Ɏɟɞɟɪɚɥɶɧɨɟ ɚɝɟɧɬɫɬɜɨ ɩɨ Ɉɛɪɚɡɨɜɚɧɢɸ Ƚɨɫɭɞɚɪɫɬɜɟɧɧɨɟ ɨɛɪɚɡɨɜɚɬɟɥɶɧɨɟ ɭɱɪɟɠɞɟɧɢɟ ɜɵɫɲɟɝɨ ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɨɝɨ ɨɛɪɚɡɨɜɚɧɢɹ ©Ɉɦɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ» Ⱦɚɧɢɥɨɜ ɋȼ., ȿɝɨɪɨɜɚ ȼȺ., Ʉɨɧɞɪɚɬɶɟɜɚ Ɍɇ. ɗɅȿɄɌɊɈɋɌȺɌɂɄȺ ɉɪɚɤɬɢɤɭɦ Ɉɦɫɤ 2006
»
., ., .
2006
2
537(075) 22.33 73
18
: . – .- , , . – .- ,
. .
18 ., ., : . – : , 2006. - 56 .
, .
. .
.
.
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© , 2006
3
© ,2006
– -
« » ().
.
, .
:1. .
.2. .
. ..
,, ,
.
. .
. . (90
) ,.
4
1. . .
1.1. . . . .
, ,.
– .,
, . ,
. , 1,6·10–19
. :
, , ,
.
. .
:, ,
q1q2 , r
.1.1).
12321
012 r
rqq
41F ,r12 F12
q2>0 q1>0
.1.1
5
0=8,85·10-12 - , r = | 12r |..
, , ,
. ,
, , -
. ,
, , ) ,
. E ,
. F ,
, :
qFE .
, q: EqF , E -
q.:
rrq
41E 3
0,
r - , q , .
. ( )
, .
1.2.
: –
– E .
6
:
.,
.
n
1iiEE ,
iE – i-, n - .
, :
= (dq/dl), dq – dl.
, : = (dq/dS),
dq – , dS.
: = (dq/dV),
dq – , dV.
, :
rr4
dqEdEq
30q
,
Ed - , dq,
.
7
1.3. .
dS ,,
dN = SdE = EdScos( n,E ) = EndS = EdS ,E —
dS, n - dS, ndSSd - , n = Ecos( n,E ) - E
n , dS = dScos( n,E ) - dS, E .1.2).
:
, :
n
1ii
S 0
q1SdE ,
Sd S,
.
: 1. q, R:
r < R E = 0
20 r4
qERr .
r – , .
2. q, R
: 3R4q3
.
r < R 300 R4rq
3r
E ,
20
20
3
r4q
r3R
ERr .
n
E
dS
.1.2
8
r – , .
3. , :
02E .
4. , :
r2E
0 .
r – , .
1.4.
:
:
L
0dE l .
, , , .
, .
.
, W,
:
qW
= p.
qi :
rq
41
0 .
:
= ii
n
1,
9
. . .
,
= dq
= dq4 0rq
.
, .
, .
.
=x
, =y
, z = zE = - grad ,
. . . ,
r,2
1
r
rr21r .drE,
drdE
, , .
ld , ld
d =
0 = 0. , , . . E = En.
1.5.
(q>0 –q),l
.l ,
, .1.3
10
. lqpe
).
-EEE , E -E - q -q ( .1.3).
, r (r>>l),
3e
0A r
p24
1E .
, , , r (r>>l)
3e
0B r
p4
1E .
=4
+ 3cos0
2
r 3 1 ,
r - , ; -r ep ( .1.3).
( . 1.3)
cosr4
= 20
eC .
, :EpM e , = e sin .
,
EpW ep = - p eE cos , - ( .1.4).
e
.1.4
11
1.6. . .
, , . , ,
. . , .
lqp . ,
, , E , , 0E ,
EEE 0 .
, , V
. .
P . ( )
:n
1ieip
V1P .
( P const) , V 0.
:
EP 0 , - .
,
( ) .
P n:
= n = cos , - .
12
1.7.
D ,:
PED 0 .ED 0 ,
= (1+ ) - ,, ,
, .
= .
:
, :
S
qSdD .
1.8.
1. , ( ),
:E2 = E1 D 2 / D 1 = 2 / 1.
2.
:D1n - D2n= 1 1n - 2 E2n= / .
1n - P 2n = .
= 0, 2 E 2n = 1 1n D n2 = D 1n .
