Bài tập phần điện, vật lý đại cương, khoa Vật lý, Đại học sư phạm
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (652.5 KB, 117 trang )
()* ( +
2 34
5
67
%
< . <= .
D=−
B
E
F
$"
G
5
&<
,
,
)
'
-
=
- =
8
D =−
9 1
&< B
B
=
,
'
.
, '
)/ ( 01) & >
8
%
9 1
. ()* (
: ;
(
?@
#
$% &'
,
'
-
0 ( 0 : )/ ( − 0 ? B
≈ 0)BC ( −+ A
:()* ( − ( ? B
HI ; 7
J= 3K
- O $#
)/ ( 01) & M 6N
8
R
-
!"
)/ ( 0 1
9
DB = −
9
J= 3K )
$
)/P ( BP &
L )
O@
B
Q
B
D
&< B
0 ( 0 : )/ ( − 0 ? B
=
=
≈ )B* ( C/ : L ?
−
− BP B
B
DB Q
/)/P ( : )/P ( ?
C
< > L
L HN 3
% < > L
Z $# /((
< > L $#
S
&
O T $% &'
H
S
"= V
X , ' <( . Y ( P1)
F
' & M 6N
- % < > L " &
. B(
T
;
>
& M 6N
6N
U
2
&
W
O
HN 3 $
%
[ \
"
]
% < > L
M
,
'
^ < > L
9
6N
@
Bα
D
_
< =
<(
= B ( −P 1
B
< > L
$#
& @
_ + D3 +
`
O) 3a 3
;
_.
=(
9
J @
tgα =
Fd =
tgα =
Fd
P
kq1 q 2
kq 02
=
2
r2
4(2l. sin α )
q 02
kq 02
=
P=
64πεε 0 l 2 sin 2 α .tgα 16l 2 . sin 2 α .tgα
q 02
4πεε 0 .16l 2 sin 2 α .P
HM@
(
)
( ) ( )
2
1.9.10 9. 4.10 −7
P=
= 0,157( N )
16.0,2 2. sin 2 30 0 .tg 30 0
m=
Y
'
L
b ?
& M 6N
3L
P 0,157
=
= 0,016(kg ) = 16( g )
9,81
g
b ) O
J
< > L
HN 3
$
$
C !" #
Z
c $#
&
*Y( :ε . B M
% < >
; 3L
[ &" < > $
C)
d O M
; < > L
S
&
& '
q 02
P=
64πε 1ε 0 l 2 sin 2 α 1 .tgα 1
`
e H f _
6N @
% < > L
6;
6N
3L
W ;
@
: ?
>)
g
^ < > L HI 8
] O) $#
'
q 02
P − P1 =
64πε 2ε 0 l 2 sin 2 α 2 .tgα 2
%
% 34
67
$
F
)
:B?
hS & % @
:C?
P = mg = ρVg ; P1 = ρ 0Vg
[ : ?) :B?
:C?)
O@
P − P1 ε 1 sin 2 α 1 .tgα 1 ρ − ρ 0
=
=
P
ε 2 sin 2 α 2 .tgα 2
ρ
ε 1 sin 2 α 1 .tgα 1 .ρ = ε 2 sin 2 α 2 .tgα 2 ( ρ − ρ 0 )
ε 2 . sin 2 α 2 .tgα 2
ρ = ρ0 .
ε 2 . sin 2 α 2 .tgα 2 − ε 1.sin 2 α1.tgα1
HM ; @ ε 1 = 1; ε 2 = 2; α 1 = 30 0 ; α 2 = 27 0 ; ρ 0 = 800(kg / m 3 )
ρ=
*
3
2. sin 2 27 0.tg 27 0
.800 = 2550(kg / m 3 )
2. sin 2 27 0.tg 27 0 − sin 2 30 0.tg 30 0
< > L
O
W 3
& M 6N
$# $
,
$#
O $% &'
A 6Z
ρ
#
\ O
HM
& M 6N
,
ε
% HN 3
$#
X
b & M 6N
&
& '
6N
J
U
,
L HN
:3L ? O
- < > L :ρ? = >
,
6
2 34
% '
%
d
U$
ρ = ρ1 .
i;
W &,
O ,
5
% HN 3
U
hX
&'
ε
ε−
& '
ε −1
J
,
6
@
ρ1
'
1
) & M 6N
0
.
