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Файл:Физика электричество и магнетизм. Ч. 2. Лабораторный практикум
.pdf
2
B
ȼ
2
X
m
ɤɪ a
qU
(4.13)
.
e
a
ɢ ɩɨɞɫɬɚɜɢɬɶ ɜ ɭɪɚɜɧɟɧɢɟ (4.13).
3) ɢɡ ɡɚɤɨɧɚ (4.12) ɜɵɪɚɡɢɬɶ
2
q
§·
¨¸
mBr
©¹
§·
e
¨¸
¨¸
©¹
2
X
2
m
Ɋɚɫɱɟɬɧɚɹ ɮɨɪɦɭɥɚ ɞɥɹ ɭɞɟɥɶɧɨɝɨ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ ɬɚɤɨɜɚ:
ȼ ɮɨɪɦɭɥɭ (4.14) ɜɯɨɞɢɬ
qU
e
m
a
(4.14)
ɤɪ
.
22
r
ɤɪ ɚ
, ɜɟɥɢɱɢɧɚ ɤɨɬɨɪɨɝɨ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ
8
ɩɨ ɮɨɪɦɭɥɟ (4.11) ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɡɧɚɱɟɧɢɹ ɤɪɢɬɢɱɟɫɤɨɣ ɫɢɥɵ ɬɨɤɚ
I
, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɩɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɪɟɡɭɥɶɬɚɬɚɦ: ɦɟɧɹɹ ɬɨɤ
ɫ(ɤɪ)
ɜ ɫɨɥɟɧɨɢɞɟ, ɢɡɦɟɪɹɸɬ ɫɢɥɭ ɚɧɨɞɧɨɝɨ ɬɨɤɚ ɢ ɫɬɪɨɹɬ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɫɢɥɵ ɚɧɨɞɧɨɝɨ ɬɨɤɚ
ɫɩɥɨɲɧɨɣ ɤɪɢɜɨɣ ɪɢɫ. 4.5) ɢ ɩɨ ɧɟɦɭ ɧɚɯɨɞɹɬ
I ɨɬ ɫɢɥɵ ɬɨɤɚ ɜ ɫɨɥɟɧɨɢɞɟ ɫI (ɩɨɞɨɛɧɵɣ
a
I .
ɫ(ɤɪ)
ɉɪɢ ɷɬɨɦ ɧɚɞɨ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɪɚɫɱɟɬɧɚɹ ɮɨɪɦɭɥɚ (4.14) ɩɨɥɭɱɟɧɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɡɚɤɨɧɚ (4.12), ɡɚɩɢɫɚɧɧɨɝɨ ɞɥɹ ɫɥɭɱɚɹ ɷɥɟɤɬɪɨɧɨɜ, ɜɵɥɟɬɚɸɳɢɯ ɢɡ ɤɚɬɨɞɚ ɫɨ ɫɤɨɪɨɫɬɹɦɢ, ɛɥɢɡɤɢɦɢ ɤ ɧɭɥɸ.
ɇɚ ɝɪɚɮɢɤɟ (ɫɦ. ɪɢɫ. 4.5) ɨɛɥɚɫɬɶ ɩɨɱɬɢ ɥɢɧɟɣɧɨɝɨ ɧɚɢɛɨɥɟɟ ɤɪɭɬɨɝɨ
ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɤɪɢɜɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɜɟɥɢɱɢɧɟ ɧɚɢɛɨɥɟɟ
ɫɩɚɞɚ
ɜɟɪɨɹɬɧɨɣ (ɫɪɟɞɧɟɣ) ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ, ɜɵɥɟɬɚɸɳɢɯ ɢɡ ɤɚɬɨɞɚ ɢ
ɭɫɤɨɪɟɧɧɵɯ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɩɨɥɟɦ ɦɚɝɧɟɬɪɨɧɚ. ɉɨɷɬɨɦɭ ɞɥɹ ɥɭɱɲɟɣ
ɤɨɪɪɟɥɹɰɢɢ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɮɨɪɦɭɥɵ (4.14) ɢ ɩɨɥɭɱɟɧɧɵɯ ɷɤɫɩɟɪɢ-
ɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɡɧɚɱɟɧɢɟ ɤɪɢɬɢɱɟɫɤɨɝɨ ɬɨɤɚ
I
ɤɪ
ɜɵɛɢɪɚɬɶ ɩɨ ɝɪɚɮɢɤɭ ɧɢɠɟ ɫɟɪɟɞɢɧɵ ɨɛɥɚɫɬɢ ɛɵɫɬɪɨɝɨ ɫɩɚɞɚ ɚɧɨɞɧɨɝɨ ɬɨɤɚ. Ⱦɚɥɟɟ, ɢɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɵ (4.12) ɢ (4.14), ɩɨɥɭɱɚɸɬ ɜɟɥɢɱɢɧɭ ɭɞɟɥɶɧɨɝɨ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ.