1. d1 = 2 , d2 = 3 . q1 = 2 , q2 = 6 ;
- q3 = 3 , q4 = 12 .
13
.
, .
, :
4321 EEEEE . .1.5.
:
.
2d
4
qE;
2d
4
qE;
2d
4
qE;
2d
4
qE 2
20
442
20
332
10
222
10
11
, , , Ex Ey
:
.EEEEE;EEEEE 4y3y2y1yy4x3x2x1xx
= - 1, = 2, = 0, = 0,
= 0, = 0, = - 3, = 4 .
:d1 = 2 d2 = 3 q1 = 2 q2 = 6 q3 = 3 q4 = 12
E, - ?
.1.5
14
.
2d4
qqE;
2d4
qqE 22
0
34y2
10
12x
E :
;106,3101085,814,34
102106E 52212
99
x
.106,3105,11085,814,34
1031012E 52212
99
y
:
.1009,5106,3106,3EEE 525252y
2x
, E .
, ,1EE
tgy
x = 45 .
: = 5,09 105 , = 45 .
2. l = 10 = 400 . ,
, , r0 = 8 .
15
:
EdE . dl ( .1.6) lddq
, , ,
rr
r4dEd 2
0
l .
,
.cos
drd;cos
rr 0 l
, -Ed , , y Ed :
sindEdE;cosdEdE yx ,
, ,
.sinr4
dE;cosr4
dE00
y00
x
0 ( . 1.6. ), :
.r4
)cos-(1dsinr4
dEE;r4
sindcosr4
dEE000 00
yy000 00
xx
– Ed .
:
;101,35101001064108
1,0109104E 3
442
97
x
:l = 10 = 400
r0 = 8
- ?
.1.6
16
.101,16108
1010010641081109104
E 32
44
297
y
:
,10)1,161,35(EEE 3yx jiji
ji – .
:
2y
2x EEE .
: .103,39101,1635,1E 3322
: = 39,3 103 .
3. l. = 1,33 . .
, ( .1.7) ,
, :4321 .
, ,
.4 14321
, 1 ,
.
dl . ,, dq = dl
,, ,
: = 1,33
- ?
17
.r4
dr4
dqd00
l
.1.7 ,
.cos4
dd,cos
drd0
l
1 2 , 1:
.cosd
4cos4d 2
1
2
1 001
, 1 = 2 = /4,
.8
3tgn4
24
tgn8
3tgn4
242
tgn4
2cosd
42
00
4
00
4
001 llll
= 4 1,
.8
3tgn2
0
l
, :
.84,42,414n1085,814,3
1033,1212
9
l
: = 84,4 .
4. ( = 7) d = 2 = 1 3.
( . .1.8 ). ( ).
. , ,
( )
: = 7 = 1 3
, , , ( ) - ?
18
, ( . .1.8).
, ., ,
, ,
D . , , , D
. , ,
, . .
:
1. 2dx .
DSdDSdDSdDN.S.S.S
DS
,D
.
.
.SD2SdD2N ..S
D
, ,
.Sx2q .
.. Sx2SD2 .
19
xD . , ,
, :
ED 0 ..
0
xE .
2. 2dx .
, .D SD2N .
, , dSq . .
dSSD2 .. .
2dD , ,
02dE ,
= 1. , ,
.
( .1.9).,
.
.1.9).1. : = 0; = 0.
2. : = d/4; 7,801085,874
102104
dE 12
26
0B .
3. : = d/2; :
.1.9
20
) 4,1611085,872
102102
dE 12
26
0C1 ;
) 11304,1617EE12 CC .
: = 0; = 80,7 ; 1 = 161,4 , 2 = 1130 .
5. ( = 3) R = 5 , = 10 3.
: 1) r1 = 3 ; 2) ; 3) r3 = 10
. (r).
. ,
D , ( ) ,
.
, D ,
, D
. ,
r ( .1.10). :1. Rr .
SS S
2D r4DSDdSDdSDSdDN .
, , 3r
34q .
32 r34r4D , 3
rD .
: = 3 = 10 3
r1 = 3 r2 = Rr3 = 10
r1, R, Er2 - ?
.1.10
21
, D EED 0 .
03rE .
2. Rr . r ,
, 2D r4DN .
, r R – :3R
34q .
32 R34r4D ,
2
3
r3RD ,
0
DE , = 1.
20
3
r3RE .
E(r) ( .1.11).
,
.
:
1) r1 = 3 . 37,31085,8331031010E 12
29
1 .
2) r2 = R . :
) 28,61085,8331051010RE 12
29
1 ;
) 8,18RERE 12 .
