Документ взят из кэша поисковой машины. Адрес оригинального документа : http://genphys.phys.msu.su/rus/lab/elmag/Lab330.pdf Дата изменения: Tue Aug 30 20:23:03 2011 Дата индексирования: Mon Oct 1 22:51:36 2012 Кодировка:

.., ..



UL U

EH

I0 UR

UC

2011


2





( ) . . , , , , . , . I. R, L C (. 1). , : ( 1) (t ) = U A cos(t + ) , U A ­ , - .
R



(t

) C

L

.1. .

. (1) : (t ) = Re U e i (t + ) = Re U A e i e it = Re U 0 e it , ( 2)

(

)

(

)

(

)

U 0 = U A e i - I :

. . U

U = I Z ,

( 3)


3

Z = Z e i ­ , . , , :
ZR = R;

Z L = i L = L e ;
i 2

i

2

1 i 1 ZC = =- = e i C C C

-i

2

.(4)

1 = ) , i ( ) , 2 . , .

e

= i ( e

-i

2

UL U

EH

I UR

0

UC
.2. .

, , , U L U C
U
C

( I0 . 2). U R , (3)-(4). U C

= ZC I0 =

I0 , = - , C 2
C


U
L

( U 2

. 2).
U
L







= Z L I 0 = L I 0 , L = , 2 ( U L . 2). 2

U R 2). U R + U C (. 1)

U R = Z R I 0 = R I 0 , ( U R .

U
+U
L


4

. (. 2) :
1 L - C U - UC = tg = L UR I0 R 1 I 0 L - C = . R
R , 2L

( 5)


2 0 =

1 , LC

=

( 6)

(5) :
tg =
2 2 - 0 . 2

. ( = I - U ), :
2 - 2 = - = arctg 0 2

(7)

() (. 3). (7) , () +/2 ­/2, =0, UC=UL =0.
+/2

0

0

-/2

. 3. ()

, P, , :
P = I U c os

(=0), . (7) .3, = 0 . 0



= 0 =

1 LC

( 8)

.


5

, , . . , , (8) L : 1 1 L= 2 = , ( 9) 2 C 4 2 f C f = - , . 2 0. = 0 + ( << 0 ) , (7) : - 20 - ( - )(0 + ) tg = 0 = , 2 2 0 0
<< , tg , .. - = , , : 1 ( 10) =- . 0 , , , , (10) (6), :

R = 2 L = -2 L

-1

= +2 L

-1

.

( 11)

. . « ». X Y , , (. 4). .

yo y
O

x

xo

. 4.


6

X Y : x(t ) = x0 cos(t ) ; y (t ) = y 0 cos(t + ) . :



x(t ) y (t ) x(t ) = cos(t + ) = cos t cos - sin t sin = c os ± 1 - x si n . y0 x0 0 , : x(t ) x(t ) y (t ) c os - = ± 1- x si n x0 y0 0 2 2 x y xy 2 c os + - 2 c os = 1 - x y x0 y 0 0 0 :
x y xy + -2 cos = sin 2 y x x0 y0 0 0 x y (12) y=0 x=0, y x = ± si n ; = ± si n x0 y0 (13) x y .
2 2

2

2

.

x x0

2

si n 2 . , ( 12)

.

.

.

( 13)



, d S, N , I. d D, . r B : r µ NI B= 0 d ( ). 1 = B S , (N ) : µ0 S N 2 I = L I = 1 N = d L :


7

L=

µ0S
d

N = µ0S d

2

N d

2 2

= µ 0Vn 2 ,

( 14)

V = S d ­ , n =

N - d

. (14) (d >> D ). , (14) d d = , : D D d d L = µ0 V n 2 . ( 15) D D , , . d/D. (15) , .

2.
: 1. , . 2. , . 3. . 4. .

C1

3

C

2

L R 1
. 5.

(t

2

)

(. 5) 1 2, R, , .


