Электричество и магнетизм: Лабораторный практикум

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  • -2001

    -

  • 2

    53 223

    45 : . . , . . , . . , . .

    , . . , . . , . . , . . ,. . , . . 45 : . / . . . /. ., 2001. 73 .: .

    .

    1- - .

    : ; - ..

    -

    - - , 2001

    . . . .

    020341 07.05.97. 16.09.01. 26.11.01. 6084 1/16. . 3. . . . . 4,18. . .-. 4,30.. -. . 4,5. 500 .

    - -

    190000, -, . . , 67

  • 3

    1

    . - , .

    . - 1010, 108, - , -, - .

    1 (. 1). - 2, 3, . - 4. - - . - 6 7, , - . 1

    1

    234

    5

    67

    8

    9

  • 4

    . - , 5, - 6 . () . - .

    - - . , -

    M = I N S B sin , (1) INS ; N , - ; S ; B ; . , = 12 .

    ( ) , = =d J Jd Mdt (2) J .

    - ( -) - . t 0 = 12 , M NSBI. (2)

    , =J NSBq (3) , - ; q , t,

    0

    ( ) .

    = q I t dt (4) ,

    2 2 2 221 1 .

    2 2= = N S B qT J

    J(5)

    T , .

  • 5

    .

    -. - ( = 1/2 ).

    -

    M = . (6)

    (6) , M - ( ).

    W = 2 /2 + J2/2; -

    , . - = 0, J0

    2 /2 - . , - max ( = 0 ). ,

    2 2 max 0 .

    2 2 =

    C J (7)

    (7) (5)

    max.= q K (8)

    =JC

    KNSB

    (9)

    . , -

    q () ,

    .= qCu (10)

    - , n -

  • 6

    . (8), , , - n

    q = Kn. (11) K -

    .C0. - (10) (11)

    q0 = C0u; (12)

    q0 = Kn0. (13) (12) (13) q0,

    0

    0.C uK

    n= (14)

    (10) (11), -

    .KnCu

    = (15)

    u , , - (14) K (15),

    0

    0.C nC

    n= (16)

    . . 2. 1 , V. R . 2 ( 1) ( 2). 3 - C0, C1, C2, -

    . 2

    2

    11 1

    2220

    V-24

    3

    1

    R

    12 3 4

    5

    1

  • 7

    C1 C2. 4 .

    . - , . 2, , . 1, - . 1. 3 - C0. 2 - C0 ( 1) - ( 2 2) - n0. . , - C1 C2, -. . . 1.

    1

    u, B n0 n1 n2 n3 n4

    . 1. - 0n! , 1n! , 2n! ,

    3n! , 4n! . . 1.2. K! , -

    0n! ( (14)).3. -

    1C! , 2C! , 3C! , 4C! ( (16) (15)).4. 1C! 2C! , -

    C3 C4. . 2.

    2, , , 3, , 4,

    5. - ( -,. , ).

    3C!1C! 2C! 4C!K!

  • 8

    6. - .

    7. - K! , 1C! , 2C! , 3C! , 4C! - .

    1. .

    2. ?3. , -

    .4. -

    ?5. -

    .6. ?

  • 9

    2

    . - -. .

    . , - C, L R ( R - ). () 0, -

    = 0 cos ( t + ), (1), , -

    dILdt

    + IR + 1C q = 0 cos ( t + ), (2)

    I ; q .,

    (2), - ( ) - . ( ), (2) .

    . , z z = arg z,

  • 10

    - ( j = 1 )

    (cos sin ) .jz z j z e = + = (3)

    - - , - , . , (2)

    ,qdIL RIdt C

    + + = (4)

    I ;

    ( )0 0 .

    + = = j t j te e (5)

    0 = ( -), 0 = (cos + j sin ) .

    (4) (2) : (4) (2). (5) (4),

    2

    02 1 .j td I dIL R I j e

    dt Cdt+ + = (6)

    , - , . . ( )I I t= . -

    0 ,j tI I e = (7)

    0I . (7) (6).

    0

    0

    I = R + jL +

    1 .j C (8)

  • 11

    , (8) - , . -

    Z = R + jL +1

    j C = R + j (L 1C ). (9)

    - Re (Z) = R.

    Im(Z) = L 1C . (10)

    .

    - 0

    jZ Z e = ,

    ( )220 1 ,Z R L C= + (11)1

    arctg .L C

    R

    = (12)

    Z0 - . ( (8); , ). (8) ,

    00

    0.I

    Z= (13)

    (11)

    1 0.L C = (14)

  • 12

    (14) . , (14),

    1 . LC = (15)

    -, 0. - , , - , -

    00max .I R

    = (16)

    . - -, I0 .

    . 1 - R1

  • 13

    ,

    .RL = (19)

    - . / ( Q).

    . ( - ). ( = 0) . E , , E/E ( E = E(t+T) E(t); T ). Q - E /E

    Q = 2 (E /E) (20 ), Q ,

    , . .

    B , - (17)

    Q

    (21)

    ( , , , ,

  • 14

    3 , R1 R2. . - .