3) r3 = 10 . 7,41,01085,83
1051010E 212
329
3 .
E
0 R r
22
: 1 = 3,37 ; (R)1 = 6,28 , (R)2 = 18,8 ; 3 = 4,7 .
6. ( = 2) R =10 = 1 3.
. (r).
grad-E .
, ,
drdE r , Er –
– r , . Er = E, .
2
1
r
r21 drE .
.
.
R
R drE , R – .
, 0 , ,
, 20
3
r3RE .
0
2
R0
3
R2
0
3
R 3R
r1
3Rdr
r3R
.
R
0R0 drE , 0 – .
: = 2
R = 10 = 1 3
(0), (R), (r) - ?
23
R
0R0 drE ,
:03
rE .
0:
211
3R
6R
3Rdr
3r
0
2
0
2
0
2R
0 0R0 .
(r) ( .1.12).
R 0.
.47222
111085,831,010;377
1085,831,010
12
26
012
26
R
: R = 377 , 0 = 472 .
1. R = 1 l = 1 . q = 4 . ,
, = 90 . :) ; ) ,
= 800 3 , = 60 .
: m = 0.016 ; = 2. 2. , ,
( 1 = 1 ). , , l.
l . , ,2 = 0,1 .
: F = 1.25 . 3. q1 = 0,1 . ,
, , . q2 = 10
. . , , R = 10 .
0 R r
.1.12
24
: F = 150 . 4. R = 10
2R. q1 q2, , = 1000 .
.: q1 = - 22,2 ; q2 = 44,5 .
5. R1 = 6 R2 = 10 q1 = 1 q2 = -0,5 .
, r1 = 5 , r2 = 9 , r3 = 15 .
: E1 = 0; E2 = 1,11 ; E3 = 200 . 6. R1 = 2 R2 = 4
, 1 = 1 2 = -0,5 .
( = 3). , r1 = 1 , r2 = 3 , r3 = 5 .
: E1 = 0; E2 = 200 ; E3 = 180 . 7. d = 0,5 .
1 =0,2 22 = -0,3 2.
.: = 141 .
8. = 2 3. R1 = 3 ,
R2 = 6 . : 1) ; 2) ; 3)
.: 1 = 238 ; 2 = 116 ; 3 = 116 .
1. q 4q l = 60 . , ,
, q1 , . , ,
, , .
25
2. l q1 = 180 q2 = 720 60 . , ,
q3 , . .
? 3. q = 1
. q1,
? ? 4. q = 0,3 .
q1 ,
? 5. l = 10 .
=1 . =20 q = 100 .
F . 6.
= 10 . = 20 q = 10 . F
. 7.
= 10 . ,, q = 10 .
=20 . F .
8. R = 10 q = 0,1 . ,
, q1 = 10 . F, q1 ,
: 1) l1 = 20 ; 2) l2 = 2 . 9. R = 10
= 1 . q = 20 . F
. 10. R = 10
= 1 . q = 0,4. F, .
.
26
11. R = 8 , = 10 .
, r = 10 ?
12. l = 10 = 3 .
, , .
13. l = 12 = 200 . ,
r = 5 . 14. l = 10 = 400 . ,
, , r = 8 .
15. R = 10 = 10 . ,
, = 5 . 16.
= 10 . , ,
, . 17. l = 10
q = 1 . , = 20 .
18. = 10 ., q = 10 .
. 19. a = 5
q = 3 .
, . 20. m = 0,2 q = 1 ,
l = 0,2 , , , . 30o,
. .
21. m = 15 q = 15 l = 15 .
27
, .
, ? 22. ,
=1 2. .
23. l1 = 12 l2 = 6 = 400 .
. , , .
24. q = 1 . R = 5 .
: 1) ; 2) , ,
= 5 . 25. , q = 2,33
, qo. , q F=0.
26. , .
qo = 0,4 2 = 60 . m ,
l = 20 . 27.
, . q , = 98 ?
l = 10 ; m = 5 . 28.
(l = 20 ) , . qo = 0,4
2 = 60o. , ,
2 = 54o. 29.
, = 800 3
= 2. 0, ?
28
30. R = 0,5 . = 800 3. ,
. =3,6 . ( = 8900 3).
31. R = 20 q = 10 .
S = 20 2. 32. , = 3 b = 2 ,
R = 1 q = 1 . ,
30o . .
33. q = 0,1 . R = 30 .
= 40 .
34. l = 10 ( =1 2)
. = 300 . .
