I = q/t,
q , t.
j = I/S,
S .
<υ>
j = qn<υ>,
q ; n .
:
) , , φ1 φ2 = U () ; R ;
) , , ; R ( );
) () , R ; Ri .
:
) ∑ Ii = 0 ;
) ∑ IiRi = ∑ ,
∑ Ii , ; ∑ IiRi ; ∑ ei .
R G
R = ρl/S, G=γS/l,
ρ ; γ ; l ; S .
:
) R = ∑ Ri ;
) 1/R = ∑(1/Ri) , Ri i- .
A = IUt, A = I2Rt, A = U2t/R.
, U, , .
P = IU, P = I2R, P=U2/R.
Q = I2Rt.
= γ ,
γ ; ; .
1. l = 20 . = 10 q1 = 40 , F = 6 . τ .
. F q1 τ . , τ. F , , . . (. 1) dr dq = τdr. . , ,
+ ,
, . :
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.
:
2. q = 40 τ = 50 /. , , , .
. xOy , Oz (. 2). dl. dq=τdl, , , d , ,
-, dl .
d : d 1, ( Oz), d 2, ( xOy), . .
.
:
. , dq dq` (dq = dq`), , d 2 d 2` : d 2 = - d 2`. () d 1 Oz ( ), . . d 1 = dE1.
,
q = 2πRτ R = q/(2πτ).
(1)
, ( / ):
, (1), (τ = 5·10-8 /, q=4·10-8 , ε0 = 8,85·10-12 /) :
3. R1 = 6 R2 = 10 q1 = 1 q2 = - 0,5. r1 = 5 , r2 = 9 , r3 = 15 . E(r).
1. 1 I S1 r1 :
( , , ). En=E1=const. , 1 ( I) , r1<R1, .
2. II r2. ( ())
( q1).
En = E = const, :
ES2 = q1/ .
II 2,
2 = q1/( S2),
S2 = 4πr22 .
(1)
3. III r3. III 3 , , , q1 + q2.
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3 = (q1+q2)/4π r32.
, q2<0,
(2)
, (1) (2) :
(q1 = 10-9 , q2= - 0,5·10-9 , r1=0,09 , r2=0,15 , 1/(4πε0)=9·109 /) :
E(r). I(r1<R1) = 0. II (R1 r<R2) E2(r) 1/r2. r = R1 E2(R1) = q1/(4π R12)=2,25 /. r = R2 (r R2 ) E2(R2) = q1/(4π R22) = 0,9 /. III (r>R2) E3(r) 1/r2, r = R2 (r R2 ) E3(R2) = (q1 - |q2|/(4π R22) = 0,45 /. , E(r) r = R1 r = R2 .
E(r) . 4.
4. R = 1 , τ = 20 /. , 1 = 0,5 2 = 2 , .
. : = -grad φ. , ,
E = - dφ/dr, dφ = - Edr.
, , r1 r2 :
(1)
, , :
E = τ/(2π r).
(1),
φ1 φ2 = τ/(2π )ln(r2/r1). (2)
, , r1 r2, (2) , (r1 = R + = 1,5 r2 = R + = 3 ):
φ1 φ2 = 2 · 10 8 · 1,8 · 1010 ln(3/1,5) = 3,6 · 102 · 2,3 ln2 = 250 .
5. 1 = 3 U1 = 40 . 2 = 5 . ?
. , ,
= W1 W2, (1)
W1 , ; W2 , , .
W = ½U2, (2)
.
(1) W1 W2 (2) , ,
= ½ C1U12 ½(C1 + C2)U22, (3)
U2 .
, , U2 :
U2 (3),
:
6 R = 100 e = 150 Ri = 50 . : 1) Rv = 500 , , ; 2) .
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. 5
. 1. , (. 5),
U1 = I1R1,
R1 ; I1 ( ).
I1 :
I1 = e /(Re +Ri), (1)
Re . :
Re = R/2 +R1. (2)
R1
(1) Re (2),
. :
U1 = 1,03·45·5 = 46,9 .
2. I 2 :
U2 = I2 ·R/ 2, (3)
I2 .
I2 = e /(R + Ri).
I2 (3),
U2 = e / (R + Ri)·R/2.
