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Файл:Физика электричество и магнетизм. Ч. 2. Лабораторный практикум
.pdf
Ɍɟɦɚ. Ⱦȼɂɀȿɇɂȿ ɁȺɊəɀȿɇɇɕɏ ɑȺɋɌɂɐ
X
ȿ
B
F
F
X
F
F
ȿ
B
ȿ
ȼ ɗɅȿɄɌɊɂɑȿɋɄɈɆ ɂ ɆȺȽɇɂɌɇɈɆ ɉɈɅəɏ
Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ ɗ.4
Ɉɩɪɟɞɟɥɟɧɢɟ ɭɞɟɥɶɧɨɝɨ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ
4.1. ɐɟɥɶ ɪɚɛɨɬɵ
ɂɡɭɱɢɜ ɬɟɨɪɟɬɢɱɟɫɤɢ ɨɫɨɛɟɧɧɨɫɬɢ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ
ɜ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɦ ɢ ɦɚɝɧɢɬɨɫɬɚɬɢɱɟɫɤɨɦ ɩɨɥɹɯ, ɨɩɪɟɞɟɥɢɬɶ
ɭɞɟɥɶɧɵɣ ɡɚɪɹɞ ɷɥɟɤɬɪɨɧɚ ɫ ɩɨɦɨɳɶɸ ɦɚɝɧɟɬɪɨɧɚ, ɩɨɦɟɳɟɧɧɨɝɨ
ɜ ɰɟɧɬɪ ɫɨɥɟɧɨɢɞɚ.
4.2. Ɍɟɨɪɟɬɢɱɟɫɤɨɟ ɜɜɟɞɟɧɢɟ
Ⱦɥɹ ɩɨɧɢɦɚɧɢɹ ɫɭɬɢ ɞɚɧɧɨɣ ɥɚɛɨɪɚɬɨɪɧɨɣ ɪɚɛɨɬɵ ɧɟɨɛɯɨɞɢɦɨ
ɪɚɫɫɦɨɬɪɟɬɶ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɚɫɩɟɤɬɵ ɨɫɨɛɟɧɧɨɫɬɟɣ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɫɬɚɰɢɨɧɚɪɧɵɯ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɢ ɦɚɝɧɢɬɧɨɦ ɩɨɥɹɯ.
ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɫɢɥɚ
ɇɚ ɱɚɫɬɢɰɭ ɦɚɫɫɨɣ m ɢ ɡɚɪɹɞɨɦ q, ɞɜɢɠɭɳɭɸɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ
ɜ ɨɛɥɚɫɬɢ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɝɞɟ ɢɦɟɟɬɫɹ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɫ ɧɚɩɪɹɠɟɧ-
ɧɨɫɬɶɸ
ɧɢɬɧɚɹ ɫɢɥɚ
G
ɢ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɫ ɢɧɞɭɤɰɢɟɣ
G
, ɪɚɜɧɚɹ
ɷ.ɦ
GG G
qE q B
ɷ.ɦ
G
ªº
¬¼
ɝɞɟ ɩɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ – ɤɭɥɨɧɨɜɫɤɚɹ ɫɢɥɚ
G
ɜɬɨɪɨɟ – ɫɢɥɚ
Ʌɨɪɟɧɰɚ
.
Ʌ
G
, ɞɟɣɫɬɜɭɟɬ ɷɥɟɤɬɪɨɦɚɝ-
, (4.1)
G
;
Ʉ
G
ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɜ ɧɟɤɨɬɨɪɨɣ ɨɛɥɚɫɬɢ ɩɪɨɫɬɪɚɧɫɬɜɚ ɫɭɳɟɫɬɜɭɸɬ
ɨɪɬɨɝɨɧɚɥɶɧɵɟ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɟ ɢ ɦɚɝɧɢɬɨɫɬɚɬɢɱɟɫɤɨɟ ɩɨɥɹ, ɬ.ɟ.
ɜ ɤɚɠɞɨɣ ɬɨɱɤɟ ɜɟɤɬɨɪɚ
ɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵ ɞɪɭɝ ɞɪɭɝɭ:
G
G
ɢ
ɧɟ ɦɟɧɹɸɬɫɹ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ
GG
ȼA
.
51
Ⱦɜɢɠɟɧɢɟ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɦ ɩɨɥɟ
`
E
`
X
X
x
X
E
ɉɪɢ ɞɜɢɠɟɧɢɢ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ
ɫɤɨɪɨɫɬɶɸ
G
XXX
000
^
;;0
xy
ɜ ɨɞɧɨɪɨɞɧɨɦ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɦ ɩɨɥɟ,
ɢɡ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ ɫɨ
0q !
G
0
Ynn
ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɤɨɬɨɪɨɝɨ
GG
0; ; 0FqE
^
ɱɚɫɬɢɰɵ ɜ ɜɟɤɬɨɪɧɨɦ ɜɢɞɟ
– 1-ɟ ɫɥɚɝɚɟɦɨɟ ɜ (4.1). ɉɪɢ ɷɬɨɦ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ
ma m qE
W
qE
a
W
m
Ɂɚɩɢɫɚɜ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɜ ɩɪɨɟɤɰɢɹɯ ɧɚ ɨɫɢ
d
x
m
;
0
dt
, ɧɚ ɧɟɟ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ
G
d
G
. Ɂɞɟɫɶ
dt
. (4.2)
const
XY:
d
X
y
mqE
dt
ɢ ɪɟɲɢɜ ɷɬɢ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɫ ɭɱɟɬɨɦ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ, ɩɨɥɭɱɢɦ
() ( )
XX
ti j
00
GG
qEt
m
. (4.3)
y
ȼɟɥɢɱɢɧɚ ɫɤɨɪɨɫɬɢ ɡɚɪɹɞɚ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɬɚɤ ɤɚɤ
qEt
2
XXX X X
xy x y
22
§·
00
¨¸
m
©¹
2
.