35. , ( = 0,3 ).
, r = 20 .
= 20 , b = 40 . 36.
= 0,1 2
. 300. N
, r = 15 . 37.
, 1 = 2 2 2 = 4 2.
: 1) ; 2).
, . 38.
, 1 = 1 2 2 = 2 2.
: 1) ; 2)
29
. , .
39. R = 15 q = 2 .: 1) r1 = 10
; 2) ; 3) r2 = 20 . E(r).
40. pa ep o R1 = 5 R2 = 8 . q1
= 2 q2 = - 1 . , : 1) rl = 3 ; 2) r2 = 6 ; 3) r 3 =
10 . E(r). 41. R = 10 pa
= 10 3. : 1) r1 = 5 ; 2) r2 = 15
. E(r). 42. R = 10
= 15 3. : 1) r1 = 5 ; 2) ; 3)
r2 = 15 . E(r). = 5.
43. , ( = 2),,
= 2 . r = 1 .
44. R1 = 1,5
1 = 0,20 . R2 = 3 2 = - 0,15 .
( = 3). ,
1) r1 = 1 ; 2) r2 = 2 ; 3) r3 = 5 . E(r). 45. = 5 3 R = 10
= 5. - r1 = 5 r2 = 15 .
E(r). 46. ( = 3) R = 5 ,
= 10 3. : 1)
30
r1 = 3 ; 2) ; 3) r2 = 10 . E(r), D(r).
47. ( = 5) . = 100 3.
R1 = 5 , - R2 = 10 . , :
1) r1 = 3 ; 2) r2 = 6 ; 3) r3 = 12 . E(r),D(r). 48. ( = 2) R = 2 ,
= 10 3.,
: 1) r1 = 1 ; 2) r2 = 3 . . E(r), D(r).
49. d = 1 , = 100 3.
. 50. R = 10 ,
q = 10 , q0 = 5 . : 1) r1 = 5 , 2) r2 = R,
3) r3 = 15 . E(r). 51. R = 5
. = 0·r, 0 = 5 3, r –.
: 1) r1 = 3 , 2) r2 = R, 3) r3 = 10 . E(r).
52. ( = 3) R = 5 , = 0·r,
0 = 1 3, r – . : 1) r1 = 1 , 2) r2 = R, 3) r3 =
10 . E(r), D(r). 53. R = 2
= 1 2. ,
r1 = 1 , r2 = 3 . E(r). 54. d = 5 l = 4
q = 500 .,
a = 1 .
31
55. R = 2 . = 0/(1+r3),
0 = 1 3, r – . : 1) r1 = 1 , 2) r2 = 10 .
56. R = 3 .
= 0·r, 0 = 2 3, r – . ,
: 1) r1 = 1 , 2) r2 = 5 . 57. R1 = 2 , R2 = 2R1, R3 = 3R1 q1 = 2 , q2 = 4 q3 = -3
. ,: 1) r1 = 1 , 2) r2 = 3 , 3) r3 = 5 ,
4) r4 = 10 . E(r). 58. R = 5 , q = 5 ,
R1 = 7 - R2 = 9 . .
: 1) r1 = 3 , 2) r2 = 6, 3) r3 = 8 , 4) r4 = 10 .
E(r). 59.
1 = 202 2 = - 50 2.
( = 5). 1) , 2) .
E D , .
60. R1 = 2 R2 = 5 q1 = 10 q2 = - 2 .
( = 5). : 1) r1 = 1
, 2) r2 = 3 , 3) r3 = 10 . E(r), D(r), r – .
61. R = 10 . l = 5
= 150 . r = 5 .
62. R = 5 , = 1 2.
, r1 =
32
10 r2 = 15 c . 63.
R = 1 q = 50 . , : 1) r1 = 0,5
2) r2 = 2 . 64. R = 8 ,
= 10 3. ,
r1 = 5 r2 = 15 . 65. R = 10 ,
= 20 3. -,
r1 = 2 r2 = 8 . 66. R = 8 ,
= 10 3. ,
r1 = 10 r2 = 15 .
67. R = 8 ,
= 10 . , r 1 = 2 r 2 = 7
.
68. d =1 , r1 = 0,5 ,
r2 = 1,5 . U = 1 .
69. R1 = 3 R2 = 6 . ( = 2).
q1 = -1 , q2 = 2 . : 1) r1 = 1 ; 2) r2 = 5 ; 3) r3 = 9
. 70. R = 5 q = 1 .