8

1 R , 2 . . ( 1, 2 3), , (.5). L . , .

1. . 1. 1, 2 3 , (.5). . 2. , , 1, R (.6). . 1-2 . L RL.

C

1

3

C2

L R 1

2 YX



. 6. . 1

3. X , Y R, (. 6). . , , , . , , , , .


9

4. . ( ). , . 5. , . , L RL ( x , , x max ). ( 2 3 ). , 8 8 (. 7). , . 6. , . f0, ( Y ). f0 . 1.

. 7. (x0= y0=4 , x= y=2,5 )

7. , , y0=4 yi 0,5 , 1 .. fif0.

1. f0,
4

y0, .
0 f 0

y, .
0°

, .

f,

y0, .

y, .

y = a r c s i n y 0 .

,

4 4 4 4

0. 5 1 1. 5 2

+30°


10

0

4 4 4 4

2. 5 3 3. 5 4

+90°
y = - arcsin , y 0

f>f
f, y0, .

0

y, .

.
4 4 4 4 4 4 4 1. 1, 0. 5 1 1. 5 2 2. 5 3 3. 5

- 30°

(9) f0=f, 1 L ( ) = ( 2f 0 ) 2 C1 L . y 2. = ± arcsin y 0 yi, . 1. 3. f (). , f
2. . 1. =40 , RL(), L(). f0, . x f0 . 2. , , , , , 0=4 =2 ( , 8 8 ). f1

11

2. , 5 , <5c, . 2. 2 f0 f1 .1 2. x, f0, f1, (f0-f1) = L(), RL, L(), f,

10-12 ( 1 ).

=.
x/ D
( x

)

1.
(2f 0 ) 2 C1 L() . L() x . 2. f1 y = arcsin = , y 6 0 (10) : 2L /6 1 1 - = , = == 2( f 0 - f 1 ) 12( f 0 - f1 ) ( R + R L ) (R+RL), , : RL ( x) = 24 L( x) f - R , R- R (. .6). 3. , , x D, (14): L( x ) = µ 0 V n 2 = µ 0 S x n 2 , (14) n ­ ; S V=Sx ­ . n D (14) L (x ).
L( x ) x = D L ( x )

L( x) =

1


12

x . D (14) . 4. , R l s : l ( x) , ( 16) R L ( x) = s - . x max N , x 1 d d = 2r = max = , , , N n d 2 s= = 2. ( 17) 4 4n l x : ( 18) l (x ) = D N ( x ) = Dnx . (17)-(18) (16), : Dnx 4n 2 R L (x ) = = 4 Dn 3 x . R L x . 2 .



(

)

3. .
.1 2 , 1. 2.

1. , 8, . x max . f0. L( x max ) :


13

. (2f 0 ) L( xmax ) : C = C1 + C 2 , C2 . 2. (. 8). : C C C= 1 2 . C1 + C 2 C2 . .
2

C=

1

C C

1

C C

1

2

2

. 8. 3

4.
, 1 .

1. 1 3 , . 9, . ( 2-1 2-3 ), ( L1 (x ) R1 ( x ) L2 ( x max - x ) R2 ( x max - x ) ), 1. x 2. x = max 2 , .2, .. f0 f1. L R .

1

, , , L12. L1 L2.


14

3
L

2

1
. 9. 4

: L L R R L = 1 2 R = 1 2 . L1 + L2 R1 + R2 L1 , L2 , R1 , R2 L(x) R(x), .2. L R L R . . 3. ( ).

.
1. ? . 2. . i . 3. . 4. ? ? 5. ? ? . 6. . ? 7. . . 8. ?

. 1. .. . .: , 1983. §48, 50, 47, 38.


15

2 1 3 § 4

. 9 . 1 .

.. . III. . .: , 96. §126, 127, 129, 55. .. . .: , 1983. 1.3, 5.4. .., , .: 2003, 221, 227, 220, 81.