(4.4)
Ɍɨ ɟɫɬɶ ɩɨɥɨɠɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɚɹ ɱɚɫɬɢɰɚ ɭɫɤɨɪɹɟɬɫɹ ɜ ɷɥɟɤɬɪɨ-
ɫɬɚɬɢɱɟɫɤɨɦ ɩɨɥɟ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɞɥɹ ɭɫɤɨɪɟɧɢɹ ɷɥɟɤɬɪɨɧɚ (
ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ ɟɝɨ ɧɚɱɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɛɵɥɚ
G
np
ɧɚɩɪɚɜɥɟɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɜɟɤɬɨɪɭ ɧɚɩɪɹɠɟɧɧɨɫɬɢ (
X
0
0
q
) ɜ
e
G
).
ɂɫɩɨɥɶɡɭɹ ɨɩɪɟɞɟɥɟɧɢɟ ɦɝɧɨɜɟɧɧɨɣ ɫɤɨɪɨɫɬɢ ɢ ɜɵɪɚɠɟɧɢɟ (4.3),
ɧɚɯɨɞɢɦ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɩɨ ɨɫɹɦ
xt
dx dt
X
0
³³
00
x
y
ɢ
dy tdt dt
³³³
000
X ɢY:
tt
qE
m
X
0
y
ɢɥɢ
52
x
x
X
2
X
E
x
X
F
X
X
B
F
X
X
B
X
B
B
B
F
yt
0
t
ɢ
qEt
X
0
y
.
(4.5)
m
2
ɂɡ ɡɚɤɨɧɨɜ ɞɜɢɠɟɧɢɹ ɩɨ ɨɫɹɦ X ɢ Y, ɢɫɤɥɸɱɢɜ ɩɚɪɚɦɟɬɪ t, ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɬɪɚɟɤɬɨɪɢɢ:
X
§·
0
yx x
¨¸
X
0
©¹
§·
y
¨¸
x
2
©¹
qEt
m
X
2
.
2
0
x
ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɡɚɪɹɠɟɧɧɚɹ ɱɚɫɬɢɰɚ, ɭɫɤɨɪɹɹɫɶ ɜ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɦ ɩɨɥɟ, ɞɜɢɠɟɬɫɹ ɩɨ
ɛɭɞɟɬ ɜɨɡɪɚɫɬɚɬɶ, ɩɨɤɚ ɫɨɯɪɚɧɹɟɬɫɹ ɭɫɥɨɜɢɟ
ɫɤɨɟ ɞɜɢɠɟɧɢɟ, ɫ – ɫɤɨɪɨɫɬɶ ɫɜɟɬɚ). Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɜɥɟɬɟɜ ɜ ɨɞɧɨɪɨɞ-
ɧɨɟ ɷɥɟɤɬɪɢɱɟɫɤɨɟ ɩɨɥɟ ɜɞɨɥɶ ɫɢɥɨɜɨɣ ɥɢɧɢɢ (
ɩɚɪɚɛɨɥɢɱɟɫɤɨɣ ɬɪɚɟɤɬɨɪɢɢ. ȿɟ ɫɤɨɪɨɫɬɶ
(ɧɟɪɟɥɹɬɢɜɢɫɬ-
c
G
G
nn
X
), ɱɚɫɬɢɰɚ ɛɭ-
ɞɟɬ ɞɜɢɝɚɬɶɫɹ ɪɚɜɧɨɩɟɪɟɦɟɧɧɨ ɢ ɩɪɹɦɨɥɢɧɟɣɧɨ.
Ⱦɜɢɠɟɧɢɟ ɡɚɪɹɠɟɧɧɨɣ ɱɚɫɬɢɰɵ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ
ɉɭɫɬɶ ɱɚɫɬɢɰɚ ɦɚɫɫɨɣ
ɨɪɞɢɧɚɬ, ɢɦɟɹ ɫɤɨɪɨɫɬɶ
m ɢ ɡɚɪɹɞɨɦ
G
0000
;;
XXX
yz
ɞɜɢɠɟɬɫɹ ɢɡ ɧɚɱɚɥɚ ɤɨ-
0!q
ɜ ɩɨɫɬɨɹɧɧɨɦ ɨɞɧɨɪɨɞ-
G
ɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ, ɢɧɞɭɤɰɢɹ ɤɨɬɨɪɨɝɨ
ɢ ɧɚɩɪɚɜɥɟɧɚ
constȼ
ɜɞɨɥɶ ɨɫɢ Z. ɉɪɢ ɷɬɨɦ ɧɚ ɧɟɟ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ Ʌɨɪɟɧɰɚ:
Ʌ
GG
ªº
qB
X
¬¼
G
. (4.6)
Ɇɨɞɭɥɶ ɫɢɥɵ Ʌɨɪɟɧɰɚ ɪɚɜɟɧ:
sinFqB D
Ʌ
ɝɞɟ D – ɭɝɨɥ ɦɟɠɞɭ ɜɟɤɬɨɪɚɦɢ
G
ɢ
, (4.7)
G
.