( = 3) d = 2 . : 1) r1 = 3 ; 2) r2 = 6 ; 3) r3 = 9
. 71. ( = 2) R = 10
= 1 3. .
33
72. E = 600 .
, , = 60o
. r = 2 . 73. ( = 3) R = 10
= 50 3. , .
74. 1 = 5 2 2 = - 2 2.
, l = 2 ,
, – . 75. R1 = 10 , R2 = 2R1,R3 = 3R1 q1 = 2 , q2 = 2q1, q3 = - 3q1 .
. 76. d = 4
= 10 . , ,
– l = 5 . 77.
1 = 6 2 2 = - 2 2. ( = 5).
, l = 1 ,
, – . 78.
1 = 8 2 2 = 3 2. ( =
3). , r1 = 1 r2 = 5
. 79. R = 5
R1 = 8 R2 = 12. . .
(r). 80.
1 = 3 2 2 = - 3 2. d = 5 .
d = 3 . , .
34
81. ( = 2) R = 5 , = 10 3.
, r1 = 1 r2 = 2 . 82.
R = 5 . r1 =10 1 = 100 . r2 = 3
( ). 83. d = 2
. , ,
l1 = 1 l2 = 2 , = 100 . 84. R = 5 q = 10 .
: 1) ; 2) l = 2 . (r).
85. . , 1 = 200 ,
, r = 50 , 2 = 40 . 86. .
r = 10 , =100 .
87. , = 5 2.
. 88. ,
= 50 .
r = 0,5 .
89. , = 1 2.
, 1 = 20 2 = 50 .
90. R = 10 q = 15 .
, r1 = 5 r2 = 15 .
35
2. . .
.
2.1. , rd
q :rd,EcosdrEqrd,FcosdrFrdFA ,
E - q. q 1 2
q ( . ). ,
q , :
= - dW 1-2= - W = W 1 – W 2, W 1 W 2 — q 1 2 .
, 1-2, q 1
1) 2 ( 2):1-2 = q ( 1 - 2).
2.2. .
, . ,
, :) 0E ,
n, . ;) ;) ;) ( )
.D
:D n = , E n = / ,
- .
36
. :
q = C .
( , ) , ,
, .C = q / .
( ) R
= 4 0R, - .
2.3. .
,
.C = q / ( 1 - 2).
=d
S0 ,
S - ; d - ; - .
= 4 0R1R2 / (R2 - R1), R1 R2 - .
= 2 h / ln (R2 / R1). R1 R2 – , h – .
= C i.
= 1 / (1/ i).
2.4. .
.
37
W = (q1q2) / 4 or12.
W = 12
q i ii=1
n,
i - , i- , , i- .
W =2
C 2
2q
2Cq2
.
W = q2C
= C( )2
=q
2
2 2
.
:
w E D (ED)2
2 2dWdV
0
02 2.
, V:
W = w dV E dVVV
02
2.
1. d = 1.
D = 10 , ( .2.1).
U = 100 . ,l = 2,5 .
).
:d = 1 D = 10 U = 100 l = 2,5 |q| = 1,6·10-19
m = 9,1·10-31
, v - ?
38
, ,
. , , ,
, F = |q|E, ,
. ,
,
.
r2E
0 , r – .
.
dDln
2dr
r2drEU
0
2D
2d 0
2D
2d
.
dDln
U2 0
dDlnr
UE .
dDlnrm
Uqm
EqmF
.
, ,
.35,25,02dr l
215331
-19
1055,210ln103101,9
100101,6.
.
, : W = A .
, ,
.2.1
39
q2
mv 2
,
– ,
. mq
v .
, :
.8,7710ln6ln100
dDln
2drln
Udr
dDlnr
UdrEr
2d
r
2d
, ,
.1023,5101,9
8,77101,6v 631
-19
: = 2,55·1015 2, v = 5,23·106 .
2. v0 = 1 = 30 . l = 5 .
, .
: = 30
l = 5 |q| = 1,6·10-19
m = 9,1·10-31
v0 = 1
E - ?
.2.2
40
, ,
. , , –
( .2.2).
2ttvtr
2
0 . tvdtrdv 0 .
:
.t-sinvv,cosvv
,2t-tsinvy
,tcosvx
0y
0x
2
0
0
x = l, cosvt
0
l ,
, vy = 0, t-sinv0 0 .
lcossinv
tsinv 2
00 .
mEq
mF
, qmE .
lqcossinvmE
20 .
: .3,4905,0101,6
30cos30sin10109,1E 19-
oo26-31
: = 49,3 .