4.4. ɉɨɪɹɞɨɤ ɜɵɩɨɥɧɟɧɢɹ ɪɚɛɨɬɵ
ɢ ɨɛɪɚɛɨɬɤɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ
1. ɍɫɬɚɧɨɜɢɬɶ 1-ɟ ɡɧɚɱɟɧɢɟ ɚɧɨɞɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ
ɫɢɪɭɹ ɟɝɨ ɡɧɚɱɟɧɢɟ ɩɨ ɜɨɥɶɬɦɟɬɪɭ 5 (ɫɦ. ɪɢɫ. 4.3).
2. Ɇɟɧɹɹ ɜɟɥɢɱɢɧɭ ɫɨɩɪɨɬɢɜɥɟɧɢɹ 7 (ɫɦ. ɪɢɫ. 4.3) ɢ ɨɬɫɥɟɠɢɜɚɹ ɭɜɟɥɢ-
ɱɟɧɢɟ ɡɧɚɱɟɧɢɣ ɫɢɥɵ ɬɨɤɚ ɫɨɥɟɧɨɢɞɚ
ɚɧɨɞɧɨɝɨ ɬɨɤɚ
I ɚɦɩɟɪɦɟɬɪɨɦ 6 ( ~ 20 ɪɚɡ), ɡɚɧɨɫɹ ɞɚɧɧɵɟ ɜ ɬɚɛɥ. 4.1.
a
I ɩɨ ɚɦɩɟɪɦɟɬɪɭ 4, ɢɡɦɟɪɹɬɶ ɫɢɥɭ
c
U
= 50 ȼ, ɮɢɤ-
a
1
61
3. ɉɨɜɬɨɪɢɬɶ ɢɡɦɟɪɟɧɢɹ
I
ȼ
ɧɚɩɪɹɠɟɧɢɹ
U ɢ
a
2
U
a
I (ɩ. 1, 2) ɞɥɹ ɞɪɭɝɢɯ ɡɧɚɱɟɧɢɣ ɚɧɨɞɧɨɝɨ
a
ɩɪɢ ɬɟɯ ɠɟ ɡɧɚɱɟɧɢɹɯ cI . ȼɫɟ ɞɚɧɧɵɟ ɡɚɧɟɫɬɢ
3
ɜ ɜ ɬɚɛɥ. 4.1.
Ɍɚɛɥɢɰɚ 4.1
= 100 ȼ
U
= 50 ȼ
a
ɇɨɦɟɪ ɨɩɵɬɚ
1 0
2 0,1
3 0,2
… …
20 1,9
I , Ⱥ
c
1
I
a
1
U
= 80 ȼ
a
2
I
a
2
U
a
3
I
a
3
4. ɉɨɫɬɪɨɢɬɶ ɧɚ ɦɢɥɥɢɦɟɬɪɨɜɤɟ ɬɪɢ ɝɪɚɮɢɤɚ ɡɚɜɢɫɢɦɨɫɬɢ ɚI
(ɨɫɶ Y) ɨɬ
ɧɚɩɪɹɠɟɧɢɹ
5. ɇɚɣɬɢ ɩɨ ɝɪɚɮɢɤɚɦ ɡɧɚɱɟɧɢɹ
ɧɟɣ ɱɚɫɬɢ ɨɛɥɚɫɬɢ ɛɵɫɬɪɨɝɨ ɫɩɚɞɚ ɚɧɨɞɧɨɝɨ ɬɨɤɚ
I (ɨɫɶ ɏ), ɩɨɥɭɱɟɧɧɵɯ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɚɧɨɞɧɨɝɨ
ɫ
U
.
a
i
, ɜɵɛɢɪɚɹ ɷɬɢ ɡɧɚɱɟɧɢɹ ɜ ɧɢɠ-
ɤɪ
I , ɢ ɡɚɧɟɫɬɢ ɢɯ ɜ
a
ɬɚɛɥ. 4.2.
6. Ɋɚɫɫɱɢɬɚɬɶ ɩɨ ɩɨɥɭɱɟɧɧɵɦ ɡɧɚɱɟɧɢɹɦ ɤɪɢɬɢɱɟɫɤɨɝɨ ɬɨɤɚ ɬɪɢ
ɡɧɚɱɟɧɢɹ
7. Ɋɚɫɫɱɢɬɚɬɶ ɭɞɟɥɶɧɵɣ ɡɚɪɹɞ
ɡɧɚɱɟɧɢɣ
ɩɨ ɮɨɪɦɭɥɟ (4.12). ȼɧɟɫɬɢ ɢɯ ɜ ɬɚɛɥ. 4.2.
ɤɪ
i
q
§·
e
ɩɨ ɮɨɪɦɭɥɟ (4.14) ɞɥɹ ɬɪɟɯ
¨¸
m
©¹
I ɬɨɤɚ ɫɨɥɟɧɨɢɞɚ. ȼɵɱɢɫɥɢɬɶ ɟɝɨ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ.