G
ɇɚɩɪɚɜɥɟɧɢɟ
ɂɫɫɥɟɞɭɟɦ ɯɚɪɚɤɬɟɪ ɞɜɢɠɟɧɢɹ ɱɚɫɬɢɰɵ. Ⱦɥɹ ɷɬɨɝɨ ɭɞɨɛɧɨ ɜɟɤɬɨɪ ɫɤɨɪɨɫɬɢ
G
ɪɚɡɥɨɠɢɬɶ ɧɚ ɫɨɫɬɚɜɥɹɸɳɭɸ
0
, ɥɟɠɚɳɭɸ ɜ ɩɥɨɫɤɨɫɬɢ XY ɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɭɸ ɜɟɤɬɨɪɭ
A
1. Ɉɱɟɜɢɞɧɨ, ɡɚɪɹɞ, ɜɥɟɬɚɸɳɢɣ ɜɞɨɥɶ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɤɨ-
nn
XX
ɝɞɚ
G
, ɬɚɤ ɤɚɤ
Ʌ
0z
,,
ɨɩɪɟɞɟɥɹɸɬ ɫ ɩɨɦɨɳɶɸ ɩɪɚɜɢɥɚ «ɛɭɪɚɜɱɢɤɚ» >5].
Ʌ
X
ɜɞɨɥɶ ɜɟɤɬɨɪɚ 0,
0z,,
G
ɢɥɢ
sin 0D
np
XX
,,
. ɉɪɢ ɷɬɨɦ ɟɝɨ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɡɚɩɢɲɟɬɫɹ
G
0z
), ɧɟ ɢɫɩɵɬɵɜɚɟɬ ɞɟɣɫɬɜɢɹ ɫɢɥɵ
G
Znn
ɢ
G
.
53
d
X
X
X
X
ȼ
X
ȼ
F
X
X
R
X
X
X
X
ɬɚɤ:
ɧɵɯ ɭɫɥɨɜɢɣ
z
. Ɉɬɫɸɞɚ ɞɥɹ ɫɤɨɪɨɫɬɢ ɢɦɟɟɦ
0
m
dt
constz X. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɞɜɢɠɟɧɢɟ
0
() const.
t
z
ɂɡ ɧɚɱɚɥɶ-
ɪɚɜɧɨɦɟɪɧɨɟ ɢ ɩɪɹɦɨɥɢɧɟɣɧɨɟ ɜɞɨɥɶ ɨɫɢ Z ɢ ɢɡ ɭɪɚɜɧɟɧɢɹ
ɩɨɥɭɱɢɦ ɟɟ ɡɚɤɨɧ ɞɜɢɠɟɧɢɹ:
t
()
zt dt t
00
X
zz
³
0
. (4.8)
dz
dt
0z
2. ɉɭɫɬɶ ɱɚɫɬɢɰɚ ɜɥɟɬɚɟɬ ɜ ɨɛɥɚɫɬɶ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɝɞɟ ɫɭɳɟɫɬɜɭɟɬ
ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ
ɫ ɜɟɤɬɨɪɨɦ
G
sin 90
qB F qB q
G
ɢ ɟɟ ɫɤɨɪɨɫɬɶ
G
GG
X
ɫɨɫɬɚɜɥɹɟɬ ɩɪɹɦɨɣ ɭɝɨɥ
A
. ɉɪɢ ɷɬɨɦ ɫɢɥɚ Ʌɨɪɟɧɰɚ ɪɚɜɧɚ
. ɗɬɚ ɫɢɥɚ (ɩɨ ɩɪɚɜɢɥɭ ɜɟɤɬɨɪɧɨɝɨ ɩɪɨ-
X
ɢɡɜɟɞɟɧɢɹ (4.1)) ɜɫɟɝɞɚ ɧɚɩɪɚɜɥɟɧɚ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ ɜɟɤɬɨɪɭ ɫɤɨ-
2
ɪɨɫɬɢ ɢ ɫɨɨɛɳɚɟɬ ɟɣ ɧɨɪɦɚɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ
aR
n
. ɍɪɚɜɧɟɧɢɟ
ɞɜɢɠɟɧɢɹ ɛɭɞɟɬ
2
ɜɟɥɢɱɢɧɚ
X
mqB
ɚ ɧɟ ɦɟɧɹɟɬɫɹ ɜ ɩɪɨɰɟɫɫɟ ɞɜɢɠɟɧɢɹ. Ɍɚɤɨɟ ɞɜɢɠɟɧɢɟ
n
, (4.9)
ɫ ɩɨɫɬɨɹɧɧɵɦ ɩɨ ɜɟɥɢɱɢɧɟ ɭɫɤɨɪɟɧɢɟɦ, ɩɪɢ ɤɨɬɨɪɨɦ ɦɟɧɹɟɬɫɹ ɬɨɥɶɤɨ
ɧɚɩɪɚɜɥɟɧɢɟ ɫɤɨɪɨɫɬɢ, ɧɨ ɧɟ ɟɟ ɜɟɥɢɱɢɧɚ, ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɪɚɜɧɨɦɟɪɧɨɟ ɞɜɢɠɟɧɢɟ ɩɨ ɨɤɪɭɠɧɨɫɬɢ, ɪɚɞɢɭɫ ɤɨɬɨɪɨɣ
q
R
, (4.10)
mB
q
ɝɞɟ
ɧɚɡɵɜɚɟɬɫɹ ɭɞɟɥɶɧɵɦ ɡɚɪɹɞɨɦ ɱɚɫɬɢɰɵ.