)/ ( 1)
\
X
W
l% 8
9 M
B+
. 0) ( & ) & >
%
X < j
\ X
$
k $%
[
. (+
"
m
\ X
1
'
V
<
< j
Fht = FCoulomb
v2
e2
m
=
r
4πεε 0 r 2
v2 =
r.e 2
e2
=
m.4πεε 0 r 2 4πεε 0 mr
v=
HM)
sin 2 α 1 .tgα
sin 2 α 2 .tgα 2
sin 2 α 1 .tgα 1 = sin 2 α 2 .tgα 2
ε
,
<
< j
&
O@
@
ρ=
/
ρ 0 = ρ1 , ε 2 = ε , ε 1 = 1 )
ε .sin 2 α 2 .tgα 2
= ρ1
ε .sin 2 α 2 .tgα 2 − sin 2 α 1 .tgα1
α1 = α 2
$\
Y)
e2
4πεε 0 mr
=
e
2 πεε 0 mr
O@
v=
1,6.10 −19
−12
−31
2 π .1.8,86.10 .9,1.10 .10
−10
= 1,6.10 6 (m / s )
k 36; % 34
-
6;
P
% c e) !) 1 - X
. C ( +1R S
e 1 $ " e1 . C
&
& '
%
6Z
L 6N S % , '
( ( +1 l% 8
% 34
n
N=
) e! . Y ) !1 . *
1%
, '
W
F1
e
F
F2
!
1
O@
oE
F1 =
F1 -
q1q 2
3.10 −8.5.10 −8
=
= 8,4.10 −3 ( N )
2
−12
−2 2
4πεε 0 rAB 4π .1.8,86.10 .(4.10 )
oE
F2 =
<@
F2 -
<@
q1q3
3.10 −8.10.10 −8
=
= 30.10 −3 ( N )
2
4πεε 0 rAC
4π .1.8,86.10 −12.(3.10 − 2 ) 2
o ]a 3
i9 )
9
J @
BC 2 = AB 2 + AC 2
% e!1
E
F
e `
O = 67
N= ;
tgα =
1 W
pX ;
- F
-
O@
e1
F1 8,4.10 −3
=
≈ 0,28
F2 30.10 −3
6
6N '
I
$#
@
X
O
V%
8
α = 15 0 42'
$U @
\ @<
, '
S
F = F12 + F22 = (8,4.10 −3 ) 2 + (30.10 −3 ) 2 = 3,11.10 −2 ( N )
+
1O
,
M
,
'
Qg ∆
3J
lf
' $#
O) = 67
, '
O
-
6Z
,
% 3J
% 34
<( : T
'
F1 =
q
3J
q1q0
4πεε 0 (B C ) 2
=
1 5
,
;
#
'
<( H
e! M
,
'
q 2 q0
4πεε 0 ( AC ) 2
S
g
H
,
!? S
'
<
\
%
; 6Z
W
q
%
1 #
∆
O@
; ∆)
F H
H
= F2
D
∆
1
D
DB
e
lf
= L
- n
N=
!
F 3g
∆@
F∆ = F1 cos α − F2 cos α = ( F1 − F2 ) cos α = 0
i9 ) F
6Z
q
c O
M
= L 6;
F = F1 sin α + F2 sin α =
0
&'
% 34
'
( . *
= 67
2 q1q0
sin α
4πεε 0
l AB
2 sin α
X
,
,
W
'
;
2
=
O
;
2 q1q0 sin 3 α
2
πεε 0l AB
\ < . :*rC? ( 01 S U
, ' s . C ( P1 : S
k
&
V
?
" $%
k V "
% 34
)
O@
' 3s 1
t u
J
,
k
'
,
3
Fx = dF sin α ;
:
= L
3
<
3D %= 34
Fy = dF cos α
V " ?
:
k
< 3DV
V " ?
