɧɨɞɚ ɩɪɢɜɨɞɢɬ ɤ ɫɠɚɬɢɸ ɩɥɚɡɦɵ ɜ ɪɚɣɨɧɟ ɜɵɯɨɞɧɨɝɨ ɨɬɜɟɪɫɬɢɹ.
ɇɟɨɞɧɨɪɨɞɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɫɨɡɞɚɜɚɟɦɨɟ ɤɚɬɭɲɤɨɣ ɦɟɠɞɭ ɩɪɨɦɟɠɭɬɨɱɧɵɦ ɚɧɨɞɨɦ ɢ ɚɧɨɞɨɦ, ɩɪɢɜɨɞɢɬ ɤ ɞɨɩɨɥɧɢɬɟɥɶɧɨɦɭ ɫɠɚɬɢɸ ɩɥɚɡɦɟɧɧɨɣ ɫɬɪɭɢ. Ⱦɢɚɮɪɚɝɦɚ ɜ ɦɟɫɬɟ ɧɚɢɛɨɥɶɲɟɝɨ ɫɠɚɬɢɹ
ɢɫɩɨɥɶɡɭɟɬɫɹ |
ɞɥɹ |
ɩɨɜɵɲɟɧɢɹ |
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ɝɚɡɨɜɨɣ |
ɷɤɨɧɨɦɢɱɧɨɫɬɢ |
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ɢɫɬɨɱɧɢɤɚ ɡɚ |
ɫɱɟɬ |
ɨɝɪɚɧɢɱɟɧɢɹ |
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ɩɨɬɨɤɚ |
ɧɟɢɨɧɢɡɨɜɚɧɧɨɣ |
Ɋɢɫ. 5. 13. ɂɫɬɨɱɧɢɤ ɢɨɧɨɜ ɬɢɩɚ ɞɭɨɩɥɚɡɦɚɬɪɨɧ: 1 – |
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ɤɨɦɩɨɧɟɧɬɵ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ. |
ɤɚɬɨɞ ɫ ɧɚɤɚɥɢɜɚɟɦɨɣ ɧɢɬɶɸ, 2 – ɩɪɨɦɟɠɭɬɨɱɧɵɣ |
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ɂɨɧɵ ɜɵɬɹɝɢɜɚɸɬɫɹ |
ɢɡ ɩɥɚɡɦɵ |
ɷɥɟɤɬɪɨɞ, 3 – ɤɚɬɭɲɤɚ ɞɥɹ ɫɨɡɞɚɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, |
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4 – ɚɧɨɞ, 5 - ɚɧɨɞɧɚɹ ɜɫɬɚɜɤɚ, 6 – ɜɵɬɹɝɢɜɚɸɳɢɣ |
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ɷɥɟɤɬɪɨɞɨɦ, ɤɨɬɨɪɵɣ ɫɬɨɢɬ ɫɪɚɡɭ |
ɷɥɟɤɬɪɨɞ, |
7 – ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɚɹ ɥɢɧɡɚ, 8 – |
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ɩɨɫɥɟ ɚɧɨɞɚ ɢ ɧɚ ɤɨɬɨɪɵɣ |
ɢɡɨɥɹɬɨɪ, |
9 – ɮɥɚɧɟɰ ɜɚɤɭɭɦɧɨɣ ɤɚɦɟɪɵ, 10 – ɬɪɭɛɤɚ |