qm
ɭɞ
ɂɡ (4.10) ɫɥɟɞɭɟɬ, ɱɬɨ ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ R ɡɚɜɢɫɢɬ: ɚ) ɨɬ
ɫɤɨɪɨɫɬɢ
– ɱɟɦ ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɶ, ɬɟɦ ɛɨɥɶɲɟ ɪɚɞɢɭɫ ɬɪɚɟɤɬɨɪɢɢ;
ɛ) ɨɬ ɜɟɥɢɱɢɧɵ ȼ – ɱɟɦ ɛɨɥɶɲɟ ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ, ɬɟɦ ɦɟɧɶɲɟ ɪɚɞɢɭɫ; ɜ)
ɨɬ ɭɞɟɥɶɧɨɝɨ ɡɚɪɹɞɚ ɱɚɫɬɢɰɵ:
ɪɟɞɟɥɢɬɶ, ɡɧɚɹ
, ȼ ɢ R. ɉɟɪɢɨɞ ɜɪɚɳɟɧɢɹ ɱɚɫɬɢɰɵ:
q
, ɤɨɬɨɪɵɣ ɦɨɠɧɨ ɨɩ-
q
ɭɞ
m
54
R
T
X
B
X
X
B
B
X
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɫɤɨɪɨɫɬɶ
ɟɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
G
ɭɝɨɥ D, ɨɬɥɢɱɧɵɣ ɨɬ ɩɪɹɦɨɝɨ, ɞɜɢɠɟɧɢɟ ɱɚɫ-
22
SS
X
m
.
qB
G
ɱɚɫɬɢɰɵ ɫɨɫɬɚɜɥɹɟɬ ɫ ɢɧɞɭɤɰɢ-
ɬɢɰɵ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɫɭɦɦɭ ɞɜɢɠɟɧɢɹ ɪɚɜɧɨɦɟɪɧɨɝɨ ɜɞɨɥɶ
cos
D
ɨɫɢ Z ɫɨ ɫɤɨɪɨɫɬɶɸ
ɧɨɫɬɢ (ɫɨ ɫɤɨɪɨɫɬɶɸ
G
ɥɹɪɧɚ ɜɟɤɬɨɪɭ
.
X
,,
A
ȼ ɪɟɡɭɥɶɬɚɬɟ ɫɥɨɠɟɧɢɹ ɷɬɢɯ ɩɪɨɫɬɵɯ ɞɜɢɠɟɧɢɣ ɱɚɫɬɢɰɚ ɞɜɢɠɟɬɫɹ
ɩɨ ɫɩɢɪɚɥɢ ɜɞɨɥɶ ɧɚɩɪɚɜɥɟɧɢɹ
ɢ ɞɜɢɠɟɧɢɹ ɪɚɜɧɨɦɟɪɧɨɝɨ ɩɨ ɨɤɪɭɠ-
sin
D
X
), ɩɥɨɫɤɨɫɬɶ ɤɨɬɨɪɨɣ ɩɟɪɩɟɧɞɢɤɭ-
G
(ɪɢɫ. 4.1).
Ɋɢɫ. 4.1
ɒɚɝ ɬɚɤɨɣ ɫɩɢɪɚɥɢ
X
hT
S
2
,,
m
X
R
m
sin
D
, ɚ ɪɚɞɢɭɫ ɫɩɢɪɚɥɢ ɢɡ (4.10):
qB
D
.
cos
qB
1. Ɍɟɨɪɟɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ
q
§·
e
¨¸
m
©¹
1, 6 02 1 0 Ʉɥ
9,108 10 ɤɝ
ɬɟɨɪ
ɭɞɟɥɶɧɨɝɨ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ ɬɚɤɨɜɨ:
19
31
= 1,7610
11
Ʉɥ/ɤɝ.
2. Ȼɥɚɝɨɞɚɪɹ ɫɭɳɟɫɬɜɨɜɚɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɨɤɪɭɝ Ɂɟɦɥɢ
ɛɨɥɶɲɢɧɫɬɜɨ ɤɨɫɦɢɱɟɫɤɢɯ ɫɦɟɪɬɨɧɨɫɧɵɯ ɪɚɞɢɨɚɤɬɢɜɧɵɯ ɱɚɫɬɢɰ
(ɩɪɨɬɨɧɨɜ, ɷɥɟɤɬɪɨɧɨɜ, ɚɥɶɮɚ-ɱɚɫɬɢɰ) ɧɟ ɞɨɫɬɢɝɚɸɬ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚ-
ɲɟɣ ɩɥɚɧɟɬɵ. Ɉɧɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɫɜɨɟɝɨ ɞɜɢɠɟɧɢɹ
ɥɢɛɨ ɭɯɨɞɹɬ ɩɨ ɫɩɢɪɚɥɢ ɜ ɤɨɫɦɢɱɟɫɤɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ, ɥɢɛɨ ɨɛɪɚɡɭɸɬ
55
ɬɚɤ ɧɚɡɵɜɚɟɦɵɟ ɜɧɭɬɪɟɧɧɢɣ ɢ ɜɧɟɲɧɢɣ ɪɚɞɢɚɰɢɨɧɧɵɟ ɩɨɹɫɚ ɧɚ ɜɵ-
B
ɫɨɬɚɯ ~1000 ɤɦ ɢ (20 000…30 000) ɤɦ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ Ɂɟɦɥɢ, ɫɨɜɟɪɲɚɹ ɞɜɢɠɟɧɢɹ ɩɨ ɨɤɪɭɠɧɨɫɬɹɦ ɜɨɤɪɭɝ Ɂɟɦɥɢ.
