»

., ., .

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

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;10210200101002

3001020010100W 621212

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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.