Электродинамика. Нетребко Н.В - 309 стр.

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§15.Ответы
309
12.41.
=
L
rt
II exp
0
, где
( )
( )
ϕψ
ω
++
= sin
22
2
0
0
Lrr
E
I ,
0
rr
L
arctg
+
=
ω
ϕ
.
12.42.
(
)
( )
LCr
LCr
arctg
+
=
2
2
1
ω
ω
ϕ
,
12.43.
n
n
arctg
2
1
max
=
ϕ
при n
L
r
=
ω
12.44.
r
L
arctg
ω
ϕ
2=
45.
C
L
C
L
L
CU
W
ω
ω
ω
ω
1
1
8
2
2
0
+
= при
LC
L
R
2
1
2
ω
ω
= .
12.46.
(
)
( )
( )
++
++
=
2
2
1
2
21
2
2
2
1
2
21
2
0
CRRRR
CRRRRE
W
ω
ω
.
12.47.
( )
12
36
2
2222
+
=
LCRC
CRLC
tg
ωω
ωω
ϕ
12.48.
(
)
(
)
(
)
[
]
(
)
(
)
[
]
tLLLLRRCItCLRCLRItE
ωωωωωωω
sincos11
2121
2
2101
2
22
2
10
+++=
12.49.
RCarctg
ω
ϕ
=
§15.Ответы                                                                                           309

                   rt                                          E
12.41. I = I 0 exp −  , где I 0 =                                             sin (ψ − ϕ ) ,
                   L                                    (r0 + r )2 + ω 2 L2
                           ωL
         ϕ = arctg                  .
                          r + r0

12.42. ϕ = arctg
                      (         ),
                     r 1 − ω 2 LC
                     ω (r C + L )
                            2


                           n −1                       r
12.43. ϕ max = arctg                    при ω =         n
                           2 n                        L
                           ωL
12.44.   ϕ = 2arctg
                            r
                                        2
                      1 
                ωL +     
        U 02 C       ωC                                       2ωL
45. W =                                         при R =                  .
         8L
                 ωL −
                        1                                   1 − ω 2 LC
                      ωC

12.46. W =
                 (
             E 02 R1 + R2 + ω 2 R12 R2 C 2                ).
             (R + R )2 + ωR R C
              1   2       1 2  
                                        (             )
                                                      2



               6ω 2 LC − ω 2 R 2 C 2 − 3
12.47. tgϕ =
                                (
                     2ωRC ω 2 LC + 1              )
12.48.
         [ (                    )           (              )]            [ (                     )
E (t ) = I 0 R1 1 − ω 2 L2 C + R2 1 − ω 2 L1C cos ωt − I 0 ωC R1 R2 − ω 2 L1 L2 + ω (L1 + L2 ) sin ωt  ]
12.49. ϕ = − arctg ω RC