4.3. Ɉɩɢɫɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɭɫɬɚɧɨɜɤɢ
ɋɭɬɶ ɷɤɫɩɟɪɢɦɟɧɬɚ ɫɨɫɬɨɢɬ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɭɞɟɥɶɧɨɝɨ ɡɚɪɹɞɚ ɷɥɟɤ-
ɬɪɨɧɚ
ɞɭ ɜ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɫɨɥɟɧɨɢɞɚ. ɉɨɥɭɱɢɜ ɡɚɜɢɫɢ-
ɦɨɫɬɶ ɚɧɨɞɧɨɝɨ ɬɨɤɚ
ɯɨɞɹɬ ɜɟɥɢɱɢɧɭ ɤɪɢɬɢɱɟɫɤɨɣ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ
ɢɫɩɨɥɶɡɭɹ ɪɚɫɱɟɬɧɭɸ ɮɨɪɦɭɥɭ, – ɭɞɟɥɶɧɵɣ ɡɚɪɹɞ ɷɥɟɤɬɪɨɧɚ
ɞɢɨɞ) ɫ ɤɨɚɤɫɢɚɥɶɧɵɦɢ (ɢɦɟɸɳɢɦɢ ɨɞɧɭ ɨɫɶ) ɷɥɟɤɬɪɨɞɚɦɢ: ɰɢɥɢɧɞɪɢɱɟɫɤɢɦ ɤɚɬɨɞɨɦ 1 (ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɷɥɟɤɬɪɨɞ) ɢ ɰɢɥɢɧɞɪɢɱɟɫɤɢɦ
ɚɧɨɞɨɦ 2 (ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɷɥɟɤɬɪɨɞ) (ɪɢɫ. 4.2).
q
, ɜɵɥɟɬɚɸɳɟɝɨ ɢɡ ɤɚɬɨɞɚ ɦɚɝɧɟɬɪɨɧɚ ɢ ɞɜɢɠɭɳɟɝɨɫɹ ɤ ɚɧɨ-
ɭɞ
I ɦɚɝɧɟɬɪɨɧɚ ɨɬ ɫɢɥɵ ɬɨɤɚ cI ɜ ɫɨɥɟɧɨɢɞɟ, ɧɚ-
a
ɩɨɥɹ, ɚ ɡɚɬɟɦ,
ɤɪ
q
½
e
.
®¾
m
¯¿
Ɇɚɝɧɟɬɪɨɧ – ɞɜɭɯɷɥɟɤɬɪɨɞɧɚɹ ɷɥɟɤɬɪɨɧɧɚɹ ɥɚɦɩɚ (ɜɚɤɭɭɦɧɵɣ
Ɋɢɫ. 4.2
Ɋɚɞɢɭɫ ɤɚɬɨɞɚ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ ɪɚɞɢɭɫɚ ɚɧɨɞɚ:
rr . ȼ ɪɚɫɱɟɬɚɯ
ɤ a
ɪɚɡɦɟɪɚɦɢ ɤɚɬɨɞɚ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. Ɇɚɝɧɟɬɪɨɧ ɩɨɦɟɳɟɧ ɜ ɫɪɟɞɧɸɸ ɱɚɫɬɶ ɫɨɥɟɧɨɢɞɚ 3, ɨɫɶ ɤɨɬɨɪɨɝɨ ɫɨɜɩɚɞɚɟɬ ɫ ɤɚɬɨɞɨɦ 1. ɋɨɥɟɧɨɢɞ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɞɥɢɧɧɭɸ ɤɚɬɭɲɤɭ, ɧɚ ɤɨɬɨɪɭɸ ɧɚɦɨɬɚɧɚ ɦɟɞɧɚɹ ɩɪɨɜɨɥɨɤɚ, ɫɨɟɞɢɧɟɧɧɚɹ ɫ ɢɫɬɨɱɧɢɤɨɦ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ
56
U . ȿɫɥɢ ɞɥɢɧɚ ɫɨɥɟɧɨɢɞɚ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɟɝɨ ɞɢɚɦɟɬɪɚ
L
ȼ
B
N
E
ȿ
F
ɫ
ɩɪɢ ɩɪɨɬɟɤɚɧɢɢ ɩɨ ɜɢɬɤɚɦ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɫɢɥɨɣ
I ɜ ɫɪɟɞɧɟɣ ɟɝɨ
ɫ
ɱɚɫɬɢ ɜɨɡɧɢɤɚɟɬ ɨɞɧɨɪɨɞɧɨɟ ɫɬɚɰɢɨɧɚɪɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɧɚɩɪɚɜɥɟɧɧɨɟ ɜɞɨɥɶ ɨɫɢ ɫɨɥɟɧɨɢɞɚ, ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ ɤɨɬɨɪɨɝɨ
D!!
ɫɫ
G
ɢɦɟɟɬ
ɜɟɥɢɱɢɧɭ >1–3@:
P
N
0 ɫ
,
I
ɫ
L
ɫ
(4.11)
,
ɝɞɟ
– ɱɢɫɥɨ ɜɢɬɤɨɜ ɫɨɥɟɧɨɢɞɚ;
c
ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ
I
– ɫɢɥɚ ɬɨɤɚ;
ɫ
ɭɫɬɚɧɨɜɤɢ ɞɚɧɚ ɧɚ ɪɢɫ. 4.3.