ɤɪi
8. Ɉɰɟɧɢɬɶ ɫɥɭɱɚɣɧɭɸ ɚɛɫɨɥɸɬɧɭɸ ɩɨɝɪɟɲɧɨɫɬɶ ɤɚɠɞɨɝɨ ɢɡ ɬɪɟɯ
ɡɧɚɱɟɧɢɣ, ɧɚɣɬɢ ɟɟ ɫɪɟɞɧɸɸ ɜɟɥɢɱɢɧɭ ɢ ɡɚɩɢɫɚɬɶ ɪɟɡɭɥɶɬɚɬ ɞɥɹ ɭɞɟɥɶɧɨɝɨ ɡɚɪɹɞɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɨɱɧɨɫɬɶɸ ɷɤɫɩɟɪɢɦɟɧɬɚ ɜ ɬɚɛɥ. 4.2.
ɋɪɚɜɧɢɬɶ ɭɞɟɥɶɧɵɣ ɡɚɪɹɞ ɷɥɟɤɬɪɨɧɚ, ɩɨɥɭɱɟɧɧɵɣ ɜ ɷɤɫɩɟɪɢɦɟɧɬɟ,
q
e
ɫ ɬɟɨɪɟɬɢɱɟɫɤɢɦ ɡɧɚɱɟɧɢɟɦ:
e
§·
G
¨¸
m
©¹
m
ɷɤɫɩ
q
§·
e
¨¸
m
©¹
ɬɟɨɪ
100 %
.
62
ɉɚɪɚɦɟɬɪɵ ɫɨɥɟɧɨɢɞɚ
ȿ
ȼ
Ɍɚɛɥɢɰɚ 4.2
2500N
3ɦɦr
rr!!
a
(
,U ȼ
ɇɨɦɟɪ
ɨɩɵɬɚ
1 456
2
3
a
a ɤ
,I Ⱥ
ɤɪ
)
ee
§· §·
¨¸ ¨¸
mm
©¹ ©¹
ɫ
,ȼ
Ɍɥ
ɤɪ
r'
e
§·
,
¨¸
m
©¹
Ʉɥ/ɤɝ
ɫ
§·
'
¨¸
m
©¹
e
0,168 ɦL
,
Ʉɥ/ɤɝ
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ
1. ɇɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢ ɢɧɞɭɤɰɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ.
2. ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɫɢɥɚ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɞɜɢɠɭɳɭɸɫɹ ɡɚɪɹ-
ɠɟɧɧɭɸ ɱɚɫɬɢɰɭ.
3. ɍɪɚɜɧɟɧɢɹ ɢ ɯɚɪɚɤɬɟɪ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɱɚɫɬɢɰ ɜ ɩɨɫɬɨɹɧ-
ɧɨɦ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ ɢ ɜɟɤɬɨɪɚ
4. ɍɪɚɜɧɟɧɢɹ ɢ ɯɚɪɚɤɬɟɪ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɩɨɫɬɨ-
ɹɧɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɜɟɤɬɨɪɚ
5. Ʉɚɤɨɜɚ ɬɪɚɟɤɬɨɪɢɹ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ, ɞɜɢɠɭɳɟɣɫɹ ɜ ɨɞɧɨ-
ɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ, ɟɫɥɢ:
ɚ) ɜɟɤɬɨɪ ɟɟ ɫɤɨɪɨɫɬɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɟɧ ɜɟɤɬɨɪɭ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬ-
ɧɨɝɨ ɩɨɥɹ;
ɛ) ɫɨɫɬɚɜɥɹɟɬ ɫ ɜɟɤɬɨɪɨɦ ɢɧɞɭɤɰɢɢ ɭɝɨɥ, ɨɬɥɢɱɧɵɣ ɨɬ ɩɪɹɦɨɝɨ?
6. Ɇɨɠɟɬ ɥɢ ɢɡɦɟɧɢɬɶɫɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰɵ, ɞɜɢɠɭ-
ɳɟɣɫɹ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ, ɟɫɥɢ ɞɪɭɝɢɟ ɩɨɥɹ ɨɬɫɭɬɫɬɜɭɸɬ?
7. ɋɢɫɬɟɦɚ ɞɜɭɯ ɭɪɚɜɧɟɧɢɣ Ɇɚɤɫɜɟɥɥɚ
ɱɟɫɤɨɝɨ ɩɨɥɹ. ɂɯ ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ.
8. ɋɢɫɬɟɦɚ ɞɜɭɯ ɭɪɚɜɧɟɧɢɣ Ɇɚɤɫɜɟɥɥɚ ɞɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɦɚɝɧɢɬɧɨ-
ɝɨ ɩɨɥɹ. ɂɯ ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ.
G
ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɚ.
G
.
ɞɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɷɥɟɤɬɪɢ-
63
9. Ɋɚɫɫɱɢɬɚɬɶ ɦɚɝɧɢɬɧɭɸ ɢɧɞɭɤɰɢɸ ɧɚ ɨɫɢ ɫɨɥɟɧɨɢɞɚ ɤɨɧɟɱɧɨɣ ɞɥɢɧɵ.
