primena gausovog zakona zadaci
TRANSCRIPT
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1. a ab 2 , QQa QQb 2 ( 1).
.
r . rE r .
1 1.1 1.2
________________________________________________________________________________
.
. .
( 1.1):
I) a ( ar ),II) a b ( bra ),III) ( b , br ).
r( ) :
240cos rESEdSEdSEdSESdE
SSSS
,
.
S dS S Sd
, (
) , Sd
.
:
0
24
QrE ,
204 r
QE
.
I) ar
. , ( 1.2)
S ,
- .
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ar ,
, 0Q , :
20
20 4
0
4 rr
QE
,
0E .
ar , :
0)0( arE .
II) bra
a , QQa . :
QQ ,
, .
, :
204 r
QE
.
ar br :
204
)0(a
QarE
,
)0(4
1
4)0(
20
arEb
QbrE
.
III) br
r, br , :
QQQQ 32 .
:
204
3
r
QE
,
br , :
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)0(4
3
4
3)0(
20
arEb
QbrE
.
,
,
.
, , ,
.
III) br
r
Qdr
r
QdrE
rr 02
0 4
3
4
3
.
,
,
rrr
drEdrEdlE .
br :
a
Q
b
Qbr
00 8
3
4
3)0(
.
II) bra
,
:
148
311
48
3
4 00002
0 r
a
a
Q
a
Q
br
Q
a
Qdr
r
QEdrEdrrdE
b
rb
b
rr
.
:
a
Q
b
a
a
Q
br 00 8
3
14)0(
,
a
Qar
02)0(
.
I) ar
.
, 2
04 r
QE
,
204
3
r
QE
:
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a
Qardr
r
Qdr
r
QdrdrEdrEdrEdrE
bb
b
a
a
r
b
a
a
rr 02
02
0 2
)0(4
3
40
.
( ar ) , .
. ,
, . ,
.
1.2 1.3,
.
1.2 1.3
. ar ar , bra bra ,
br br .
,
.
2. , a b
QQa 2 QQb ( 2).
r . .
: cm4a , cm6b , nC6Q .
2
________________________________________________________________________________
.
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r , .
.
:
I) ar
, , 0Q , 0E .
II) bra
QQ 2 ,
0
2 24
QErEdSSdE
SS
,
0
2 2
4 Q
Er ,
:
202 r
QE
.
III) br
QQQQ 2 ,
0
24
QErEdSSdE
SS
,
204 r
QE
.
: a
b .
, . :
V90011
211
22 0
02
0
ba
Qkba
Qdr
r
QEdrldEU
b
a
b
a
b
a
ab
,
gde jeF
m109 90 k .
3. , a ab 2 ,
QQa QQb 5 ( 3). .
.
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3
________________________________________________________________________________
:
I) ar
,
, 0Q , 0E , 00 arE .
II) bra
QQQ a ,
0
24
Q
rEdSEEdSSdE
SSS
,
204 r
QE
.
(
)
:
2
040
a
QaE
,
041
1640
20
20
aEa
Q
b
QbE
.
III) br
QQQQ ba 4 ,
QrEdSEEdSSdE
SSS
44 2
,
20rQE
. 3.1
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, .
rEE
. rE r .
3.1
.
, , .
,
.
:
2
02
0 40
a
Q
b
QbE
.
:
III) br
r
QEdr
r 0
,
a
Q
b
Qbr
00 20
.
II) bra
aar
Q
a
Q
br
QEdrEdr
b
b
r
2
2
11
42
11
4 000 ,
ar
Q
2
51
4 0 .
022
5
2
1
40
00
br
a
Q
aa
Qbr
,
a
Q
aa
Qar
00
8
3
2
51
40
.
I) ar
a
Qardr
r
Qdr
r
QdrdrEdrEdrEdrE
bb
b
a
a
r
b
a
a
rr 02
02
0 8
3)0()(
40
.
3.2 3.3, .
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3.2 3.3
4. , a b ( a
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, .
( ar , bra ,
br ).
I) ar
, 0Q , 0E (
).
II) bra
22
0
2
0
24 aradrrr
adVQ
r
aV
,
24rESdE
S
,
2
0
220
0
2202
2
24
r
araE
araEr
.
III) br
22
0
2
0 24 abadrrr
a
dVQ
b
aV
,
2
0
220
0
2202
2
24
r
abaE
abaEr
.
2
1
bar
2
0
220
2 r
araE
.
r 1r :
0
0210
2210
194
21
araraEE rr .
bar 2 ,
20
220
2 r
abaE
, r 2r
:
0
0220
220
23
4
22
a
r
abaEE rr
.
