1. .
1
t = 8 R = 8 Q = 500 . q, , .
.
: I = I(t) = kt,
k .
, dt - , :
dQ = I2(t)R(t)dt.
, :
(1)
: , dq = I dt.
, t:
(2)
(1): ; .
(2):
.
: q = 19,36 .
2
N = 400 . , I = 2 . 0 = 10-3 .
.
wm V. wm = BH/2; V = 2πR π(R - r)2, R , r ( ). = S = π(R - r)2. W = wm V = (/2)2πR (/). = Ni/2πR, :
W = nI/2 = 400×2×10-3/2 = 0,4 ().
3
, 103 , 40 10 2.
, , 1.
.
= μ0nI, n . ,
= nBS;
().
: = 10-3p = 3, 14.10-3 .
4
( 1) , I = 0,5 , N = 1000, 8 2, R = 10 c .
r R
. , .
:
= NI/2πR = 103. 0,5/6.28. 0,1 = 0, 796. 103 /. , μ = 200. = μ μ0 = 200. 4π.10-7. 0,796.103 = 0,2 . = . S = 0,2.8.10-4 = 1,6. 10-4
5
, . , O?
.
|
|
. , , , - . , , , (.).
q1 = 3,3×10-9 q2 = -13,3×10-9 (2,0,0) (-2,0,0) . :
1) (0,3,4);
2) , . .
, , . r1= r2 =
. ,
= 1/()
= 1/() ( )
, . , r = , :
= (k|q1| / (r2)) ; 2 = (k|q2| / (r2)) ,
= + ; = ( / r2 r)(-q1x1 q2x2),
y = ( / r3)*(-q1y1 q2y2); z = ( / r3)(-q1z1 q2z2)
= (9*109*103 / ()3)((10-11)(3,3*4 13,3*4)).
, . , q1 . :
F1 = kq1q / x2; F2 = kq2q / (4 + x)2;q1 / x2 = q2 / (4 + x)2;
(x + 4) / x = ; x = 4 / ( - 1).
6
R =5 l = 6*10-6 /.
j .
.
dl. :
dE = (tdl/4pee r2)×(r/r), t - , r -: dj = tdl/4pee0r.
:
= òdE dEy dEx.
E = òdE = `iòdE + `jòdE..
dE dE.
dEy = dE cosq, q - dE dEy q = 450, : dEy = dEcosq = tdlcosq/4pee0r -2.
dl. , :
dl = Rdq, R - , dq - , . :
dEy = tRdq/4pee0r2cosq = t/4pee Rcosqdq.
Ey, 0 p/2
: E = t/4pee R.
j : dj = tdl/4pee0 R,
dl = rdj, dj = =
j,
j = = = = .
7
R R1. , r. , .
c, D r.
|
|
=Sgi,
, . .
.
D1, D2 D3:
1) r < R1 .. .
, , .. eqi = 0. , r = 0. , D1 = 0.
2) R1 < r < R, .. .
eqi ¹ 0, r ¹ 0.
: S = 2prl.
: V = p l (r2 R12).
: D2 p r l = r p l(r2 R12)
.
3) r > R, ..
8
= 40 . , , t = 2 .
.
:
,
DF - Dt.
.. t = 2 , DF = ,
= 2, - , .
9
, . j(r).
.
, ;
dj = -Edr.
, dr, ..
.
.
10
I = 2A , . = 2. . = L = 100 , BF = h = 50 .
.
, , , = R = R1.
= a = 45.
= I/4pR(sina1 + sina2) = (I/4pR)2 /2 = I /4pR;
a1 a2 a..
, h = R2, :
: = 2,24 /
11
I = 5 A = 10 = 20 , . I1 = 0,2 A. d = 5. , .
.
, .
= . I1 d = , g = .
, . : .. F Fg, b, F, . F , , . F = Fd - Fg. .
Fd = I2bHdmo, Fg = I2bHgmo.
:
F = Fd - Fg = (moI1I2b/2p)(1/d 1/(d+a)) = 5,33 10-7 H
: F = 5,33×10-7H.
12
n . L. , - n ? ?
|
|
; - .
:
;
, n .
, , , , :
, .
. .
13
, , .
:
, S s. q R S (OA ^ . S)
S dr dj dS0, .
, dS0, . dq d S0
dq = s×dS0. (1)
dS0 - , ,
dS0 = dr×dl, (2)
dl - dj, dl = r×dj.
dS0 = r×dr×dj. (3)
dE0 , () dS0 :
(4)
r - dS0 .
j , dr.
dE, , , .
