Методическое пособие по физике 2
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= ('* ) 1" ϕ " ( + 1 ) (3.4.6), ) 1 *, &
) &:
Ex = − |
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= − |
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R2 + x2 |
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dx |
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4πε |
0 dx |
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! " & ' " & ) ' & (1 ( :
Ex = |
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(3.4.9) |
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4πε0 (R2 + 2 )3 2 |
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4 + & , -" (1 * ) ) *, "
' " 0 (4.3.9) ( * 0:
dE |
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1 q (R2 + 2 ) − 3qx2 |
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= 0 . |
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4πε |
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3 2 |
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" ", &
x2 + R2 – 3x2 = 0 .
& *
x = ± R
2
! " 2 % ) (4.3.9), & ):
q
Emax = 3
6πε0 R2 .
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% %&-
3.4.01. " R ) ' (1 *0 '- (" σ . 3 (1 * $ ".
3.4.02. " * $ $ *$ ) " ) ) D = 0,6 )
) " ) ) d = 0,4 ), @) ) " @ ' (" q = 6·10–7 .
3.4.03. 3 ( r1 = 4 ) & " ' (1 - " ( & & + ' (" q = 2 ). ! " " ) ( ' (" ) # ( "
( ( r2 = 2 ). 2 ) ( # = 10 2. 3 0
* ' (" .
3.4.04. ' (1 & (1 " ( - & & + ' (" q = 22 . ! " " ) ( ' (" ) # (
( Dr = 2 ), 2 ) ( = 50 2. 3
0 * ' (" .
3.4.05. , ' (1 + " $ 792 , ) 0 -
* ' (", 0 3,33·10–7 /)2. 4 ) " ?
3.4.06. '" + $" & " ) " - $" r = 1,5 ) " - $" R = 3,5 ). 1" $"- ) 1 ' * $ U0 = 2300 . 0 * &
2 " " ) ( 2- ", "-( * ( ( 1 = 2,5
) " ( ( 2 = 2 ) $".
3.4.07. " - '"- % &- " R1 = 1 ), " - R2 = 4 ). 1" ) 1 ' * -
$ U0 = 3000 . 3 (1 * ( ( r = 3 )
$ .
3.4.08. , & '" & " +) $" ) " R1 = 1 ), ) ' (1 +) *0 λ = 2·10–8 /).
" * ' * $ " & 2- (, "(# ( -
( r1 = 0,5 ) r2 = 2 ) $".
3.4.09.(" ) " & -
*0 σ = 10–7 /)2. " * ' * $ " &
(, " ' + " ( , "-( " @ -
( r = 10 ).
3.4.10.(" q = 2·10–6 " ) B ) % + " R = 40 )). 3 $ ϕ ' (1 % + %$0 -
( ( r $ % +. +& * ϕ " ( r = 20 )).
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3.5. . / )" % -/% -9 / )-/"# - 2)"#" !-/"#."! ! % ")+.
") -& /-' *-!-* *
! ) # " 2 2 & @) ' 0 -
( '$+ ' ("+ q , + ( " + '-
(", '" 0# 2 & . 2 ) 1 " * -
* *- & " " * +) 2 & ) ) ) )
pi = qil |
(3.5.1) |
-" qi — 0 ( & ' (" " (, l — , + -
$*- ' (" " ( 1 * ) + & (-
0 ) 1" 2 ) ' (" ).
! ( '$0 " 2 ' 0 ) ( '$ ,
+ B@) " *- ) ) " 2:
n
pi
P = |
i=1 |
; P = σ , |
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n |
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-" σ — ( * (' + (( '$+) ' (" "-
2, ) # ) 2 & , Pn — ) * ( -
(0# ( ( '$ .
( " 2 " , 1" 0#, &
( '$ & ' ' * 0 ' ) 0 * ))
( '$+ ' (" 2 :
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(PdS) = −qp . |
(3.5.2) |
S
" ) * + ( 2 " 2 & 0
# ) 2 ) & ) ( ( " 2-
& ' ( '$+ ' ("+.