5. , cm4a cm1b , m3d ( bad , ) (5).
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?
nC10Q .
5 5.1
________________________________________________________________________________
,
Q . . , a a
aQ , b bQ .
.
,
:
QQQ ba .
bad , ,
.
.
(.. ). .
( 0E (A B), a b ,
0B
Edr ):
ba ,b
Qk
a
Qk ba 00 .
:
bba QQb
aQ 4 , ba QQQ , bQQ 5 ,
nC25
Q
Qb , nC85
4
QQa .
, :
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20x
QkE aa ; 20 )( xd
QkE bb
.
( ba EE ):
2020 )(4
xdQk
xQk bb
,
0483 22 ddxx ,
:
m2
3
2
dx . ( dx 2 ).
6. , cm3a , cm1b cm4c , ( 6).
c nC40Q , a , :
) ;
) .
6
________________________________________________________________________________
a) , , . Q ,
:
cba QQQQ .
,
cba ;c
Qk
b
Qk
a
Qk cba 000 ;
c
Q
b
Q
a
Q cba ,
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( 2: 2Srang ).
bQ cQ aQ ,
:
ab Qa
bQ , ac Qa
cQ , aQa
c
a
bQ
1 ,
:
nC15aQ ; nC5bQ ; nC20cQ .
b)
, :
m
kV15020 a
QkE aa ; m
kV45020 b
QkE bb ; m
kV5.11220 c
QkE cc .
7. , cm1a , cm4b cm5c , nC100Q .
( 7). a
(), :
) ;
) :
) .
7
________________________________________________________________________________
.
) nC50cQ ; nC10aQ ; nC40bQ .
)m
MV9.0
20 a
QkE aa ;
m
MV225.0
20 b
QkE bb ;
m
MV18.0
20 c
QkE cc .
) kV90 aEaQk aa
cba .
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8. a , Q ,
b bc ( 8). . ,
r .
rE r . : .
8 8.1
________________________________________________________________________________
ar0 crb . ,
( 8.1).
, , ,
. , .
.
0
QSdE
S
,
2
4rEdSEdSESdESSS
,
0
24
QrE .
ar , 0Q , , , 0E .
( ).
:
bra : QQ 204 r
QE
;
crb : 0 QQQ 0E ;
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cr : QQQQQ 204 r
QE
.
:
cr :r
Q
r
Qdr
r
QdrE
rrr 002
0 4
1
44
;c
Qc
04 .
crb : cc
c
rr
drr
QdrrdE
2
040
;c
Qcb
04 .
bra : drr
Qdrdr
r
QdrEdrEdrEdrE
c
c
b
b
rc
c
b
b
rr
2
02
0 40
4 ,
cbr
Q
c
Q
br
Q 111
44
11
4 000 ;
cba
Qa
111
4 0 .
ar : drr
Qdrdr
r
QdrdrEdrEdrEdrEdrE
c
c
b
b
a
a
rc
c
b
b
ar
a
r
2
02
0 40
40
,
cba
Qa
111
4 0 .
8.2 8.3.
8.2 8.3
9. , a ab 2 , , qq 1 qq 32 ,( 9). r )(rE )(r .
arp 4 .
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9
9.1
________________________________________________________________________________
, .
I) ar0 , , , 0E , , 0)0( arE .
II) bra , , r L ( 9.1).
( S
SdE
) - .
( GBS
DBS
)
2
. ,
.
.
:
LrEdSEdSEdSESdESdESdESdE
SSSS SSS
20cos2
cos2
cos
0DBGBGB 0DB
0
0
DB
0
GB
.
:
LqLqdlqQ
L
''' 1 .
:0
2
Lq
ErL
,
r( ):
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r
q
r
qE
00
1
22
.
, :
a
q
arE02
)0(
, a
q
b
q
brE00 42
)0(
.
III) br , LqLqqdlqQL
'2)''(' 21 ,
:
r
q
r
qqE
00
21
2
.
:
a
qbrE
02)0(
.
: pp r
r
r
r
rErE dd
.
III) br , :
r
aq
r
rqr
r
qrE
p
r
r
r
r
pp
4lnlndd
000
,
,
2ln)0(0
q
br
.
II) bra , :
pr
b
b
rrr
q
rr
q
dd2 00 ,
:
2ln2
ln2 00
q
r
aq
.
, ,
:
)0(2ln)0(0
brq
br
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:
2ln2
2ln2ln2
)0(000
qqq
ar
.
I) ar0 , :
pr
b
b
a
a
r
rr
qr
r
qr dd
2d0
00 ,
2ln2
)0()0(0
q
arar
.
,
9.2 9.3:
9.2
9.3
10. a , q , b
bc ( 10). . r .