O@
3D
;
dF =
dQ.q
4πεε 0 r02
dQ =
Q
dl ;
πr0
]
'
M V5
dl = r0 .dα
dF =
2
4π εε 0 r02
)
V
dα
J
D . ()
π
2
F = Fx =
2
−
π
2
0 0
4π εε r
cos α .dα =
2
2π εε 0 r02
2
HM@
F=
3.10 −7.(5 / 3).10 −9
= 1,14.10 − 3 ( N )
2
−12
−2 2
2.π .1.8,86.10 .(5.10 )
( 1O
(
,
'
&
16Z
X
,
hA . 3 . (
\ < . + ( +1
& ':
? '
@
$U %
'
6Z
) he . Y
,
) h! . *
O
%
) h1 . 0
A1 . P
B E
% 34
,
'
< . * ( (1 S
1
)
\
%
e) !) 1 1
X & >
$"@
3.
1
<
!
= 34
op,
6Z
t
3 <
u
J
h
e
,
6Z
e T
A
@
= 67
T
W @
v1
1
v1
v!
h
!
E A = E A1 + E A2 =
EA =
q1
4πεε 0 ( AM )
2
v1B
<
+
ve
e
q2
4πεε 0 ( AN ) 2
1
8.10−8
3.10 −8
+
4π .1.8,86.10 −12 (4.10 − 2 ) 2 (6.10 − 2 ) 2
= 52,5.10 4 (V / m)
op,
6Z
3 <
E B = E B1 − E B2 =
EB =
! T
q1
4πεε 0 ( BM )
2
−
= 67
6N
W @
q2
4πεε 0 ( BN ) 2
1
8.10 −8
3.10 −8
−
= 27,6.10 4 (V / m)
−12
−2 2
−2 2
4π .1.8,86.10
(5.10 )
(15.10 )
o _ 67
)
W
]T
8
t
- ve
HM
v! 6N V%
H)
6N @
8
6
I
EC = EC21 + EC22 − 2 EC1 EC 2 cos α
w
O@
2
2
MC 2 + NC 2 − MN 2 9 2 + 7 2 − 10 2
cos α =
=
= 0,23
2 MC.NC
2 .9 .7
2
MN = MC + NC − 2 MC.NC. cos α
8.10 −8
=
=
= 8,87.10 4 (V / m)
−12
−2 2
2
4πεε 0 (CM )
4π .8,86.10 .(9.10 )
q1
EC
1
q2
3.10−8
=
= 5,50.10 4 (V / m)
−12
−2 2
2
4πεε 0 (CN )
4π .8,86.10 .(7.10 )
EC =
2
i9 @
EC = (8,87.10 4 ) 2 + (5,50.10 4 ) 2 − 2.8,87.10 4.5,50.10 4.0,23 = 9,34.10 4 (V / m)
p\ V%
8
= 67
EC
1
sin θ
=
- v1)
EC
sin α
V%
8
O θ
1 W
v1
1A
8
t
HM H @
E C sin α
sin θ =
1
EC
8,87.104. 1 − (0,23) 2
= 0,92
sin θ =
9,34.104
B
O
θ = 67 009'
O@ FC = q.EC = 5.10 −10.9,34.10 4 = 0,467.10 −4 ( N )
-
D1
1
6N
,
,
6Z
O@
'
J
M
E = E1 − E2 =
;
'
,
W
-
<
B< S
6Z
,
,
' )
q
2
0 1
4πεε r
−
,
2q
2
0 2
4πεε r
,
6Z
%
(
6Z
=
v1
3
q
4πεε 0
I
b
\
6Z
T
1 2
−
r12 r22
= 67
M
6N
W
Q>H
\ h %
, ' < X & >
' B< X & >
: ? ;
& >
%
q
E=
4πεε 0
)
,
<
6Z
B<
,
p\
h %
,
1
2
=0
−
2
r
(l − r ) 2
1
2
−
=0
2
r
(l − r ) 2
(l − r ) 2 = 2 r 2
l − r = 2r
r=
i9 )
, '
,
l
1+ 2
6Z
8 ' %
,
'
B C
,
'
10
≈ 4,14(cm)
1+ 2
,
B l% 8
6Z
- O O S@
/
=
,
'
X
,
'
<
6Z
$#
T
C
,
<
B<
Y) Y : ?