L
– ɞɥɢɧɚ ɫɨɥɟɧɨɢɞɚ.
c
Ɋɢɫ. 4.3
ɉɪɢ ɩɨɞɤɥɸɱɟɧɢɢ ɤ ɤɚɬɨɞɭ 1 ɛɚɬɚɪɟɢ (ɧɚɩɪɹɠɟɧɢɟɦ
U
) ɩɪɨɢɫɯɨ-
ɤ
ɞɢɬ ɟɝɨ ɧɚɝɪɟɜɚɧɢɟ, ɱɬɨ ɜɵɡɵɜɚɟɬ ɹɜɥɟɧɢɟ ɬɟɪɦɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ, ɩɪɢ ɤɨɬɨɪɨɦ ɱɚɫɬɶ ɫɜɨɛɨɞɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɩɨɤɢɞɚɟɬ ɦɟɬɚɥɥɢɱɟɫɤɢɣ ɤɚɬɨɞ ɢ ɩɨɩɚɞɚɟɬ ɜ ɩɪɨɫɬɪɚɧɫɬɜɨ ɦɟɠɞɭ ɤɚɬɨɞɨɦ 1 ɢ ɚɧɨɞɨɦ 2.
ɂɫɬɨɱɧɢɤ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ
ɚɧɨɞɨɦ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɟ ɩɨɥɟ ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ
ɩɪɚɜɥɟɧ ɩɨ ɪɚɞɢɭɫɭ ɨɬ ɚɧɨɞɚ ɤ ɤɚɬɨɞɭ ɢ
ɧɨɢɞɚ. ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜ ɫɨɥɟɧɨɢɞɟ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ (
G
ɞɭɤɰɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
ɧɵ ɞɟɣɫɬɜɭɟɬ ɬɨɥɶɤɨ ɤɭɥɨɧɨɜɫɤɚɹ ɫɢɥɚ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɨɬ ɤɚɬɨɞɚ
ɤ ɚɧɨɞɭ:
GG
qE
ɤ e
. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɬɨɣ ɫɢɥɵ ɷɥɟɤɬɪɨɧɵ ɞɜɢɠɭɬɫɹ ɤ
0ȼ
U ɫɨɡɞɚɟɬ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ
ɚ
G
. ȼɟɤɬɨɪ
G
ɧɚ-
ɩɟɪɩɟɧɞɢɤɭɥɹɪɟɧ ɨɫɢ ɫɨɥɟ-
I = 0) ɢɧ-
c
ɢ ɧɚ ɜɵɥɟɬɚɸɳɢɟ ɢɡ ɤɚɬɨɞɚ ɷɥɟɤɬɪɨ-
57
ɚɧɨɞɭ ɫ ɭɫɤɨɪɟɧɢɟɦ (4.2) ɢ ɩɪɨɣɞɹ ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ
X
X
X
X
F
X
B
ɪɟɬɚɸɬ ɫɤɨɪɨɫɬɶ
, ɤɨɬɨɪɭɸ ɦɨɠɧɨ ɧɚɣɬɢ ɢɡ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ
U , ɩɪɢɨɛ-
ɚ
ɷɧɟɪɝɢɢ
2
m
qU
e
a
ɇɚɩɪɢɦɟɪ, ɷɥɟɤɬɪɨɧ, ɩɪɨɯɨɞɹ ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ
q
§·
ɩɪɢɨɛɪɟɬɚɟɬ ɫɤɨɪɨɫɬɶ
X
e
2
¨¸
m
©¹
(4.12)
.
2
U
~ 100 ȼ,
ɚ
U
~ 6105 ɦ/ɫ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɜ ɡɚ-
ɚ
ɤɨɧɟ (4.12) ɫɱɢɬɚɸɬ, ɱɬɨ ɷɥɟɤɬɪɨɧɵ ɜɵɯɨɞɹɬ ɢɡ ɤɚɬɨɞɚ ɫɨ ɫɤɨɪɨɫɬɹɦɢ,
0
ɛɥɢɡɤɢɦɢ ɤ
. ɗɬɨ ɞɨɩɭɳɟɧɢɟ ɜɨɡɦɨɠɧɨ, ɬɚɤ ɤɚɤ ɫɪɟɞɧɹɹ ɬɟɩ-
0
ɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜ ɦɟɬɚɥɥɚɯ ɩɪɢ Ɍ = 300 Ʉ
ɩɨɱɬɢ ɜ 10 ɪɚɡ ɦɟɧɶɲɟ, ɱɟɦ ɫɤɨɪɨɫɬɶ
ɉɪɢ ɜɤɥɸɱɟɧɢɢ ɢɫɬɨɱɧɢɤɚ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ
ɬɨɤ, ɜɨɡɧɢɤɚɸɳɢɣ ɜ ɫɨɥɟɧɨɢɞɟ, ɫɨɡɞɚɟɬ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ. ɉɪɢɱɟɦ ɜɟɤɬɨɪ
ɫɢɥɵ Ʌɨɪɟɧɰɚ
G
ɩɟɪɩɟɧɞɢɤɭɥɹɪɟɧ ɜɟɤɬɨɪɭ
Ʌ
.