Y - dE , - , .
(4) (3), :
(5)
dj, ..
(6)
:
(7)
a dEx, dEx = dEcosa (8)
, BD = ds, ds - BD r , ÐCDB = 90. , X, :
(9)
(9) r, r a, r . . da, dr . , : r, r, dr.
DABD BD, ..
BD = rda (10)
ÐCBD = da,
(11)
DAOR r r:
r = Rtga, (12)
(13)
D .
(10); (11);(12) (13) (9), :
(14)
, (14) (7) a 0 p/2, , .
|
|
(15)
(15) , , .
14
2 /(2.). , , .
:
;
m Hm .
m = 1, = n .
, ( ):
;
( ) . m = 1,03×103 /; m = 2,72 /.
15
, R, 2a . . , (. ). , , , . y(t) , y(0) = 0. .
oz (. .). , , n = - `.
= (, n) S(y) = - BS(y),
S(y) , , . ,
(1)
, S(y) = y2/tga.
S(y) R(y) (1),
,
(2)
A = 2B2sin2a/ (Rcosa(1+sina)).
(2)
(y)1/2 = (P/A)1/2 (3)
= const, , (3),
(0) = 0, = 0. ,
16
I = atn, a - . , k- Q1. , t, R.
. -
dq = Idt, dQ = I2(t)Rdt;
; ;
2n + 1 > 0; n > 0,5;
, . , .
.
, I , , , r. , I , I. ,
B = 5 / 2 · μ0I / 2π r + 1 / 2 · μ0I / 2π r = μ0I / 4π r ·(2+π).
.
, , . I. , , .
I. ( ) , R
, , , , - , - . P = H E sin α, α - . , , . . I , α = 900, sin 900 = 1).
|
|
, . P , .. . , .
s =P 2πr l, (*)
e P - - ,
r - ,
l -
, P = H E (1)
, . = U/l,
U - , l - .
I = U/R, U = I R,
R - ,
E = IR/l, (2)
H = I/2πr, (3)
I - , r - , , .
(2) (3) (1), (*)
s = P 2πr l = (I2 R/ 2πr l). 2πr l = I2 R.
- , , .
17
. ( ) ( - ; ; z ). , ( - ). , I = 13A, - = 9, = 10, = 11. .
. = + + , .. .
=(i/4p r1) (sina1+ sina3), (1)
=(i/4p r3) (sina1+ sina2) (2)
=(i/4p r2) (sina3+ sina2) (3)
.
. a1, a2, a3. , , :
2 = 2 + 2 - 2 × cos2a1
cos2a1 = (2 + 2 - 2)/2 = 81 + 100 -121/2×9×10 = 0,333,
cos2a2 = ( 2+2-2)/2 =81+121-81/2×10×11= 0,6363;
cos2a3 = (2+2- 2)/2=81+121-100/2×9×11= 0,05151.
cosa1, cosa2, cosa3:
a1, a2, a3
a1 = 35026439, a2 = 250241763, a3 = 290497929.
sina = Ö1-cos2a sina1, sina2, sina3. :
sina1 = 0,4284, sina2 = 0,3154, sina1 = 0,4923.
r1, r2 r3 - .
r1 . = , = . :
/ sina1 = / sing. <a = < .
= ×sina1/sing.
S = ××sina3/2 , ×sina3 = r1 .
:
S = 2×sina1 × sina3/2sin[p - (a1+a3)] =
= 2×sina1×sina3/2sin(a1+a3).
r1:
r1 = ×sina1×sina3/sin(a1+a3) =
= 9×0,4284×0,4923/0,9045×64,7623 = 2,0985.
r2 r3
r2 = ×sina2×sina3/sin(a2+a3) =
= 11×0,3154×0,4923/0,8165×54,7396 = 2,0918
r3 = ×sina1×sina2/sin(a1+a2) =
= 10×0,4284×0,3154/0,8704×60,5060 =1,5523
r1 =2,0985, r2 = 2,0918, r3 = 1,5523 (1), (2), (3). : = 0,4538, = 0,4956, = 0,39997. :
= + + = 1,3491 (/).
{0; 0; z }; z = -1,3491. ,
d 1,2 = m04p
I3dl3 = {4; 8; 3} .
d 1,2 = (-(8×1,3491) + (4×1,3491) )×10-7 =(- 0,7928 +5,3964 )×10-7 [].
2. .
1
l = 244 NaCl, r = 2,16 /3. . a .
.
NaCl . a .
