2
F Q1 Q2; r ; e - ; e0 :
- , ; n .
= F/q,
F , q, .
:
) S, ,
; dS ; ;
) , ,
=EScosa.
.
. , q1, q2,, qn,
,
; .
, q r ,
, R, q, r :
) ( < R)
=0;
) ( = R)
) ( > R)
() , , ( ) , () :
= 1+2++ .
1 2
1 2.
, ( ) r ,
t .
, , , ():
, ,
s .
, , , :
, s ( )
( ) , .
D
|
|
.
, . .
:
- , , :
j= /q,
1. , :
j = A/q.
2. .
, :
= - .
, q ,
, , q R, r :
(r < R) ;
(r = R) ;
(r > R)
e , .
, , j1, j2,, jn, q1, q2,, qn:
W q1, q2,, qn , ,
ji , n - 1 ( i-) , qi.
= - gradj.
, ,
, .. , , ,
E = (j1 - j2)/d,
j1 j2 ; d .
, Q , j1, , j2,
El ; dl .
= qE.l cos a,
l ; a l.
=D q / D j
D q , (); Dj , .
|
|
R, e,
, .
S ( ); d ; e , .
, di ei ( ),
( R1 R2, e)
( l R1 R 2, e)
:
n ;
n 1
:
1 = 1.
Q, j :
; U .
( , )
ŗ e; D .
Q , t.
, S :
k , .
r ; l .
G g
r r0 t 0; t ( ); a .
:
Ri i- : .
:
(j1=j2) I = e /R
(j1 - j2) ; e12 , ; U ; R ( .
. : , , , . .
n , .
: , . .
Ii i- ; Ri i- ; ξ i i- ; , ; k , .
, t,
Q , t.
, .
|
|
dB , ; m ; m0 = 4p×10-7 / ; d l , dl ( ); I ; r -, , .
dB
a d l r.
( , )
R .
, ,
r .
, ,
, , -cosj2 = cosj1 = cosj , ,
, ( ),
n , ; I .
: B1, B 2,, , . .
a 1 2.
. , ,
I ; I , I ; .
F
I .
I1 12, d , I,
S , S, , .
, , ,
a .
()
, e, x,;
, c ; B.
F, Q, v ( ),
a , v .
=I D,
D , , ; I .
( )
e i ; N ; y .
:
) U l, v ,
a v ;
|
|
) ξi, , N , S, w
wt .
Q, ,
R ; Dy .
ξi, ,
L .
L .
()
() (. . 24.1),
I , R L:
)
; t , ;
)
I0 t = 0; t , .
W , L,
I .
() (, )
1. l = 30 t = 1 /. r0 = 20 Q1 = 10 , . F .
. . , , , . dl, d Q = tdl Q1 d Q:
(1)
r Q1.
, , r0 Q1 . r dl (1),
(2)
, d F , , , : d F1, , d F2, .
, dF1 = dF×cosa, dF2 = dF×sina. dF (2) , :
-b +b,
Q1 :
, , Q1,
(3)
, . sinb (3).
(4)
(4):
2. , s=400 /2, , t = 100 /. r = 10 Q = 10 . , , , , .
. , , ,
F = Eq, (1)
, q.
, , , . , , ,
(2)
, , .
(3)
, , Q, 1 2 , (. 14.5): = 1 + 2. 1 2 ,
1 2 (2) (3) ,
F, , (1):
(4)
Q, e0, s, t, p r (4) ,
F = 289 .
F, Q, . . ,
|
|
tg a = , a = arctg ().
s, t, p r ,
= 5134'.
3. R1 = 6 R2 = 10 Q1= 1 Q2 = - 0,5 . , r1 = 5 , r2 = 9 r3 = 15 . (r}.
. , , , : 1(r < R1}, II(R1 < r2 < R2), III(r3 > R2).
1. 1 I S1 r1, . I ,
(1)
En .
, . . En = E1 = const.