U
(ɫɦ. ɪɢɫ. 4.3)
ɫ
G
. ɍɫɤɨɪɟɧɢɟ, ɜɵɡɜɚɧɧɨɟ
ɫɢɥɨɣ Ʌɨɪɟɧɰɚ, ɹɜɥɹɟɬɫɹ ɧɨɪɦɚɥɶɧɵɦ (4.9). ɉɪɢɦɟɪɧɵɣ ɜɢɞ ɬɪɚɟɤɬɨɪɢɣ
ɷɥɟɤɬɪɨɧɨɜ ɩɪɢ
0
Bdd ɩɨɤɚɡɚɧ ɧɚ ɪɢɫ. 4.4.
c ɤɪ
Ɋɢɫ. 4.4
ȿɫɥɢ
ɬɪɚɟɤɬɨɪɢɹ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɪɹɦɭɸ ɥɢɧɢɸ (ɬɪɚ-
0 ȼ
ɟɤɬɨɪɢɹ a ɧɚ ɪɢɫ. 4.4), ɬɚɤ ɤɚɤ ɩɪɢ ɷɬɨɦ ɷɥɟɤɬɪɨɧɵ ɞɜɢɠɭɬɫɹ ɜɞɨɥɶ
58
ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɩɪɹɦɨɥɢɧɟɣɧɨ ɢ ɭɫɤɨɪɟɧɧɨ
B
ȼ
ȼ
ȼ
I
ȼ
(4.2) – (4.9).
ȿɫɥɢ ȼ > 0 ɫɢɥɚ Ʌɨɪɟɧɰɚ ɢɫɤɪɢɜɥɹɟɬ ɬɪɚɟɤɬɨɪɢɸ ɷɥɟɤɬɪɨɧɨɜ
ɬɟɦ ɛɨɥɶɲɟ, ɱɟɦ ɛɨɥɶɲɟ ɜɟɥɢɱɢɧɚ ȼ (4.10) ɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɬɪɚɟɤɬɨɪɢɢ ɦɟɧɶɲɟ. Ⱦɥɹ ɭɜɟɥɢɱɟɧɢɹ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ (4.11) ɭɜɟɥɢɱɢɜɚɸɬ ɫɢɥɭ ɬɨɤɚ
I ɜ ɫɨɥɟɧɨɢɞɟ c ɩɨɦɨɳɶɸ
c
ɩɟɪɟɦɟɧɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ 7 (ɫɦ. ɪɢɫ. 4.3). ɇɚɞɨ ɩɨɦɧɢɬɶ, ɱɬɨ
ɩɪɢ ɨɞɧɨɦ ɢ ɬɨɦ ɠɟ ɡɧɚɱɟɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ȼ, ɪɚɞɢɭɫ ɤɪɢɜɢɡɧɵ ɬɪɚɟɤɬɨɪɢɢ ɛɭɞɟɬ ɦɟɧɶɲɟ ɭ ɬɟɯ ɷɥɟɤɬɪɨɧɨɜ, ɤɨɬɨɪɵɟ ɞɜɢɠɭɬɫɹ
ɫ ɦɟɧɶɲɢɦɢ ɫɤɨɪɨɫɬɹɦɢ (4.10).
ȼ ɫɥɚɛɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ, ɩɨɤɚ ɜɟɥɢɱɢɧɚ
ɤɪɢɬɢɱɟɫɤɨɝɨ ɡɧɚɱɟɧɢɹ
, ɛɨɥɶɲɚɹ ɱɚɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɞɨɫɬɢɝɚɟɬ
ɤɪ
ɦɟɧɶɲɟ ɧɟɤɨɬɨɪɨɝɨ
ɚɧɨɞɚ (ɤɪɢɜɵɟ b, d ɧɚ ɪɢɫ. 4.4) ɢ ɩɪɢ ɷɬɨɦ ɚɦɩɟɪɦɟɬɪ 6 (ɫɦ. ɪɢɫ. 4.3),
ɜɤɥɸɱɟɧɧɵɣ ɜ ɚɧɨɞɧɭɸ ɰɟɩɶ, ɪɟɝɢɫɬɪɢɪɭɟɬ ɚɧɨɞɧɵɣ ɬɨɤ
ɱɢɧɟ, ɛɥɢɡɤɢɣ ɤ ɦɚɤɫɢɦɚɥɶɧɨɦɭ
I
(ɧɚɱɚɥɶɧɨɦɭ ɩɪɢ
max
I ɩɨ ɜɟɥɢ-
a
).
0ȼ
ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɜɟɥɢɱɟɧɢɢ ɫɢɥɵ ɬɨɤɚ ɜ ɫɨɥɟɧɨɢɞɟ, ɤɨɝɞɚ
ȼ
, ɦɟɞɥɟɧɧɵɟ ɷɥɟɤɬɪɨɧɵ ɩɟɪɟɫɬɚɸɬ ɩɨɩɚɞɚɬɶ ɧɚ ɚɧɨɞ (ɤɪɢɜɚɹ
ɤɪ
k ɧɚ ɪɢɫ. 4.4) ɢ ɫɨɜɟɪɲɚɸɬ ɫɥɨɠɧɨɟ ɞɜɢɠɟɧɢɟ ɜɧɭɬɪɢ ɦɚɝɧɟɬɪɨɧɚ.