10. ɋɯɟɦɚɬɢɱɟɫɤɨɟ ɭɫɬɪɨɣɫɬɜɨ ɦɚɝɧɟɬɪɨɧ ɢ ɯɚɪɚɤɬɟɪ ɞɜɢɠɟɧɢɹ
ɷɥɟɤɬɪɨɧɨɜ ɜ ɧɟɦ.
11. Ʉɚɤ ɞɜɢɠɭɬɫɹ ɷɥɟɤɬɪɨɧɵ ɜ ɦɚɝɧɟɬɪɨɧɟ ɜ ɨɬɫɭɬɫɬɜɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ?
12. Ʉɚɤɨɟ ɡɧɚɱɟɧɢɟ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɹɜɥɹɟɬɫɹ ɤɪɢɬɢɱɟɫɤɢɦ?
13. ȼɵɜɟɫɬɢ ɪɚɫɱɟɬɧɭɸ ɮɨɪɦɭɥɭ ɞɥɹ ɭɞɟɥɶɧɨɝɨ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ.
64
Ɍɟɦɚ. əȼɅȿɇɂȿ
ȼ
ȼ
ɗɅȿɄɌɊɈɆȺȽɇɂɌɇɈɃ ɂɇȾɍɄɐɂɂ
Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ ɗ.5
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɣ ɦɟɬɨɞ ɢɡɭɱɟɧɢɹ
ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ ɪɚɡɥɢɱɧɨɣ ɤɨɧɮɢɝɭɪɚɰɢɢ
5.1. ɐɟɥɶ ɪɚɛɨɬɵ
ɉɨɥɭɱɢɬɶ ɫ ɩɨɦɨɳɶɸ ɢɧɞɭɤɰɢɨɧɧɨɝɨ ɞɚɬɱɢɤɚ (ɜ ɨɫɧɨɜɭ ɟɝɨ ɪɚɛɨɬɵ ɡɚɥɨɠɟɧɨ ɹɜɥɟɧɢɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ) ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ
ɤɨɨɪɞɢɧɚɬ ɜɟɥɢɱɢɧ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɞɨɥɶ ɨɫɢ ɜɧɭɬɪɢ ɫɨɥɟɧɨɢɞɚ ɢ ɤɨɪɨɬɤɨɣ ɤɚɬɭɲɤɢ. ɉɪɨɚɧɚɥɢɡɢɪɨɜɚɬɶ ɨɩɵɬɧɵɟ ɪɟɡɭɥɶɬɚɬɵ
ɢ ɫɪɚɜɧɢɬɶ ɫ ɬɟɨɪɟɬɢɱɟɫɤɢɦɢ ɪɚɫɱɟɬɚɦɢ.
5.2. Ɍɟɨɪɟɬɢɱɟɫɤɨɟ ɜɜɟɞɟɧɢɟ*
ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɧɟɨɛɯɨɞɢɦɨ ɧɟ ɬɨɥɶɤɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɨɩɪɟɞɟɥɢɬɶ ɜɟɥɢɱɢɧɭ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ɧɚ ɨɫɢ ɫɨɥɟɧɨɢɞɚ ɢ ɤɨɪɨɬɤɨɣ
ɤɚɬɭɲɤɢ, ɧɨ ɢ ɫɞɟɥɚɬɶ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɪɚɫɱɟɬɵ, ɢɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɵ,
ɩɨɥɭɱɟɧɧɵɟ ɫɩɨɫɨɛɚɦɢ ɢɡɥɨɠɟɧɧɵɦɢ ɧɢɠɟ.
ɋɧɚɱɚɥɚ ɧɟɨɛɯɨɞɢɦɨ ɪɚɫɫɦɨɬɪɟɬɶ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɫɨɡɞɚɧɧɨɟ ɨɞɧɢɦ ɤɪɭɝɨɜɵɦ ɜɢɬɤɨɦ.
Ɂɚɞɚɱɚ ɮɨɪɦɭɥɢɪɭɟɬɫɹ ɬɚɤ: ɨɩɪɟɞɟɥɢɬɶ ɢɧɞɭɤɰɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨ-
G
ɜ ɩɪɨɢɡɜɨɥɶɧɨɣ ɬɨɱɤɟ Ɇ ɧɚ ɨɫɢ Z (ɧɚ ɪɚɫɫɬɨɹɧɢɢ z ɨɬ ɧɚɱɚɥɚ
ɥɹ
ɤɨɨɪɞɢɧɚɬ, ɤɨɬɨɪɨɟ ɧɚɯɨɞɢɬɫɹ ɜ ɰɟɧɬɪɟ ɜɢɬɤɚ – ɜ ɬɨɱɤɟ 0) ɨɞɧɨɝɨ
ɤɪɭɝɨɜɨɝɨ ɜɢɬɤɚ ɪɚɞɢɭɫɨɦ R, ɩɨ ɤɨɬɨɪɨɦɭ ɬɟɱɟɬ ɬɨɤ ɫɢɥɨɣ I (ɪɢɫ. 5.1).