: cm20a , cm60b , cm65c , m/nC100q .
10
________________________________________________________________________________
,
( q ),
( q ). ,
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, ,
.
, r
h , ,
.
, :
I) ar , 0Q , , . 0E .
II) , bra ,
hqQ , :
hrEESSdE oSo
2
,
:
0
2
hq
hrE
,
r
qE
02
.
III) , crb , 0 hqhqQ , 0E .
IV) , cr , hqhqhqhqQ , :
r
qE
02
.
, ,
10.1.
10.1
11. , ,
( L ) , a
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( 11).
( r), 2
2
0a
r ,
0 . arp 2 .
11 11.1________________________________________________________________________________
,
L , r . ,
.
, ,
.
,
.
I) ar0 , , :
VS
dVSdE 0
1;
r
SSS
drrLa
rEdSEdSEdS
ODBGB 0
2
2
0
0
00
21
0cos2
cos2
cos
;
r
drra
LLrE
0
3
20
022
;
4
4
20
0 r
aEr
;
2
0
30
4 a
rrE
.
II) , ar , :
VS
dVSdE 0
1;
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a
SSS
drrLa
rEdSEdSEdS
ODBGB 0
2
2
0
0
00
21
0cos2
cos2
cos
;
a
drra
LLrE
0
3
2
0
022
;
4
4
20
0 a
aEr
;
r
aE
0
20
4
.
:
ar :
r
radr
r
a pr
r
p
ln44 0
20
0
20
;
r
aa 2ln
4 0
20
;
2ln4 0
20
aar .
ar0 :
pr
a
a
r
drr
adrr
a 0
203
20
0
44
;
a
rara
a
pln
444 0
20
44
20
0
;
2ln41
16 4
4
0
20
a
ra
;
2ln41160 0
2
0
ar ;
2ln4 0
20
aar .
11.2 11.3
.
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11.2 11.3
12. , mm1a
mm718.2b ,
4r .
)
?
)
kV2U ?________________________________________________________________________________
) , ,
.
.
,
( 1C ), ( 2C ), :
a
bC
ln
2 r01
;
a
bC
ln
2 02
.
:
pF/m8.1663 212 CCCC .
, .
.
) kV2U , .
1q 2q , .
:
UCq 11 , UCq 22 ;
nC/m6.3333 212 qqqq .
:
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211
2
1UCW , 222
2
1UCW ,
J/m106.333 6
12 WWW .
13. , C100Q ,
5r . , -.
mMV20krE .
________________________________________________________________________________
,
.
5r . ,
, 0 , , 0r .
:
ar
r
Q
ar
E
r
,4
,0
20
.
. ,
, ar :
2
0
max4 a
QEarE
r
a
.
.
, .
.
,
.
.
mMV3Vkr E , , , ,
...
,
, (
).
,
.
, . . ,
.
, .
.
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, :
kr
r
Ea
QE
20
max4
; krr
Ea
Q
2min04
; mm868,944 0
min krrE
Qa
.
14. ( a b ) r ( 14).
U . :
) ;
) , q .
: mm8a , mm16b , 3.2r , kV35U .
14
________________________________________________________________________________
:
br
bra
r
r
qE
0
,
,0
2
,0
r0;
abq
rr
qrErEU
b
a
b
a
b
a
ln2
d2
ddr0r0
m
C452.6
ln
2 r0 U
a
bq
m
MV156.3
ln2 r0
min
a
bb
U
b
qEE b
,
m
MV312.6
ln2 r0
max
a
ba
U
a
qEE a
.
15. , a c ,
q .
b d(
15).
) r ;
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) cm1a , cm2.1b cm2c , ,
( 0C ) (C )
5.00
C
C.
15
________________________________________________________________________________
15.1 15.2
) ,
( q ),
, q ( 15.1).
. :
hErESSdESdESdESdE oSSSS BBo
2
00
21
;
ar : 00 EQ ;
bra :r
qEhqQ
02
;
dbrb : 00 EhqhqQ ;
crdb :r
qEhqhqhqhqQ
02
;
cr : 00 EhqhqhqhqQ .
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b) :
a
cC
ln
2 00
,
:
I) :
dbacbq
db
c
a
bqr
r
qrr
r
qrErEU
c
db
db
b
b
a
c
a
c
a
ln2
lnln2
d2
d0d2
dd0000
,
:
dbacb
C
ln
2 0 .
II)
( 15.2): ,
a
bC
ln
2 01
,
,
db
cC
ln
2 02
. :
dbacb
CCC
CCC
CCC
ln
2111 0
21
21
21
.
CC 2
10 , :
cm5.01
a
cbd .