    . 1 . 10 . 0 R1. 1 , .

    , . , - ( - ). R1 R2, -.

    , C0, - R1 R2.

    - 1.

    . - C0 - , R1 R2. - , f = 2f. I, .

    . 3

    2

    x 0

    3

    1

    R2

    R1L

  • 15

    ( ). - - 1 2 (. 2). Q1 Q2, R1 R2, - 1 2. - (15), L . , , , -. - , .

    , Cx R1 R2, . - L Cx. - , Q3 Q4, 3 4, - R1 R2. - . .

    : . 1. (22) - (19). . - Z0min = R. (18)( (13) (16)) , (Z0)2 / (Z0min )2 = 2 = 1, 2., (11)

    2 21( ) ; =L RC (23)

    201 ,R LCL

    = = (24)

    , (LC)1 = 02 ( - 0 = ). = R/L, (23)

    = 2 2 . = (25)

  • 16

    = 1, 2. 1 < 0, 2 > 0, ,

    w 1 =2 20 1 , w 2 =

    2 22 0 . (26)

    (2 + 1) = 2 2.2 1

    (2 + 1) , g = R/L,

    R/L = 2 1, (27). . (19).

    2. , . -

    1 0dIL IR qdt C

    + + =

    ( (2 ), = 0 ),

    q'' + 2q' + 02 q = 0 (2 = R/L, 02 = 1/LC ).

    , -

    = (02 2) 1/2,

    /0 0 .

    t tA A e A e = = (28)

    . , - , e . - N,

    Q = N = /T. (29) = 1 /, = 2/T

  • 17

    1. .2.

    ? ?3. ?4. ? ?5. -

    , ?6. -

    .

  • 18

    3

    ,

    . - , - .

    . - . - . , - . , - H. , , .

    . - - , .

    H - , , - . , - . H

    H = H1 + H2, (1) H1 = H ; H2 .

    - , H1 H2

  • 19

    , , , (. 1)

    tg = H2 / H1. (2)

    H2 -

    2 .2INHR

    = (3)

    , , - , , , R N,

    .2INHRtg

    = (4)

    , - , .

    = K0, (5) 0 ; ( 1); K -, o , - .

    , , -. - , - , - , , (. 2). U,

    q = CU = K0 U. (6)

    , . 2 b, -. , , -,

    I = n q = K 0 U. (7)

  • 20

    - - 1, (4)

    12 tg .RHIN

    = (8)

    H . (8) (9) ( = I).

    10

    2 tg ,RHNvU

    = (9)

    ( K ). 0, , -

    0 0

    1 ,c = (10)

    0 = 4107 / .

    . - . 3. - R A. - , , N . - , .

    , . 2. - , . - ( = 50 ).

    . - , . , . 3. - R. -

  • 21

    R , -- 3035. - 1 I. , , , 2. . - . 1.

    1

    I, A 1 2 H, A/

    , . 2. - - . . (). - , -. . 1.

    . 3

    . 2. 1

    !

    M

    N

    S

    NS 0'

    0

    NS 0'

    0

    a bc

    1

    R

    C

    H1

    H2

    H

  • 22

    . - , - , , - . - , .

    1. -?2. , -

    ?3. -

    . ?4. -

    ?5. -

    ?6. .

  • 23

    4

    . .

    . - ,

    121 (cos cos ),2H nI= (1)

    H ; n ; I ; 1 2 , (. 1, ). , , (. 1, ), , (1) :

    ( )2 31 cos cos ,2H nI= + (2) 3 = 1. , - ( . 1, ), -

    H=nI. (3),

    1 .2H nI= (4)

    , -. , , -

  • 24

    (1) (2). , o . - (1) (2).

    . . - , 1. - (. 2). , - K1 K2. K K, . - 1 . R - A K

    . 1

    . 2

    ) ) 1 1 2

    2 30 0

    R

    K1 K2

    KxK

    2

    R

    1

  • 25

    K. 2 .

    K K1 , - . K1 , - K. K (3). 1, K1

    1 0 1 1 0 1 1 ,HS N S N In = = (5)

    Nn L= K; N K; L ; 0 - ; ( = 1); N1 K1; H = nI K, - I. K - , K1, 21, K1 -. - . - , . . -, K1 - , - ,

    1 ,q C= (6)

    C , - . q1 -

    11

    2 ,qR

    = (7)

    R . (6) (7)

    12 .CR

    = (8)

  • 26

    1 (5) (8),

    0 1 12 2 ,nS N I MIR R

    = = (9)

    M K K1

    0 1 1 1.M nN S= (10)

    K K1 -, . , C, - C' = CR, . , (9),

    2 .MIC = (11)

    , I, K, - , - C'.

    N2 ; S2 - Kx. Kx, - , , K2

    2 0 2 22 2 .xH N S = (12)

    q2,

    22

    2 , Cq CR R

    = = = (13)

    . (13) 2, -

    2 20.

    2xCHN S=

    (14)

    . - -

  • 27

    C'. 1 K R , - (100150 ). - K 2, - (11) -. I K. K2 Kx, 1 - Kx . Kx 2, - . - K