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ɩɨɞɚɟɬɫɹ |
ɨɬɪɢɰɚɬɟɥɶɧɵɣ |
ɞɥɹ ɧɚɬɟɤɚɧɢɹ ɝɚɡɚ, 11 – ɞɢɚɮɪɚɝɦɚ |
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ɨɬɧɨɫɢɬɟɥɶɧɨ ɚɧɨɞɚ ɩɨɬɟɧɰɢɚɥ. Ⱦɢɚɮɪɚɝɦɚ ɜɵɬɹɝɢɜɚɸɳɟɝɨ ɷɥɟɤɬɪɨɞɚ ɹɜɥɹɟɬɫɹ ɮɨɤɭɫɢɪɭɸɳɟɣ ɫɢɫɬɟɦɨɣ. Ʉɪɨɦɟ ɬɨɝɨ, ɝɪɚɧɢɰɚ ɩɥɚɡɦɵ, ɢɡ ɤɨɬɨɪɨɣ ɜɵɬɹɝɢɜɚɸɬɫɹ ɢɨɧɵ, ɹɜɥɹɟɬɫɹ ɬɚɤɠɟ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɣ ɥɢɧɡɨɣ. Ɏɨɪɦɚ ɝɪɚɧɢɰɵ ɩɥɚɡɦɵ ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɟɬ ɧɚ ɪɚɫɯɨɞɢɦɨɫɬɶ ɮɨɪɦɢɪɭɟɦɨɝɨ ɜ ɢɨɧɧɨɨɩɬɢɱɟɫɤɢɣ ɫɢɫɬɟɦɟ ɢɨɧɧɨɝɨ ɩɭɱɤɚ. Ɇɟɧɹɹ ɤɨɧɰɟɧɬɪɚɰɢɸ ɩɥɚɡɦɵ (ɧɚɩɪɢɦɟɪ, ɦɟɧɹɹ ɬɨɤ ɪɚɡɪɹɞɚ) ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɦ ɭɫɤɨɪɹɸɳɟɦ ɧɚɩɪɹɠɟɧɢɢ, ɦɨɠɧɨ ɭɩɪɚɜɥɹɬɶ ɮɨɪɦɨɣ ɩɥɚɡɦɟɧɧɨɣ ɝɪɚɧɢɰɵ. ɉɪɢ ɛɨɥɶɲɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɥɚɡɦɵ ɝɪɚɧɢɰɚ ɜɵɩɭɤɥɚɹ – ɩɭɱɨɤ ɫɢɥɶɧɨ ɪɚɫɯɨɞɢɬɫɹ. ɋɧɢɠɚɹ ɤɨɧɰɟɧɬɪɚɰɢɸ ɩɥɚɡɦɵ, ɦɨɠɧɨ ɫɨɡɞɚɬɶ ɩɥɨɫɤɭɸ ɟɟ ɝɪɚɧɢɰɭ, ɬɨɝɞɚ ɪɚɫɯɨɞɢɦɨɫɬɶ ɦɨɠɟɬ ɛɵɬɶ ɦɢɧɢɦɚɥɶɧɨɣ, ɚ ɜɵɬɹɝɢɜɚɟɦɵɣ ɢɡ ɢɫɬɨɱɧɢɤɚ ɬɨɤ ɩɨɞɱɢɧɹɟɬɫɹ ɡɚɤɨɧɭ «3/2» (ɫɦ. § 42). ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɦɟɧɶɲɟɧɢɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɥɚɡɦɵ ɝɪɚɧɢɰɚ ɫɬɚɧɨɜɢɬɫɹ ɜɨɝɧɭɬɨɣ, ɢ ɪɚɫɯɨɞɢɦɨɫɬɶ ɩɭɱɤɚ ɜɧɨɜɶ ɜɨɡɪɚɫɬɚɟɬ. Ɋɚɫɱɟɬ ɩɚɪɚɦɟɬɪɨɜ ɮɨɤɭɫɢɪɨɜɤɢ ɩɭɱɤɚ ɫ ɭɱɟɬɨɦ ɝɪɚɧɢɰɵ ɩɥɚɡɦɵ ɹɜɥɹɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɨɣ ɡɚɞɚɱɟɣ ɢ ɜɨɡɦɨɠɟɧ ɥɢɲɶ ɱɢɫɥɟɧɧɵɦɢ ɦɟɬɨɞɚɦɢ.