" ( " 2 " 0-
# )
) " ( ):
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E dl = 0 . |
(3.5.3) |
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! " ( " 2 * " ') ( (:
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(EdS) = |
ε0 |
(q + qp ) , |
(3.5.4) |
S |
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& ) (3.5.3) |
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(ε 0 E+P)dS = q , |
(3.5.5) |
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S
'" * ε 0 E+P = D – 2 & "$ .
/& + (, & " ( '- " 2 P = ε0 χE , -" χ – " 2 & (
)& *, & )
D= ε0 ( χ + 1) E = ε0ε E ,
ε= χ +1– " 2 & ( $) *.
= ) ' ), I–e " ( " 2 (3.5.4) " 1 + * ' ":
(DdS) = q , |
(3.5.6) |
S |
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-" q — )) + " + ' (" " 2. ( +- -
" ( ' (" I–e ' ( ":
(DdS) = ρdV . |
(3.5.7) |
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V |
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3 - $ '" " " 2 " ( ) * - $*
(0# (1 2 &- ( " + " 0#
-& + (:
E1τ = E2τ ; |
(3.5.8) |
ε1E1n = ε2 E2n . |
(3.5.9) |
A " ) * 2 & , (
* ) " ( ( ( ( '$+ ' ("+, -
+ ) ) -" *0 ) 0 2 & -
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, 2 ) " . ' (" "
" ( * ( - ' ( *' * "
& , ) ' (".
& 2 @) " " ( ( % )
$ = ϕq ,
-" q ϕ — ' (" $ ".
, @) * "
q
$ = ϕ1 − ϕ2 =
(3.5.10)
q |
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(3.5.11) |
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U |
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-" q – 0 ( & ' (" " ", U = ϕ1 − ϕ2 –
' * $ .
( )+ * " + " ) ): $#= $1 + $2+… (3.5.12)
( )+ " * " + ":
1 |
= |
1 |
+ |
1 |
+ .... |
(3.5.13) |
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$%& $1 $2
,-(, ' @ ( ",
W = |
CU 2 |
(3.5.14) |
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2 |
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,-( ' ) " ( " & & + ' ("
W = |
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q1q2 |
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(3.5.15) |
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4πεε0 |
r |
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)-* )+ ) 3 !- $% %&
)-* ) 6. ! " " 0& 2 & ,
"" 1 0# @ " ' * $ U0.
) 1" " ) ' "-( ' " 2 " 2 &
$) *0 ε , & 2 *0 ' ( ( " 2-
). ' ( " 2 ) " ' (" + q0.
1." * , ( ( 2 & .
2.0 0 ) & +?
3 !- . (( 2-( " & ) (3.5.10) (3.5.14)
' + ( " 0# ) ' )
W = |
q2 |
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(3.5.16) |
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2$
-" q — ' (" .
' " & ) & + (-0 " 2, ') (( )-
* ", ( ') 0 ' (" dq.
') 2- " ) 1 " 0# ) -
' ) (" %%$) (3.5.16)):
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dW = |
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dq − |
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q2 |
dC . |
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C |
2$2 |
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" * |
dA = |
q |
dq — , ( 2 & ')- |
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C |
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0 ' ("; dA = |
q2 |
dC — ) & . |
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2 |
2C 2 |
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= ' * $ "" 1 ( " 1 |
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U |
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, ) 1 ' *: |
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dA = U |
dq ; |
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dA = − |
U02 |
dC . |
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1 ) 1 " & *, ' (, & & * ) ( ' ("
+ q0, & ) — q = ε q0 :
ε q0
A1 = U0dq = U0q0 (ε −1) .
q0
2 "@), ' (, & @) * & * ) ( C0 = q0 ,
U0
& ) C = ε q0 :
U0
ε q0 /v0 |
U 2 |
U q |
(ε −1) . |
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A2 = |
2 dC = − |
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q0/v0
) ' & " ( 2 ' &, & * " "-
2 ).