Ⱦɥɹ ɷɬɨɝɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɡɚɤɨɧ
ɩɪɢɧɰɢɩ ɫɭɩɟɪɩɨɡɢɰɢɢ (3.9) – (3.10). (ɉɨɞɪɨɛɧɨɟ ɪɟɲɟɧɢɟ ɩɪɢɜɟɞɟ-
ɧɨ ɜ ɫɛɨɪɧɢɤɟ [5]).
Ȼɢɨ – ɋɚɜɚɪɚ – Ʌɚɩɥɚɫɚ (3.7) – (3.8) ɢ
–––––––––
*
Ɉɩɪɟɞɟɥɟɧɢɟ ɨɫɧɨɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɢɧɞɭɤɰɢɢ
ɜ ɥɚɛɨɪɚɬɨɪɧɨɣ ɪɚɛɨɬɟ ɗ.3 – (3.3), (3.8).
G
) ɞɚɧɨ
65
Ɋɢɫ. 5.1
ȼ
I
Ɂɞɟɫɶ ɢɫɩɨɥɶɡɭɟɦ ɩɨɥɭɱɟɧɧɵɣ ɪɟɡɭɥɶɬɚɬ: ɜɟɤɬɨɪ
ɧɚɩɪɚɜɥɟɧ
ɜɞɨɥɶ ɨɫɢ Z ɜɢɬɤɚ ɢ ɪɚɜɟɧ
G
P
0
B
2
2
IR
22
()
Rz
(5.1)
.
3
2
Ⱦɥɹ ɫɨɡɞɚɧɢɹ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ ɢɫɩɨɥɶɡɭɸɬɫɹ ɤɚɬɭɲɤɢ ɪɚɡɥɢɱɧɨɣ
ɞɥɢɧɵ, ɫ ɨɛɦɨɬɤɚɦɢ ɢɡ ɦɟɬɚɥɥɢɱɟɫɤɨɣ ɩɪɨɜɨɥɨɤɢ, ɩɨ ɤɨɬɨɪɵɦ ɩɪɨɩɭɫɤɚɸɬ ɬɨɤ. Ʉɚɬɭɲɤɚ ɫɨɫɬɨɢɬ ɢɡ N ɜɢɬɤɨɜ, ɩɥɨɬɧɨ ɩɪɢɥɟɝɚɸɳɢɯ
ɞɪɭɝ ɤ ɞɪɭɝɭ ɢ ɧɚɦɨɬɚɧɧɵɯ ɜ ɧɟɫɤɨɥɶɤɨ ɫɥɨɟɜ.
Ʉɚɬɭɲɤɚ ɫɱɢɬɚɟɬɫɹ ɤɨɪɨɬɤɨɣ, ɟɫɥɢ ɟɟ ɞɥɢɧɚ L ɦɚɥɚ ɢ ɜɵɩɨɥɧɹɟɬɫɹ
ɫɨɨɬɧɨɲɟɧɢɟ L << 2R, ɝɞɟ R – ɪɚɞɢɭɫ ɤɚɬɭɲɤɢ (ɪɢɫ. 5.2 ).
Ɋɢɫ. 5.2
ɉɪɢ ɷɬɨɦ ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɚ ɨɫɢ ɜɧɭɬɪɢ ɤɚɬɭɲɤɢ (ɨɫɶ Z) ɹɜɥɹɟɬɫɹ ɩɨɥɟɦ ɨɞɧɨɝɨ ɤɪɭɝɨɜɨɝɨ ɜɢɬɤɚ ɜɢɞɚ (5.1),
ɩɨ ɤɨɬɨɪɨɦɭ ɬɟɱɟɬ ɬɨɤ ɫɢɥɨɣ
66
ɤɨɪ.ɤɚɬ
, ɝɞɟ N – ɱɢɫɥɨ ɜɢɬɤɨɜ ɤɚ-
IN
ɬɭɲɤɢ. ɉɨɞɫɬɚɜɢɜ
R
I
ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ
ɜ ɮɨɪɦɭɥɭ (5.1), ɩɨɥɭɱɢɦ ɞɥɹ ɡɚɜɢɫɢɦɨɫɬɢ
I
ɤɨɪ.ɤɚɬ
B
ɨɬ ɤɨɨɪɞɢɧɚɬɵ z, ɤɨɬɨɪɚɹ ɨɬɫɱɢɬɵɜɚɟɬɫɹ
ɤɨɪ.ɤɚɬ
ɨɬ ɰɟɧɬɪɚ (ɬɨɱɤɚ 0) ɤɚɬɭɲɤɢ:
2
INR
P
B
ɤɨɪ.ɤɚɬ
0
22
2
zR
(5.2)
.