:
7 R = 20 Δt = 2 I0 = 0 I = 6 ( 6). Q 1, , Q2 , q1/q2.
. 6
. Q = I2Rt (I = const). ,
dQ = I2Rdt. (1)
I .
I = kt, (2)
k , :
(2) (1)
dQ = k2Rt2dt. (3)
, Δ t, (3) t 1 t 2:
:
Q1 = 1/3 · 32 · 20(1 0) = 60 ;
Q2 = 1/3 · 32 · 20(8 1) = 420 .
,
Q2 / Q1 = 420 / 60 = 7,
. . , .
8 V = 375 3 , . S = 250 2. U I, , 2, n 5,3 · 107 3. b += 5,4 · 10 4 2 / ( · ), b -=7,4 · 10-4 2/( · ).
. U d
U = Ed. (1)
j = qn(b+ + b-)E,
q .
d , (1),
d = V/S.
d (1),
(2)
, :
(2) :
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1. q1=20 , q2=-10 d =5 . , r1=3 r2=4 . , q= 1 .
2. q1=q2=q3=2 =10. , .
3. q 9q d=100 . , , , , . , , , , .
4. . a. . r , ? r0=1,5×103 /3, e = 2,2.
5. q1= q2=q3=q4=40 =10. , .
6. q1=30 q2=-20 d =20 . , r1 = 30 , r2 = 15 .
7. = 10 q1=10, q2=20 q=30 . , q1 .
8. q1=q2=q3=q4= 8×10-10 . q , ?
9. d=20 : q1=-50 q2=100. , q3=-10 , , d.
10. d q1=2 q2=4 60. , q3 , . q3 . ?
11. l =20 t=0,1 . , , =20 .
12. R=10 t = 1 /. , , .
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13. q=0,2 . , A, =20 . R=10.
14. R=10 q=50. , , .
15. , , t=0,5 /. , , =20 .
16. R=20 t=0,2 / . , A, h=2R .
17. q=20 t=0,1 /. , , .
18. R=10 q=0,05 . , , .
19. q=10 t=0,01 /. , , , .
20. R=10 t=0,2 / . , , .
21. R 2R s1 s2 (. 18). : 1) -, E(r) : I, II III. s1=4s, s2=s; 2) , r, . s=30/2, = l,5R; 3) E(r).
22. . 21. . 1 s1=s, s2=-s. . 2 s=0,1/2, r=3.
23. . 21. . 1 s1=-4s, s2=s. . 2 s=50 /2, r=1,5R.
24. . 21. . 1 s1=-2s, s2=s. . 2 s=0,1/2, ==3R.
. 18 . 19
25. s1 s2 (. 19). : 1) - , () : I, II III. s1=2s, s2=s; 2) , , ; 3) ()
26. . 25. . 1 s1=-4s, s2=2s. . 2 s=40 /2 .
27. . 25. . 1 s1=s, s2=-2s. . 2 s=20 /2 .
28. R 2R s1 s2 (. 20). :
1) -, (r) : I, II III. s1=-2, s2=s; 2) , r,
. 20
. s= 50/2, r = 1,5R; 3) E(r).
29. . 28. . 1 s1=s, s2=-s. . 2 s= 60/2, r =3R.
30. . 28. . 1 s1=-s, s2=4s. . 2 s= 30/2, r =4R.
31. q1=6 q2=3 d=60 . , ?
32. , j 300 . q= 0,2 1 2 (.21).
33. q1=2 q2=-2, =10 . , q=0,5 1 2 (.22).
. 21 . 22
34. , s1=2/2 s2=-0,8/2, d =0,6 . U .
35. = 100 × =200/. , a=180.
36. , j=10, . j1 ?
37. R =10 . t=800/. j , h = 10 .
38. = 200×. U , r =40 .
39. , t= 20/. U , r1=8 r2= 12.
40. t=200/. j .
41. =200, q=40, . U = 200 u = 10 /. u0 , .
42. , T = 10 , . , U= 8?
43. u++ +, .
44. = 400 ( ) R = 10 . , , q = - 10 .
45. , , u = 105 /. d = 8 . : 1) U ; 2) s .
46. = 5 , N = 10 , U = 1 MB. ? u ?
47. umin , j = 400 (.23)?
48. = 200 / ( ) u0=2 /. l, , .
49. (t = 10 /). 2 2, 1 T1= 200 (.24).
. 23 . 24
50. . j1 = 100 = 6 /. j2 , .
