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TRANSCRIPT
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., ., .
2006
2
537(075) 22.33 73
18
: . – .- , , . – .- ,
. .
18 ., ., : . – : , 2006. - 56 .
, .
. .
.
.
.
© , 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.