3. . d = 2 .
U1 = 600 . , ,,
U2 = 1800 . .
41
,
. q = CU,
, 1U1 = C2U2 .
dSC 0
1 - ,
dS
C 02 - .
,
.3600
1800UU
CC
1
2
2
1
= – 1, = 2. ,
. , = .
P = 0 E.
,
: dUE 1 .
dU1
0 .
.103,5102
6001085,82 263
12
: = 2, = 5,3·10-6 2.
4. R1 = 1 R2 = 5 ,
:d = 2 U1 = 600 U2 = 1800
, - ?
42
, 3ra
, = 53 – , r – .
. q, –
-q ( .2.3).
. D , .
r.
2
SD r4DSDSdDN . ,
, – q. : D·4 r2 = q D:
2r4qD .
,
(),
: D =0E.
a4rq
r4qE
02
0.
:
a8RRqdr
a4rqdrE
0
21
22
R
R
R
R 021
2
1
2
1
.
, ,
21
22
0
21 RRa8qC .
:
.1067,401,005,0
5108,853,148C 722
-12
:R1 = 1 R2 = 5 = 5 3
- ?
43
: = 4,67·10-7 .
5. 1 = 100 2 = 200 U = 300 .
, .
, .
q = CU, :
C1U1 = C2U2 .
C ,
U = U1 + U2 .
,
: .CC
CUU;CC
CUU21
12
21
21
,
;CC2UCC
2UCW 2
21
2221
211
1
.CC2UCC
2UCW 2
21
2212
222
2
, ,
;10210200101002
3001020010100W 621212
221212
1
.10110200101002
3001010010200W 621212-
221212
2
: W1 = 2·10-6 , W2 = 1·10-6 .
:1 = 100 2 = 200
U = 300
W1, W2 - ?
44
6. R = 10 .
= 0·r, 0 = 1 3. ,.
, , ,
, .
, . r < R ( .2.4).
, .
S S
2
SE r4ESEdSEdSESdEN
., ,
:V
dVq , ,
r, dV – r dr,
dV = 4 r2dr. q
4r4drr4rdVq
40
V
r
0
20 .
, S ,
0:
0
402
4r4
r4E .
:0
20
4rE .
:
:R = 10
0 = 1 3
W - ?
.2.4
45
.32
r2Ew
0
420
20
, , , :
.56
R327
R4drr432
rdVwW0
720
0
7202
V
R
0 0
420
:
.1034,61085,856
1,0103,14W 412
72-3
: W = 6,34·10-4 .
1. r1 = 4 q = - 0,66 .
r2 = 2 ; = 5. .: = 0,6 .
2. U = 90 , r = 1 .
? v ? t ? .
: = 1,58·1016 2; v = 5,63 ; t = 0,356 . 3.
v0 = 3,6·107 . = 3,7 ;
= 20 .
?: y = 1 .
4. = 1 .
q = 1 ( .2.5).
: = 2,62 . .2.5
46
5. . 6400· 103 . , q = 1 ?
: = 711 , = 1400 . 6. , R1 = 0,05 R2 = 0,15 , .
q = 5 . = 2000 . .
: 1 = 2900 , 2 = 1700 . 7. S = 8 10-3 2
d = 5 . = 6·104 .
. . ,
.: 1 = 14,2 , 2 = 7,1 , U1 = 300 , U2 = 600 , 1 = 2 = 0,53
2. 8. 1 = 3·10-6
2 = 6·10-6
= 120 . ,
: 1) , 2) .: 1) U1 = U2 = 120 , q1 = 0,36 , q2 = 0,72 ;
2) U1 = 80 , U2 = 40 , q1 = q2 = 0,24 . 9. d1 = 4·10-4 U = 2000 .
, d2 = 6·10-3 .
.: w = - 0,61 3.
10. , ( = 2), = 4,5 = 11 2.
.: W = 65 .
11. F = 50 . S = 200 2.
w .: w = 5 3.
47
12. ( = 2). S = 40·10-4 2, d = 2·10-3 . E = 32·103 .
, .?
: W = - 36 .
1. . ,
r1 = 10-2 , r2 = 2·10-2 , v1 = 2·105 v2 = 3·106 .
. 2.
= 2·10-7 . , r1 = 10-2
r2 = 5·10-3 ? 3. r1 = 6·10-2
= 10-6 q = -10-9 . r2 = 3·10-2 .
. 4. ,
= 10-6 2 q = 10-9 . r = 3·10-2 .