51. C1 = 5 2 = 10 U1 = 60 U2 = 100 . , .
52. C1 = 10 U = 10 . , , , 2 = 20 .
53. C1 = 2 , 2 = 5 3 = 10 U = 850 . .
54. C1 = 2 2 = 5 U1 = 100 U2 = 150 . , .
55. =100 . , , .
56. C1 = 5 2 = 8 e = 80 . q1 q2 U1 U2. .
57. R = 10 . d = 2 . U = 80 . q : ) ; ) .
58. R1 = 5 R2 = 10 q1 = 40 q2 = -20 . W, , .
59. : d1 = 0,2 d2 = 0,3 . U = 300 . E .
60. S = 200 2 U =2 . d=2 . . W w .
61. . r = 4 . I = 0,3 , U = 120 . R. e, , , .
62. = 80 , Ri = 5 . = 100 . I , U, , R.
63. , = 600 , l = 1 . = 5 . , d = 0,5 .
64. R1 = 8 I1 = 0,8 , R2 = 15 I2 = 0,5 . I.. .
65. = 24 . , , Imax = 10 . Pmax, .
66. = 12 U = 15 . , Ri = 10 .
67. U = 800 = 10 . , 10% ?
68. U = 220 I = 5 . , , , R 6 .
69. U = 100 R1 = 2 , . U1 = 80 . , U2 = 60 . R2 .
70. = 12 . I = 4 A h = 0,6. Ri .
71. t = 20 R = 5 Q = 4 . , R = 5 .
72. u I =I0-at, I0 = 20 , a=102c-1. , t = 10-2 .
73. R = 10 t = 50 I1 = 5 I2 = 10 . Q, .
74. t = 10 I1 = 1 I2 = 2 Q = 5 . R .
75. I = I0 sinwt. q, t, , = 10 , w = 50p-l.
76. t = 10 Q = 40 . < I > , R = 25 .
77. t = 8 R = 8 Q = 500 . q, , .
78. Q, t = 10 R = 10 , , , I1 = 10 I2 = 0.
79. I = I0 sin wt. , R=10 , ( t1 = 0 t2 = /4, = 10 ).
80. I = I0 e-at. , R = 20O , . a 2×10-2c-l.
81. , 2 1,66 2 2·1019 .
82. 0,88 2 80 . , , . ρ = 8,9 /3.
83. , 0,5 . 0,1 2200 ; 5 2. ( ρ = 5,5·10-8 · , α = 0,0045 1/).
84. S = 0,17 2 I = 0,15 . , .
85. , , , 5,3·10-9 .
86. 60 0,1 , .25. . = x 0,2 ?
87. 100 , .26. .
. 25 . 26
88. , .27, R1=1, R2=3, R3=R4=R6=2, R5=4 .
. 27
89. , , ω = 100 -1. R = 10 . ?
90. + , j = 5 · 10-11 /2, n = 109 -3, = 1000 /. = 1,9 · 10-4 2/( · ).
91. S, d. , +, _ U, I.
92. , U=13,5, . φi.
93. APt/ACs = 1,58. , .
94. , α = 5,3 · 10-5 / R = 15 , . , , . , I = 0,2 , r = 150 .
95. 130 /. , 1 3 n =7 · 108 -3 , .
96. , 100 ... e = 0,011 ?
97. , , APt/ACs = 2,7.
98. = 2,5 . , W = 10-18 .
99. Ui = 13,6 . , , .
100. 1 , 0,01 ?
1. ( )
g G NA R Vm k | 9,81 /2 6,67×10-11 3/(×2) 6,02×1023 -1 8,31 /(×) 22,4×10-3 3/ 1,38×10-23 / |
2.
6,37×106 5,98×1024 6,95×108 1,98×1030 1,74×106 7,33×1022 1,49×1011 3,84×108 |
3.
, /3 | , /3 | ||
2,70×103 3,50×103 6,02×103 9,80×103 7,88×103 0,53×103 | 8,93×103 8,90×103 11,3×103 10,5×103 1,90×103 7,15×103 |
4.
, /3 | , /3 | ||
( 4 ) | 1,00×103 1,26×103 13,6×103 | 1,26×103 0,80×103 |
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: 2016-11-03; !; : 1053 |
:
: , , , , .
==> ...
: 0.253 .