ɑɟɦ ɛɨɥɶɲɟ ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ, ɬɟɦ ɛɨɥɶɲɟɟ ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɩɟɪɟɫɬɚɟɬ ɛɵɬɶ ɧɨɫɢɬɟɥɹɦɢ ɚɧɨɞɧɨɝɨ ɬɨɤɚ. ɗɥɟɤɬɪɨɧɵ ɫɨɡɞɚɸɬ ɜ ɥɚɦɩɟ
ɨɛɴɟɦɧɵɣ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɡɚɪɹɞ, ɤɨɬɨɪɵɣ ɞɜɢɠɟɬɫɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ
ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ, ɢ ɩɪɢ ɷɬɨɦ ɚɧɨɞɧɵɣ ɬɨɤ
0I
ɭɦɟɧɶɲɚɟɬɫɹ:
.
a
ɞɨɫɬɚɬɨɱɧɨ ɛɵɫɬɪɨ
ɇɚɞɨ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɟɫɥɢ ɛɵ ɜɫɟ ɷɥɟɤɬɪɨɧɵ ɩɨɤɢɞɚɥɢ ɤɚɬɨɞ ɫ ɨɞɢɧɚɤɨɜɵɦɢ ɫɤɨɪɨɫɬɹɦɢ,
ɬɨ ɩɪɢ
ɛɵ ɧɚ ɚɧɨɞ ɜɩɥɨɬɶ ɞɨ ɡɧɚɱɟɧɢɹ
B
(
ɤɪ
ɫɫ(ɤɪ)
B (
II ), ɩɪɢ ɤɨɬɨɪɨɦ ɜɫɟ
ɤɪ
ɫɫ(ɤɪ)
) ɜɫɟ ɨɧɢ ɩɨɩɚɞɚɥɢ
I
ɜɵɥɟɬɟɜɲɢɟ ɷɥɟɤɬɪɨɧɵ ɞɪɭɠɧɨ ɩɨɜɨɪɚɱɢɜɚɥɢ ɛɵ ɨɬ ɚɧɨɞɚ, ɫɤɨɥɶɡɧɭɜ
ɜɞɨɥɶ ɧɟɝɨ, ɢ ɚɧɨɞɧɵɣ ɬɨɤ ɞɨɥɠɟɧ ɛɵɥ ɛɵ ɪɟɡɤɨ ɭɩɚɫɬɶ ɨɬ ɡɧɚɱɟɧɢɹ
I ɞɨ ɧɭɥɹ
ɚ(max)
ɜ ɫɨɥɟɧɨɢɞɟ ɢɦɟɥɚ ɛɵ ɜɢɞ, ɤɨɬɨɪɵɣ ɩɪɟɞɫɬɚɜɥɟɧ
ɜɨɣ
ɧɚ ɪɢɫ. 4.5.
0I . ɉɪɢ ɷɬɨɦ ɡɚɜɢɫɢɦɨɫɬɶ ɚɧɨɞɧɨɝɨ ɬɨɤɚ ɨɬ ɬɨɤɚ
a
ɩɭɧɤɬɢɪɧɨɣ ɤɪɢ-
59
B
ȼ
B
R
X
Ɋɢɫ. 4.5
ȼ ɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢ ɷɥɟɤɬɪɨɧɵ, ɢɫɩɭɫɤɚɟɦɵɟ ɧɚɝɪɟɬɵɦ ɤɚɬɨɞɨɦ,
ɨɛɥɚɞɚɸɬ ɪɚɡɥɢɱɧɵɦɢ ɧɚɱɚɥɶɧɵɦɢ ɫɤɨɪɨɫɬɹɦɢ. ɉɨɷɬɨɦɭ ɞɥɹ ɪɚɡɧɵɯ
ɷɥɟɤɬɪɨɧɨɜ ɤɪɢɬɢɱɟɫɤɢɟ ɭɫɥɨɜɢɹ ɞɨɫɬɢɝɚɸɬɫɹ ɩɪɢ ɪɚɡɧɵɯ ɡɧɚɱɟɧɢɹɯ
I
(
ɤɪ
). Ɂɚɜɢɫɢɦɨɫɬɶ
ɫ(ɤɪ)
ɪɢɫ. 4.5 ɩɨɤɚɡɚɧɨ
ɫɩɥɨɲɧɨɣ ɤɪɢɜɨɣ.
I
ɚ
ɨɬ
I
ɬɟɪɹɟɬ ɫɬɭɩɟɧɱɚɬɵɣ ɜɢɞ ɢ ɷɬɨ ɧɚ
ɫ
Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɪɚɫɱɟɬɧɨɣ ɮɨɪɦɭɥɵ, ɧɟɨɛɯɨɞɢɦɨ:
1) ɭɱɟɫɬɶ, ɱɬɨ ɪɚɞɢɭɫ ɤɚɬɨɞɚ ɝɨɪɚɡɞɨ ɦɟɧɶɲɟ ɪɚɞɢɭɫɚ ɚɧɨɞɚ
rr
(
ɤ a
), ɩɨɷɬɨɦɭ ɪɚɞɢɭɫ ɬɪɚɟɤɬɨɪɢɢ ɷɥɟɤɬɪɨɧɨɜ ɩɪɢ
ɫɱɢɬɚɬɶ ɪɚɜɧɵɦ
r
a
.
R
ȼ
ɤɪ
ɦɨɠɧɨ
2
ɇɚ ɪɢɫ. 4.4 ɷɬɨɦɭ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɤɪɢɜɚɹ k.
2) ɡɚɩɢɫɚɬɶ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ (4.9) ɷɥɟɤɬɪɨɧɚ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨ-
ɥɟ, ɤɨɝɞɚ
G
G
X
:
A
ɤɪ
2
qB m
X
e
ɤɪ
ɢɥɢ
60
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