. 5. ,
= 2·10-6 2 q = 2·10-9 .
v1 = 2·105 v2 = 2·106 . , .
6. = 2·10-6 2 .
r = 2·10-2 . A = 4·10-7 . .
7. .r = 2·10-
2 v1 = 107 v2 = 108 . .
48
8. A1,2 q = 1 1 2 , ( .2.6).
1 . 9.
= 0,1 ). 1,2 q = 50 1 2 ( .2.7).
10. 1 ( =20 ) (v0 = 0). W 2, 9R
, R – ( .2.8). 11. d = 4 .
, . ?
12. d = 1 . - .
S - , ?
13. , d = 2 .
U = 120 . , r = 3 ?
.2.8 .2.9
.2.6 .2.7
49
14. = 1012 2. E, v,
t = 1 , U,
. . 15.
= 35,4 2. , , . lmin,
, l0 = 5 W = 80 .
16. , v0 = 1,6 , = 90 ,
. v 1 ?
17. . 1 = 100 v1 = 0,1
. 2 , n = 2 . /m = 96 .
18. = 1 v0 = 1 .
l, , v1.
19. vmin , = 400
( . 2.9)? 20.
. 1 = 100 v1 = 6 . 2 , v2
0,5v1. 21.
v = 10 , .
( ), d = 16 , U = 30
l = 6 ? 22. , v = 10 ,
. = 35
. U
50
), l = 10 d = 2 .
23. , v = 10 ,
, d = 2 . l = 10 . U
, ? 24. ,
v0 . U = 300 ; d =
2 ; l = 10 . v0 , ?
25.
. = 100 ; d = 4 . , , ?
, U = 60 ?
26. v0 = 9 106 .
U = 100 ; d = 1 . , t = 10
. 27. , ,
. ?
28. , ,
. ?
29. v0 = 1 107 .
= 10 ; l = 5 .
. 30.
v0 = 1,2 105 . = 3 ; l = 10 .
51
? 31.
, ( = 3,2). ,
r =1,3 , R = 3,0 . 32. = 2 10-12
1000 . r = 0,03 .
33. , = 800 , = 8,85 10-7 2. .
34. , 0 2000 . r = 0,04
1200 . .
35. = 1,77 10-12 N = 2 1019
. . 36. N,
, = 3, 54 10-
7 2, = 0,45 10-11 . 37. , ,
, m = 18,2·10-20 . = 700 . R.
38. R1 = 2 R2 = 2,1 .
, ( = 2,1). 39. . R1
10 , R2 = 10,2 . ( = 2,1). q = 5
. U . 40. ,
U = 600 , : d1 =7 ( = 7) d2 = 3 ( = 3). S
200 2 . : 1) C ; 2) D, E .
41. d = 1,33 , S = 20 2 .
: d1 = 0,7 ( =7) d2 = 0,3 ( = 3). C .
52
42. = 0,2 2.
d1 = 1 . d2 = 3 ?
43. ( = 2,1) d = 1 , .
, ? 44. 1,5 . d
5 . , ( = 3) d1 = 3 ?
45. .
U1 = 100 . U2, ( = 7) ?
46. , U = 600 ,
, ( ).
, U1 = 100 .
47. 1 = 3 2 = 6 = 120 .
q1 q2 U1 U2 ,: 1) ; 2) .
48. 1 = 0,2 U1 = 320 .
, U2 = 450 , U 400 . 2 .
49. 1 = 0,6 U1 = 300
2 = 0,4 , U2 = 150 . q,.
50. . = 89 .
S = 100 2, – ( = 7). d ? 51. , .2.10.
: C1 = 0,2 ; C2 = 0,1 ; 3 = 0,3 ; 4 =0,4 . .
53
52. C1 = 0,2 , C2 = 0,6 , C3 = 0,3, C4 = 0,5 , .2.11.
U 320 . Ui qi (i = 1,2,3,4).
53. C1 = 10 , C2 = 40 , C3 = 2 C4 = 30 , .2.12.
. 54. C1 = 2 , C2 = 2 , C3 = 3 ,C4 = 1 , 2.13.
U4 = 100 . ,
. 55. 0,05 q1 = 7 10-9
0,01 q2 = 7 10-9 . . ?
? 56. R1 = 0,015 R2 =0,06 .
= 780 . 1 2 q1, q2 = 6,0 10-9 .
57. R1 = 0,03 R2 = 0,06 1 = 6,0 102 2 = 9,0 102 . .
, q .