% %&-
3.5.01. 3 @) * ", '- " )( $& )
% ) " R1 R2, ' (1 +) ' (" ) q. 1" " ) 2- % &- " " ( " 2 " 2 & - $) *0 ε .
3.5.02. ' " "- " 2 ε = 5 '" " " 2 & (1 *0 ! = 100 /). 3 ) ) * 0 -
0 * (' + ' (".
3.5.03. ( ( " " 2 & -
(1 *0 !1 = 10 /) 1 , & - α1 ) 1" ) *0
) - ( 30°. 3 (1 * (
!2 * (' + ' (", ' -
. 2 & ( $) * "+ ε 1 = 1.
3.5.04. ! '" + " ' " , -
1 + ( 4 )) "- "- , # # "*0 100 )2. "-
' (1 0 200 0& 0 . 0 " -
*, & + & * ( ) 1" " ) " '? *
' " & , -" " 0& 0 .
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3.5.05. ! # "* 1" + - " 314 )2. (
) 1" ) 2 )). ! + "( ( '" (1 * (
) 1" ) 600 /). 0 1 ' *, & + " * ) 1" ) - " ( 0 , -
*0 ' ( " " ' (1 ( -
0&@ *0 (ε = 6)?
3.5.06. = & & + ' (" q = 3·10–6 ) # ( $ - ( ' "-
"- '- " 2 ε = 3. " ( r = 25),
R = 50 ). 3 2-0, ' 0&@ 0 " 2.
3.5.07. ( ) 1" ) - " 8 )).
! # "* 62,8 )2. 0 1 ' *, & + " * )-
1" ) " ' 1 # " #
6 )), + " " + & (1 ( 600
.
3.5.08. ! " ' " 2 ), - + "-
( ' * $ . A- 2-( 2 ) 2·10–5 1. !-
- " 0& & (1 (, " 2 +-
' ". , 0 " + * 2-
&- (, & + + * " 2, 7·10–5 1. 3 " 2-
& 0 $) *.
3.5.09. +& * @) * $" &- ", " - ) 0 " + R1 R2 ' (1 + ' (" ) q. " . 1" -
" ) " ( " 2 ε .
3.5.10. 3 @) * ", '- " )( " +) -
) " a , "(# ) ( " " 2 & $) *0
ε . ( ) 1" $) b, & ) b >> a () 1 & *, & ' (" ) " ( ( ).
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"! )" 8!% )%," % ; 3
" " 1 * 5 ' " & - , ) - "
" $% % ' & 1.
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3 ) ' " & |
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1 |
3.1.01 |
3.2.02 |
3.3.04 |
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3.4.05 |
3.5.07 |
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2 |
3.1.02 |
3.2.03 |
3.3.05 |
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3.4.06 |
3.5.08 |
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3 |
3.1.03 |
3.2.04 |
3.3.06 |
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3.4.07 |
3.5.09 |
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4 |
3.1.04 |
3.2.05 |
3.3.07 |
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3.4.08 |
3.5.10 |
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5 |
3.1.05 |
3.2.06 |
3.3.08 |
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3.4.09 |
3.5.01 |
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6 |
3.1.06 |
3.2.07 |
3.3.09 |
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3.4.10 |
3.5.02 |
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7 |
3.1.07 |
3.2.08 |
3.3.10 |
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3.4.01 |
3.5.03 |
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8 |
3.1.08 |
3.2.09 |
3.3.01 |
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3.4.02 |
3.5.04 |
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9 |
3.1.09 |
3.2.10 |
3.3.02 |
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3.4.03 |
3.5.05 |
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10 |
3.1.10 |
3.2.01 |
3.3.03 |
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3.4.04 |
3.5.06 |
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29
IV
30