'
U
,
\
X 4
%
h #
W
)$" #
367
v( . ( :3
? 1%
,
9
%
,
'
' 367
6H @
367
$
6N
J @ % S= , 6Z
6Z
O T
X ;
M
U H%
c
3J
W 8 HM W $#
A"
S
H% c
- 4 % W % , ' $#
, ' U % c
M 3 , HI
% , 6Z $#
,
K
] 9 ) , 6Z
n
X
B p\ S $
,
O $ % V"=
6Z
'
,
S V
M V5
'
T
3J )
6
% $#
4
%
6N
&
S=
W )
?
T
&I ;
:v ) vY?) :vB) v*?
X ;
H%
c
-
4
%
W )
@
:vC) v/? T
= 67
T
W
1%
S=
, '
N= ;
$#
]
'
Y) B *
C/
% O $#
M V5
,
6Z
%
B(( :
n
,
/
vB*
I?
N= O
*
6Z
B((
Y
x
% 8 $#
v
Y
vC/
(
$? 1%
1%
,
'
367
S=
6
,
'
I@
S
Y) B *
E = 2 E14 =
? 1%
,
'
C/
%
,
6Z
q
=
4πεε 0 a 2
Y
x
*
πεε 0 a
Y
2
6
B
C
v 6;
v
E = E14 =
Y ( 1r
vB*
vC/
q
B
/
2πεε 0 a 2
Y
/
x
$ @
S= , '
T 3J S
% c
M 3,
x %
, 6Z
O T
X ;
6
6N
W ] O)
, 6Z 3
S= , ' B * C /
x $# &
$#
, 6Z 3 S= , '
Y
x@
0
*
q
6N @ , 6Z
n
X
O X ; $# @
6Z v Y
,
C
B
$#
v
'
S
C
Y
E14 = E25 = E36 = 2 E1 = 2
O \ 3a 3
= 67
-
"=@
B
C
i9 )
,
6Z
x
q
2πεε 0 a 2
B) eey
X S = q
!
X < > L '
6N
- < > L $#
L ,
X O $#
.
$
)
'
3J
,
;
W ; 9 X ,
S σ.
, T
, '
S = q
` M
0
< >
, '
- O $# < . ( 1 b HN 3
H ; = 67
q
5
e
α
!
ey
8 '
$#
@
T +F+P=0
O@
[
P = mg ;
I
tgα =
F = Eq =
σq
2εε 0
J @
F
σq
4.10 −5.10 −9
=
=
= 0,2309
P 2εε 0 mg 2.1.8,86.10 −12.10 − 3.9,81
α = 130
e
α
D
ey
_
Y hX
G
l% 8
$./
B 1 5
6Z
k $% &'
6Z
X
#
X
,
.+
,
6Z
'
z
,
X
W
\
" $→(
$\
5
6Z
$U X S = q
;
9
X
,
4
-
G
S σ . ( +1r
%
6N HI
\
,
W
B
G
X
$\
5
'
C 1 5
X ,
#
" $
$U X
6Z
$\
, '
5
\
6N
\
$\
5
'
6Z
3v
3vB
e
3v
$
x
3<
1
i
G
& {
O
[
'
,
3>
n
& {
@
X
O $W X
3 lf 3>
& {
O $% &'
:| ?
dQ = σ .2πr.dr
1
8
& {
t
p,
%
u
%
J
6Z
,
dE O
6Z
,
)
'
,
&
6Z
3
3< 1
,
e $#
n
J > %
= L dE 1
dE 2 ]
;
O
dE
(
)
> G
(
)
3/ 2
.dQ =
'
M V5
bσ .r.dr
(
2εε 0 r 2 + b 2
e @
a
0
r.dr
(r
2
+b
)
2 3/ 2
bσ
1
=
−
2
2εε 0
r + b2
a
=
0
e
% 8 dE O
xe
dE
dq
b
b
=
.