58. R1 = 0,04 R2 = 0,06 . = 4000 . ,
.2.11 .2.12 .2.13.2.10
54
q , 2000 .
59. R1 = 0,05 R2 = 0,1 ,1 = 600 , q2 = 3 10-8 .
. , .
60. q1 1 R1 = 0,02 , R2 = 2 10-3
q2 = 10-8 . 61. R = 1 m = 0,15
= 3 r1. W = 1,0
10-17 . r2. , , = 2·10-5 .
. 62. 1 R1 = 10 , = 3 ,
() 2,
, 2, 3. 2 3 R2 = R3 = 10 . : )
1; ) 1 2 ; ) 1 3 .
63. R1 = 2 2, R2 = 3 .
, 2 0,4 . 1 2? 64. R1 = 0,05 , 1 = 3000 ,
R2 = 0,04 , W2 = 4,5 10-4 . .
65. , 0 = 2000 . = 4 10-2
1 = 1200 . W. 66. W,
= 5 10-7 2, = 5 10-11 . 67. R1 = 0,04
R2 = 0,02 . , q = 10-8 .
55
68. R1 = 0,02 , = 4000 ,
R2 = 0,03 . W1 W2.
69. R1 = 10-2 . = 5 10-2 500 . W.
70. d = 4 10-2 = 2000 . W.
71. W1 =2 10-7 . W2
= 2, .
72. W1 = 2 10-7 . W2
= 2, .
73. 1 =2 10-6
U1 =2000 .
2 = 3 10-6 . , , ?
74. S = 0,01 2, d1 = 1 .
U = 0,1 . d2 = 25. W1 W2 ,
: ) ; ) . 75. 1 = 666
U = 1,5 . ,
2 = 444 . , , .
76. 1 = 1 , 2 = 2 , 3 = 3 U = 1,1 .
: 1) ; 2) .
77. 111 . –. U = 600
. , ? ( = 5).
56
78. ( ), V 100 3.
8,85 2. , ,
. ( =5). 79.
( = 4,5). 1 = 9 10-6 . U1 = 200 .
, . 3 .
W1 W2 . 80. ( = 5)
. W1 = 1,5 10-5 . ,
, . ,?
81. R = 3 q = 20 . d = 2 . W
, ( = 2). 82. R = 10
= 10 8. W1, , W2 ( =
2). 83. .
, ( = 3)?
84. = 10 = 3 . W ,
, , .
85. R1 = 6 q.
) , . R2
. 86. (q = 0,1 ) R = 10 . W , ,
,
57
87. S = 120 10-4 2
q = 4 10 - 9 . = 6).
, . .
88. R1 = 20 , q = 2 10-6 , R2 = 30 .
, . 89. , q = 5 , q0 = 1,5 .
– R1 =50 R2 = 100 . 90. S = 0,01 2
F = 30 . . q, ,
w0 ( = 7).
1 21 1 31 61 1 31 612 2 32 62 2 32 623 3 33 63 3 33 634 4 34 64 4 34 645 5 35 65 5 35 656 6 36 66 6 36 667 7 37 67 7 37 678 8 38 68 8 38 689 9 39 69 9 39 6910 10 40 70 10 40 7011 11 41 71 11 41 7112 12 42 72 12 42 7213 13 43 73 13 43 7314 14 44 74 14 44 7415 15 45 75 15 45 7516 16 46 76 16 46 76
58
17 17 47 77 17 47 7718 18 48 78 18 48 7819 19 49 79 19 49 7920 20 50 80 20 50 8021 21 51 81 21 51 8122 22 52 82 22 52 8223 23 53 83 23 53 8324 24 54 84 24 54 8425 25 55 85 25 55 8526 26 56 86 26 56 8627 27 57 87 27 57 8728 28 58 88 28 58 8829 29 59 89 29 59 8930 30 60 90 30 60 90
.
1. . : .2. .. . : , 1987. 496 .
2. . : . . .- .. 4- ., . .: . , 1997. 542 .
3. ., . : . . . .:, 1989. 608 .
4. . . .: », 2003. 384 .
5. . : . ..: , 1988. 288 .
6. ., . : . . – .: . , 1981. 318 .
7. . : .. – .: , 1986. 334 .
59
8. ., ., . : .. – .: . , 1973. 512 .
9. . : . / .:. , . , . , . . :
, 1999. 72 .
60
. 06039 12.10 2001.
2006.
19.04.06. . 60 x 841/16. . . . . 3,5. .- . .
. ____________________________________________________________
. 644050, . , . , 11.