3
2
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɦɚɤɫɢɦɚɥɶɧɚɹ ɜɟɥɢɱɢɧɚ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ɛɭɞɟɬ
ɜ ɬɨɱɤɟ
:
0 z
P
max
ȼ
ɤɨɪ.ɤɚɬ
IN
0
,
2
ɚ ɩɪɢ ɢɡɦɟɧɟɧɢɢ (
zr ) ɜ ɨɛɟ ɫɬɨɪɨɧɵ ɨɬ ɰɟɧɬɪɚ
B ɛɵɫɬɪɨ ɭɛɵ-
ɤɨɪ.ɤɚɬ
ɜɚɟɬ ɞɨ ɧɭɥɹ. ɗɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ȼ ɨɬ z ɩɨɤɚɡɚɧɚ ɪɢɫ. 5.3.
Ɋɢɫ. 5.3
Ɂɚɦɟɬɢɦ, ɱɬɨ ɜ ɤɨɪɨɬɤɢɯ ɤɚɬɭɲɤɚɯ ɨɬɫɭɬɫɬɜɭɟɬ ɨɛɥɚɫɬɶ ɨɞɧɨɪɨɞ-
ɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ.
Ⱦɥɢɧɧɭɸ ɤɚɬɭɲɤɭ ɧɚɡɵɜɚɸɬ ɫɨɥɟɧɨɢɞɨɦ, ɟɫɥɢ ɜɵɩɨɥɧɹɟɬɫɹ ɫɨɨɬ-
ɧɨɲɟɧɢɟ
2LR!! (ɞɥɢɧɚ ɫɨɥɟɧɨɢɞɚ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɟɝɨ ɞɢɚɦɟɬɪɚ).
ɇɚɣɬɢ ɦɚɝɧɢɬɧɭɸ ɢɧɞɭɤɰɢɸ ɧɚ ɨɫɢ ɜɧɭɬɪɢ ɫɨɥɟɧɨɢɞɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɨɨɪɞɢɧɚɬɵ z ɦɨɠɧɨ, ɢɫɩɨɥɶɡɭɹ ɫɥɟɞɭɸɳɢɟ ɫɨɨɛɪɚɠɟɧɢɹ. ȼɵɛɟɪɟɦ ɛɟɫɤɨɧɟɱɧɨ ɬɨɧɤɢɣ (ɷɥɟɦɟɧɬɚɪɧɵɣ) ɩɨɹɫ dz (ɨɧ ɹɜɥɹɟɬɫɹ ɤɨ-
dI
ɪɨɬɤɨɣ ɤɚɬɭɲɤɨɣ), ɜ ɤɨɬɨɪɨɦ ɬɟɱɟɬ ɬɨɤ ɫɢɥɨɣ
,dI Indz
(5.3)
, ɩɪɢɱɟɦ
– ɫɢɥɚ ɬɨɤɚ, ɩɪɨɬɟɤɚɸɳɟɝɨ ɩɨ ɤɚɠɞɨɦɭ ɜɢɬɤɭ;
ɝɞɟ
67
N
n
– ɩɥɨɬɧɨɫɬɶ ɜɢɬɤɨɜ ɨɛɦɨɬɤɢ (ɱɢɫɥɨ ɜɢɬɤɨɜ, ɩɪɢɯɨɞɹɳɟɟɫɹ
L
ɧɚ ɟɞɢɧɢɰɭ ɞɥɢɧɵ ɫɨɥɟɧɨɢɞɚ), ɡɞɟɫɶ N – ɩɨɥɧɨɟ ɱɢɫɥɨ ɜɢɬɤɨɜ ɫɨɥɟ-
ɧɨɢɞɚ; L – ɞɥɢɧɚ ɫɨɥɟɧɨɢɞɚ;
ndz dN
– ɱɢɫɥɨ ɜɢɬɤɨɜ ɜ ɫɥɨɟ dz.
Ɋɢɫ. 5.4
ɉɨɥɟ ɧɚ ɨɫɢ ɫɨɥɟɧɨɢɞɚ ɜ ɩɪɨɢɡɜɨɥɶɧɨɣ ɬɨɱɤɟ M, ɫɨɡɞɚɜɚɟɦɨɟ ɷɥɟɦɟɧɬɚɪɧɵɦ ɩɨɹɫɨɦ dz, ɤɨɬɨɪɵɣ ɧɚɯɨɞɢɬɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ z ɨɬ ɧɟɟ,
ɦɨɠɧɨ ɧɚɣɬɢ ɩɨ ɮɨɪɦɭɥɟ (5.1), ɜ ɤɨɬɨɪɨɣ ɫɢɥɚ ɬɨɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ
ɜɵɪɚɠɟɧɢɹ (5.3):
2
InR dz
P
dB
0
22
2
Rz
.
3
2
Ʉɨɨɪɞɢɧɚɬɚ z ɨɬɫɱɢɬɵɜɚɟɬɫɹ ɨɬ ɥɟɜɨɝɨ ɬɨɪɰɚ ɜɧɭɬɪɢ ɫɨɥɟɧɨɢɞɚ
ɪɢɫ. 5.3 ɜɞɨɥɶ ɟɝɨ ɨɫɢ.
ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɨɫɥɟɞɧɟɝɨ ɜɵɪɚɠɟɧɢɹ ɞɚɟɬ ɫɥɟɞɭɸɳɭɸ ɡɚɜɢɫɢɦɨɫɬɶ:
§·
nI
P
0
ȼ
1
¨¸
¨¸
2
©¹
z
22
zR
. (5.4)
ɂɫɩɨɥɶɡɨɜɚɜ ɮɨɪɦɭɥɭ (5.4), ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɦɚɝɧɢɬɧɭɸ
ɢɧɞɭɤɰɢɸ ɜ ɨɫɨɛɵɯ ɬɨɱɤɚɯ ɧɚ ɨɫɢ Z ɫɨɥɟɧɨɢɞɚ ɩɪɢ ɭɫɥɨɜɢɢ, ɤɨɝɞɚ
2LR!! . ɉɪɢ ɷɬɨɦ ɜ ɰɟɧɬɪɟ ɫɨɥɟɧɨɢɞɚ, ɤɨɝɞɚ
L
ɫ ɭɱɟɬɨɦ ɭɫɥɨɜɢɹ
z
2
2LR!! , ɩɨɥɭɱɢɦ
68
B
I
ɢɥɢ
§·
¨¸
nI
P
0
¨¸
B
ɰ
1
¨¸
2
¨¸
¨¸
©¹
nI
P
0
P
ɰ 0
2
2
L
2
4
21
R
L
2.
2
L
(5.5)
nI
ȼ ɬɨɱɤɟ ɫ ɤɨɨɪɞɢɧɚɬɨɣ
ɰɢɢ ɜ ɬɨɪɰɟ ɫɨɥɟɧɨɢɞɚ ȼ
, ɤɨɬɨɪɚɹ ɜ ɞɜɚ ɪɚɡɚ ɦɟɧɶɲɟ, ɱɟɦ ɜ ɰɟɧɬɪɟ:
ɬ
ɩɨɥɭɱɢɦ ɜɟɥɢɱɢɧɭ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤ-
0 z
nȼP
0
ɬ
(5.6)
.
2
Ɂɚɦɟɬɢɦ, ɱɬɨ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɜɧɭɬɪɢ ɫɨɥɟɧɨɢɞɚ ɜɛɥɢɡɢ ɟɝɨ ɨɫɢ
ɹɜɥɹɟɬɫɹ ɨɞɧɨɪɨɞɧɵɦ ɜ ɫɪɟɞɧɟɣ ɱɚɫɬɢ. ȼ ɷɬɨɣ ɨɛɥɚɫɬɢ ɧɚɩɪɚɜɥɟɧɢɟ
ɢ ɜɟɥɢɱɢɧɚ ɜɟɤɬɨɪɚ ɢɧɞɭɤɰɢɢ (5.5) ɩɨɫɬɨɹɧɧɵ.
ɗɬɨɬ ɮɚɤɬ ɢɫɩɨɥɶɡɭɸɬ ɞɥɹ ɫɨɡɞɚɧɢɹ ɨɞɧɨɪɨɞɧɵɯ ɦɚɝɧɢɬɧɵɯ
ɩɨɥɟɣ, ɜɟɥɢɱɢɧɭ ɤɨɬɨɪɵɯ ɦɨɠɧɨ ɭɜɟɥɢɱɢɜɚɬɶ, ɩɨɦɟɳɚɹ ɜ ɫɨɥɟɧɨɢɞ
ɮɟɪɪɨɦɚɝɧɢɬɧɵɟ ɫɟɪɞɟɱɧɢɤɢ; ɧɚɦɚɬɵɜɚɹ ɜɢɬɤɢ ɜ ɧɟɫɤɨɥɶɤɨ ɫɥɨɟɜ;
ɢɫɩɨɥɶɡɭɹ ɩɪɨɜɨɥɨɤɭ ɢɡ ɫɜɟɪɯɩɪɨɜɨɞɹɳɢɯ ɦɚɬɟɪɢɚɥɨɜ
(ɩɪɢ ɷɬɨɦ
ɫɨɥɟɧɨɢɞ ɩɨɦɟɳɚɸɬ ɜ ɠɢɞɤɢɣ ɝɟɥɢɣ ɬɚɤ ɤɚɤ ɞɥɹ ɩɟɪɟɯɨɞɚ ɜ ɫɜɟɪɯɩɪɨɜɨɞɹɳɟɟ ɫɨɫɬɨɹɧɢɟ ɧɟɨɛɯɨɞɢɦɚ ɧɢɡɤɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ~ 4,2 Ʉ
(– 268,8 ɋ).
ɍ ɬɨɪɰɨɜ ɫɨɥɟɧɨɢɞɚ ɜɟɥɢɱɢɧɚ ɜɟɤɬɨɪɚ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ɞɨɫɬɚ-
ɬɨɱɧɨ ɪɟɡɤɨ ɭɦɟɧɶɲɚɟɬɫɹ, ɱɬɨ ɩɪɟɞɫɬɚɜɥɟɧɨ ɧɚ ɪɢɫ. 5.5.