2
2
2
2
4πεε 0 r + b
4πεε 0 r 2 + b 2
r +b
bσ
E = dEr =
2εε 0
6Z
i9 @
dE r = dE 2 = dE cos α )
p,
6Z
\=
= L dE1 $#
dEr =
\
σ
1
1−
2εε 0
1 + a 2 / b2
)
3/ 2
n
10 −8
1
E=
1−
≈ 226 (V / m )
−12
−2 2
−2 2
2.8,86.10
1 + (8.10 ) / (6.10 )
B A"
$ → ()
O@
1
σ
σ
=
1−
b → 0 2εε
2εε 0
1 + a2 / b2
0
E = lim
p,
6Z
&
C A" $
$→( O$\
) %= 34
5
5
M
L
;
,
6Z
3
S = q
'
,
W
l%
8
@
a2
≈1− 2
2b
1 + a2 / b2
1
i9 @ E =
p,
a2
σ
1− 1− 2
2εε 0
2b
6Z
&
* hX
X
$
O$\
S
,
=
$%
L
6Z
q
σ .a 2
σ .(πa 2 )
=
=
2
2
4εε 0b
4πεε 0b
4πεε 0b 2
5
'
M
,
x - $%
;
W )
,
9
6Z
X
3
X
,
'
\
S σ . ( 01r
,
B
6Z
L
3v
x
3
1
$% L
6N '
, ' @
dQ =
; θ
O
;
L
O $W X
3 :'
σ .2πrh .dh 2πσrh .dh
=
= 2πσR.dh.
cosθ
(rh / R )
S
; L
4
M V5
-
; L
= 67
4
-
O? p;
L
'
67
x O 6;
dE =
EJ
6= L
I
6
h
(
2
h
4πεε 0 r + h
'
)
2 3/ 2
L
.dQ =
=
- $
Y)
O X ; $# @
[ ( " z)
O@
/ hX
X
(
#
6
3v 3
R
=
;
L
0
σ
4εε 0
< . B ( P1 l% 8
z . C((
%
$M W
>
1
6Z
10 −9
= 28,2 (V / m)
4.1.8,86.10 −12
E=
&
\
,
O@
h2
σ .h.
σ
=
E = dE =
dh
2εε 0 R 2
2εε 0 R 2 2
0
ε = 1)
6N
h.2πσR.dh
4πεε 0 R 3
R
1
'
,
%
'
,
L
6N =
1
'
b 3V 1
O
,
'
6Z
X
,
6Z
z( .
\
q
l
@ dq = dx =
q
2 R 2 − R02
dx
dE
dE2
dE1
(
z
z(
V
rB
lf
,
6Z
= L dE1
'
M V5
3
dE
dE 2 p ,
n
J > %
3V
6Z
\
n
X
E
= L dE1 $#
Vf
n
&
J
O
> %
O@
\ %
,
6Z
dE
dE
O ]
dq
dE2 =
=
2
4πεε 0 r
. cos α =
qR0
(
4πεε 0l R02 + x 2
)
3/ 2
l/2
E = dE 2 =
(
dx
4πεε 0lR 0
HM@
4πεε 0 l(R 02 + x 2 )
cos α .dα =
−α 0
E=
α0
qR 0
α0
q
)
3/ 2
−l / 2
=
1
R0
q
.
. dx
2
2
2
2
4πεε 0 R0 + x
R0 + x l
q
4πεε 0lR 0
qR 0
R0
dα
dx =
2
2
2
2
3/ 2
x = R tgα 4πεε l
cos
.(
R
+
R
tg
)
α
α
0 −α
0
0
0
0
[sin α ]
2.10 −7
≈ 6.103 (V / m)
4π .1.8,86.10 −12.3.0,1
P hX S = q
'
, W ;
$% &'
b H ; &'
6;
#
6Z
q
O
X
$
O
\
9
X σ
op,
6Z
W
S = q
X
3
'
,
S = q
6Z
3
op,
6Z
3
#
'
,
&
'
8 ' ^ '
W
,
,
,
6
W
\
X
;
Vf
S O X ^ n
6Z
X \
^ n ) %
O
S = q
9
X σ
@
σ
2εε 0
G
E2 =
9 Xσ
& >
S '
6Z
X
; S = q
<
O ^ n
G $% &'
E1 =
op,
α0
l
q
2q sin α 0
q
.
