. , , l r .
, .
:
= q × . (2.3.26)
,
= sinq, (2.3.27)
q .
8. , 1010 , 1,6×1019 . .
: l = 1010 ,
q = 1,6×1019 .
: .
. (2.3.26):
= q × l = 1,6×1029 ×.
: 1,6×1029 ×.
9. = 1000 /. 4×1020 ×. . , .
: = 1000 /,
= 4×1020 ×,
: .
. , , (2.3.27):
= sinq.
q = 90, sinq = 1,
= (2.3.28)
(2.3.28), :
= pe×E = 4×1017 ×.
: 4×1017 ×.
.
, W
W = ee 0 E 2 V /2 = CU 2/2 = q 2/2 C. (2.3.29)
W , e , , e 0 , E , V , C , U , q .
:
C = q/U = ee 0 S / d, (2.3.30)
S , d .
, e = 1.
E U :
U = E×d, (2.3.31)
s , :
q = s×S, (2.3.32)
S () ,
S = a×b ,
S = a 2 ,
S = p×r 2 - .
|
|
, ,
= S i, (2.3.33)
1/ = S(1/ i), (2.3.34)
i .
10. , = 1000 /, S = 10 2, d = 1 .
: = 1000 /,
S = 10 2 = 1×103 2,
d = 1 = 0,001 .
e = 1.
: W.
. (29):
W = ee0E 2 V /2.
,
V = S×d (2.3.35)
(2.3.35) (2.3.29):
W = ee 0 E 2 V /2 = ee 0 E 2 S×d /2. (2.3.36)
(2.3.36) , :
W = ee 0 E 2 S×d /2 = 4,4×1012 .
: 4,4×1012 .
11. , 2 ( ) 1 . 10 . .
: e = 1,
d = 1 = 0,001 ,
r = 10 = 0,1 ,
q = 2 = 2×109 .
: W, U.
. (2.3.29):
W = q 2/2 C,
(2.3.30):
C = ee 0 S / d.
,
S = p×r 2. (2.3.37)
(2.3.37) (2.3.30) :
C = ee 0 S / d = ee 0 p×r 2/ d. (2.3.38)
(2.3.38) (2.3.29) :
W = q 2/2 C = q 2/2(ee 0 p×r 2/ d) = q 2 d /(2 ee 0 p×r 2) = 7,2×109 .
(2.3.31):
U = E×d,
E = s / e 0, (2.3.39)
s , (2.3.32): s = q / S.
,
E = s / e 0 = q / Se 0 = q / p×r 2 e 0,
U = E×d = (q× d)/(p×r 2 e 0) = 7,2 .
: 7,2×109 ; 7,2 .
12. , . 1 /3, 60 .
: r = 1 /3 = 1000 /3,
m = 60 ,
: .
.
C = 4 pe 0 R.
: V = (4/3) p R 3, :
R = [(3 V)/(4 p)]1/3.
:
V = m / r, R = [(3 m)/(4 pr)]1/3, ,
C = 4 pe 0 R = 4 pe 0[(3 m)/(4 pr)]1/3 = 9 .
, :
|
|
I = dq / dt. (2.3.40)
:
j = I / S, (2.3.41)
S , .
:
U = IR, (2.3.42)
U ( ) , I , R .
, :
R = rl / S, (2.3.43)
r , l , S .
-:
Q = ò I 2 Rdt, (2.3.44)
Q , R t.
, R , :
P = IU = I 2 R. (2.3.45)
:
h = / . (2.3.46)
. , .
m , ,
m = (AIt)/(FZ), (2.3.47)
A , Z , F (F = 96000 /), I , t .
, 6080 .
:
2030 ,
1520 ,
35 ,
23 .
. . , , .
13. , , q (t) = t 2 +t 3. .
: q (t) = t 2 +t 3,
= 1/2, = 1 /3,
t = 1 c.
: I.
. (2.3.40) :
I = dq / dt = 2 t + 3 t 2 = 5 .
: 5 .
14. 107 ×, 4 . 1 , 1 2. .
: r = 107 ×,
I = 4 A,
l = 1 ,
S = 1 2 = 1×106 2.
: U.
. (2.3.42) (2.3.43):
U = IR,
R = rl/S.
(2.3.43) (2.3.42), :
U = IR = (Irl)/ S = 0,4 .
: 0,4 .
15. 2 , 1 . , 20 .
: I = 2 A,
R = 1 ,
t = 20 .
: Q.
. - (2.3.44):
Q = ò I 2 Rdt = I 2 R = 80 .
: 80 .
16. , 20 , 15´15 2.
: I = 20 = 20×103 ,
S = 15´15 2 = 225×104 2
: j.
. (2.3.41):
|
|
j = I / S = 0,089 /2.
: 0,089 /2.
17. 1, 50 1000 , , , 16 .
: = 16 ,
U = 50 ,
R = 1000 .
: h.
. (2.3.46):
h = / ,
, , , (2.3.45) (2.3.42),
= IU = I 2 R,
U = IR Þ I = U / R, = U 2/ R.
(2.3.46) :
h = / = U 2/(R ) = 502/(1000×16) = 0,16,
: h = ( / )×100% = 16%.
: 16%.
18. , , 4 0,05 /2 25 2.
: t = 4 = 240 ,
j = 0,05 /2 = 0,5 /2,
S = 25 2 = 2,5×103 2,
Z = 1 ( ),
F = 96000 /.
: N.
. , , , , :
N = N×n. (2.3.48)
, , (2.3.47):
m = (AIt)/(FZ),
:
n = m / A =(It)/(FZ). (2.3.49)
(2.3.41):
j = I / S Þ I = jS, (2.3.49) :
n = m / A =(It)/(FZ) = (jSt)/(FZ).
(2.3.49) (2.3.48) :
N = N × n = (NjSt)/(FZ) = 1,9×1018.
: 1,9×1018.