. (1)
,
E1=0,
. . , r1 < R1, .
2. II r2. Q1, , ,
(2)
En = 2 == const,
.
,
(3)
3. III r3. Q1 + Q2., , ,
, , ,
(4)
, (3) (4) :
(Q1 =10-9 , Q2 = - 0,5 ×10-9 , r2 = 0,09 , r2 = 0,15 , 1/(4pe0) = 9 × 109 /) :
2 = 9×109 / =1,11×103 / =1,11/;
3 = 9×109 / = 200/.
4. (r). I (r1 <.R1) = 0. II(R1 £ r < R2) 2(r) 1/2. r = R1 E2(R1) = = 2500 /. r = R2 (r R2 ) E2(R2) = = 900 /. III (r>R2) (r) 1/r2, r = R2 (r R2 ) E3(R2)= = 450 /. , (r) r = R1 r = R2, . (r) .
4. , R, t = 10 /. j , , . I 1/3 15 .
. , , . dl. dQ = tdl, , .
. dE , dQ:
r -, dl , . dE dEx dEy :
i j (). :
l. dEx .
r=R=const dl=Rdu,
dEy (1) , , 0 p/3, :
R (3 l = 2pR),
, . l ,
. dj, dQ
r R :
l = 2pR/3,
,
5. U0 = 10 , U1 = 100 , , . d 2. 20 . , l 2 = 1 .
. :
1) v 0, U0, ;
2) . v, .
,
|| = h1 + h2,
h1 , ; h 2 D , , v 0, , .
h1 h 2.
,
, ; t .
= F/m, F , ; . , F = = eU1 /d, ; U1 ; d .
t = v0 t,
t1 . v 0 , , : mv /2 = eUo.
(1) , F, t v ,
h2 MDC :
v1 ; l2, .
v1 v1 = at, , F t
v1 (3),
, v (3),
||
U1, Uo, d, l1 l2 ,
6. 1 = 2 = ξ. U1 , , , e = 7?
. : U1 = U2 = e /2. e :
, . . = . , , .
Q . ,
,
(1),
, , :
e
, 1,75 .
7. C1 = 3 U1 = 40 . 2 = 5 . DW, .
. , ,
W1 , ; W2, , , .
(1) W = CU2/2 , ,
1 C2 ; U1 , ; U2 .
, , U2 : U2 = . U2, (2),
, DW=1,5 .
8. 100 , 150 r = 50 . RB = 500 , . ?
. U1 , -A B (.),
I1 ; R1 .
I1 :
R .
R :
R1 ,
,
,
(2) (3), :
I1 R1 (1), :
I2, , . . U2 = I2(R/2),
f, ,
9. R=20 Dt = 2 I0 = 0 Imax = 6 . Q 1, , Q 2 , Q 2/ Q 1.
. Q = I2Rt (I = const.). ,
I .
k - , , :
(2) (1)
, Dt, (3) t1 t2.
, , t1 = 0, t2 = 1 , ,
t1 = 1 , t2 = 2
,
. . 7 , .
10. I = 50 a = 2p/3. . d = 5 .
. , . 1 2 , 1 2, . . = 1 + 2. B2 . , , , dB = 0([d lr ] = 0).
1 , (3), 3:
r0 1
a1 0 ( ),
a2 = a = 2p/3(cosa2 = cos(2p/3)) = 1/2. r0 = dsin(p a) = dsin(p/3) = d .
= 1 (2 = 0),
B1 . . 21.6 ( ).
1.
:
11. l = 2,5 , d = 20 , I=1 . F .
. , , . , . , ( I1 I2) .
F1,2, , I1, I2. ( .), I2. B1. 2
, I2 dl2
dl B1,
(2) 1 (1),
F1,2 :
, I1 = I2 = I l2 = l,
, ():
:
.F1,2 dF1,2 ( ) .
12. , v = 2 /, = 30 = 30 . R h , .
. , , , , v :
Q