Ɋɢɫ. 5.5
69
5.3. Ɉɩɢɫɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɭɫɬɚɧɨɜɤɢ
ȼ
ȼ
ȼ
Ɏɢɡɢɱɟɫɤɚɹ ɢɞɟɹ ɷɤɫɩɟɪɢɦɟɧɬɚ ɫɨɫɬɨɢɬ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɜɟɥɢɱɢɧ
ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ ɧɚ ɨɫɹɯ ɜɧɭɬɪɢ ɫɨɥɟɧɨɢɞɚ ɢ ɤɨɪɨɬɤɨɣ
ɤɚɬɭɲɤɢ ɩɨ ɢɡɦɟɪɟɧɢɹɦ ɗȾɋ ɢɧɞɭɤɰɢɢ, ɧɚɜɨɞɢɦɨɣ ɜ ɢɧɞɭɤɰɢɨɧɧɨɦ
ɞɚɬɱɢɤɟ. (Ɍɟɨɪɢɹ ɹɜɥɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ɢɡɥɨɠɟɧɚ
ɜ ɥɚɛɨɪɚɬɨɪɧɨɣ ɪɚɛɨɬɟ ɗ.6.)
ȿɫɥɢ ɧɟɛɨɥɶɲɭɸ ɤɚɬɭɲɤɭ, ɧɚɡɵɜɚɟɦɭɸ ɢɧɞɭɤɰɢɨɧɧɵɦ ɞɚɬɱɢɤɨɦ,
ɩɨɦɟɫɬɢɬɶ ɜ ɩɟɪɟɦɟɧɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ
ɜɢɬɤɨɜ ɛɵɥɚ ɛɵ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚ ɫɢɥɨɜɵɦ ɥɢɧɢɹɦ ɩɨɥɹ
G
K
( ɫos( ) 1BS
), ɬɨ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɤɚɠɞɵɣ ɜɢɬɨɤ ɩɥɨɳɚɞɶɸ Sɞ
ɛɭɞɟɬ ɩɪɨɧɢɡɵɜɚɬɶ ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ, ɪɚɜɧɵɣ
G
G
Ɏ (() ) () ɫos90 ( ) .
tS BtS ȼ tS q
ɞɞ ɞ
G
ɬɚɤ, ɱɬɨ ɩɥɨɫɤɨɫɬɶ ɟɝɨ
()
t
(5.7)
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ
ɡɚɤɨɧɨɦ Ɏɚɪɚɞɟɹ ɞɥɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ
ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɬɨɤɚ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɱɟɪɟɡ ɩɥɨɳɚɞɶ ɥɸɛɨɝɨ ɡɚɦɤ-
ɧɭɬɨɝɨ ɩɪɨɜɨɞɹɳɟɝɨ ɤɨɧɬɭɪɚ ɜ ɧɟɦ
ɧɚɜɨɞɢɬɫɹ ɗȾɋ ɢɧɞɭɤɰɢɢ
Ɏ.d
H
(5.8)
dt
ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɩɨɦɟɳɚɸɬ ɢɧɞɭɤɰɢɨɧɧɵɣ ɞɚɬɱɢɤ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɣ ɫɨɛɨɣ ɧɟɛɨɥɶɲɭɸ ɤɚɬɭɲɤɭ 1, ɨɛɦɨɬɤɚ ɤɨɬɨɪɨɣ
N
ɢɦɟɟɬ ɢɡɜɟɫɬɧɨɟ ɱɢɫɥɨ ɜɢɬɤɨɜ
(ɪɢɫ. 5.6).
ɞ
Ɋɢɫ. 5.6
Ʉɚɬɭɲɤɚ ɫɨɟɞɢɧɟɧɚ ɫ ɦɢɥɥɢɜɨɥɶɬɦɟɬɪɨɦ 3 ɢ ɤɪɟɩɢɬɫɹ ɧɚ ɤɨɧɰɟ
ɞɥɢɧɧɨɝɨ ɲɬɨɤɚ 2, ɩɨɡɜɨɥɹɸɳɟɝɨ ɩɨɦɟɳɚɬɶ ɞɚɬɱɢɤ ɜ ɨɩɪɟɞɟɥɟɧɧɭɸ
ɬɨɱɤɭ ɜɧɭɬɪɢ ɤɚɬɭɲɤɢ, ɫɨɡɞɚɸɳɟɣ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ
ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ (5.7), ɩɪɨɧɢɡɵɜɚɸɳɢɣ ɜɫɟ ɜɢɬɤɢ ɞɚɬɱɢɤɚ ɜ ɦɨɦɟɧɬ
ɜɪɟɦɟɧɢ t, ɪɚɜɟɧ
Ɏ () .
70
tNS
ɞɞɞ
(5.9)
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