NaCl A = 22,99(Na) + 35,45(Cl) = 58,44 .
58,44 NaCl :
Na = 6,02×1023 (), 2,16 (.. 13) n . :
n = Nar/A = 6,02×1023×2,16/58,44 = 2,2×1022 (./3)
, ,
V = 1/n = 1/2,2×1022 = 0,45×10-22 (3)
. , Na Cl :
= V1/3 = 3,6×10-10 ().
-
2sina = 2l; a
sina = l/ap = 2,44×10-10/3,6×10-10 = 0,68;
a = 42, 67.
Na Cl 5,63×10-10(). a1
sina1 = 2,44×10-10/5,63×10-10 = 0,43.
a1 = 25,68.
: a = 42,67; a1 = 25,68.
2
n0 = 4×107(-3). n n = 100 .
.
()
w2 = no2/meeo; no ; ; me .
w2 = 2,4×1013(1,6×10-19)2/9,1×10-31×8,85×10-12 = 7,63×1016
w = (7,63×1016)1/2 = 2,76×108 (-1).
:
w = 2pn = 6,28×108(-1).
w < w, n :
n2(w) = 1- wp2/w2 = 1 - 7,63/39,44 = 0,81, n = 0,9.
: n = 0,9.
3
.
.
(n = 1) (n = 2).
W = -Rh/n2; R , h , n .
DW = Rh(1/n12 - 1/n22) = Rh/3 = 3,29×1015 ×6,63×10-34/3=
= 7,27×10-19 .
, DW = DU, , DU , .
DU = DW/e = 7,27×10-19/1,6×10-19 = 4,54 B.
: DU = 4,54 B.
4
r, , h ( ) . ( 1,4 / 2), , . , (/2) , , .
h
m3 , ,
.
:
.
: S (1,4. 103 /2); 0 ; .
F F . :
, .
, S, h
= Bdw,
dw - , : dw = S/h2.
B = rEc/p,
, , = 1,4.105 .
5
. R = 0,080. , .
.
. ,
P = (I1-I2)/(I1+I2), (1)
I1 I2 , (.. , , ).
, , (1), . 4 (.), , .
, , ,
I0^= I0ll = 0,5 I0. (2)
, , . , . 1 ( 1). , ( 2), , ( ll), , ( *). 2 , .. . 2 , 3, , . , , ( 4), . . 1 3 , , , ,
I4ll > I0^ I4 ll = I0ll (3)
( ). I4^ , : R = I1/I0
, I1 = I1^ (.(2)):
R = I1^/I0 = I1^/2 I0^ I (4)
, ( E^) ( ) . , , (4) :
(5)
. , , I 2^= I 0^ I1^ , (5),
I 2^= I 0^(1-2R) (6)
, , ,
I4^ =I 2^ - I3^ (7)
(6) (5) (7):
I4^ =I 0^(1-2R)2 =0,5 I 0(1-2R)2
(8), (3), (2) (1),
6
, n1, n2. , h0, , , ?
, A0 (.) n1 n2 , , N. , , A0C A0D. . , , . : n1 > n2 ( ) n1 < n2 ( , , ).
A0D , , D, 1/. , 1. , A0, A/1, A1. A0, h/1 h1 .
, D a,
b b1
, , A0DC A1DC D .
CD = h0 tga = h1 tgb ( h0 tg a = h1 tg b1)
h1= h0 * (h1= h0* ).
, a b
h1 = h0* (h11=h0* ).
= , , h1=h0* .
. , h1 < h0 , n1 < n2 (, , ). (, ), , , n2 > n1 h1 > h0
7
. , θ
0 (. )
|| = 0 sin (900 - θ) = 0 cos θ
,
Imax = 0 2, - Im = 0 2 cos2 θ
=
: ( ) n1 n2. . n1 = 1,5 n2 = 1,9.
.
( ) , , ( ) (. .).
n2 sin x = n1 sin 90o sin x = n1/n2 = 1.5/1.9 = 0.7895.
α = 52,1363
. ( ) ( ). , , .
. α,
tg α = n1/n2,, (1)
r , ( ).
, , , .
112 .. .., .. (. 588) :
Rp = (n1cosα2 - n2cosα1) /(n1cosα2 + n2cosα1) (1)
- . Rp = 0,
n1cosα2 = n2cosα1 (2)
n2sinα2 = n1sinα1 (3)
(2) n 12 cos 2 α2 = n 22 cosα 12,
n 12(1 sin2α2) = n 22(1 sin2α1). (4)
(2) sinα1 = n2 sinα2 / n1.
,