=
=
=
− α 0 4πεε 0lR 0 2πεε 0lR 0 2R 4πεε 0 RR 0
\
Vf
@ :V
%
'
$
Y?
σ
1
1−
2εε 0
1 + a 2 / b2
S = q
E = E1 − E2 =
G
T
σ
2εε 0 1 + a 2 / b 2
= 67
6N
W
@
'
,
+ hX
$4
X
, ' X 3 3K
q
X
& > ()Y
U L 6Z
- 3 3K J p
3 3K
3
% 34
$4 Q > " #
*( )
, ' < . B ( P1 l% 8
< 6N =
$M W
HN 3
H O S - >
6U
" H =
$M O
lf
S Q V
U T
W
S
HN 3
2 34
8
4 %
% HN 3
X & >
txV
V& Q V)
E.2πR0 .h =
E=
E
,
z( O 4
k $% &'
q0
εε 0
=
T
z(
O@
; HN 3 )
)
O
W
\
,
W
O S
O O 6
O
:
6Z
?
S
4
1 q1h
.
εε 0 l
q1
2πεε 0 R0l
% 34
$4
@
q1q2
1,7.10 −16.2.10 −7
F = Eq2 =
=
≈ 10−10 ( N )
−12
−3
2πεε 0 R0l 2π .1.8,86.10 .4.10 .1,5
0
,
6
X
E
6Z
b
# H
% 34
X S = q
% 34
, 6Z
H
; S = q
k
#
F1 =
Fi =
% 34
]
,
6Z
H
H
Fk =
3
S = q
Ei = Ek
,
&
#
'
&
; S = q
@
q Ei
#
F2 =
'
O
@
q Ek
'
F1 = F2
,
W
,
6Z
W
@
,
"
i9 )
% 34
B( hX
S = q
% 34
$"
9
J )
op,
op,
X
X
'
3
S = q
- 3
@
X
λ . C ( +1r
&
= 4
X
%
@
7
E=
S 3
,
6Z
O@
σ
2εε 0
8
W 3 3
@
σλL 2.10 −5.3.10 −6.1
=
≈ 3,4( N )
2εε 0 2.1.8,86.10 −12
l% 8
8 ' $# &
$" & >
%
if 7 6Z
8
S σ .B ( 01r B b
, W 1
q = λL
^
F = Eq =
, W O 9 X , '
W 3 X HN 3 3
- 3
3
% 34
B
7
, 3
% 34
6Z
i9 )
6
,
\
6Z
<
U L
N= H
, '
\ <
@ ? < )
6Z
X
\
h $J &} $#
E = E1 + E2
; E1
%
E2
p\ E . ()
= > O@
V
,
,
'
6Z
v
X
,
6Z
3 < )
E1 = − E2
h
<
o
f 7 6Z
vB T
= 67
)h= >
#
6Z
q
<
\
S
%
o
,
6Z
vB T
v
X ; @
E1 = E 2
q1
4πεε 0 x
2
=
q2
4πεε 0 (l − x )
2
q
x
=± 1
l−x
q2
q1
q2
±l
x=
o
,
6Z
1±
q1
q2
v
vB
A" < )
3J
q1
=
q1 ±
6N
BB Q
l
#
q1 + q2
h= >
x < 0 hay x > l
x=
' @
l
#
,
q1
q1 −
l
3K
4H
H
,
,
" ~ . *((i !% &'
6Z
X , 6Z
\
3 3K S
&
& '
V
E=
1
N= n < % @ " g &
, 6Z
h @
λ
2πεε 0 x
+
λ
l−x
=
λl
2πεε 0 x(l − x)
' @
q2
3
Vf 6Z
6Z
X
q1
q2
=
W @
q1
x=
B A" < )
q2
2
q1
(l − x )
q2
x=±
h= >
0< x
x
l−x
%
" 3,
- & >
X & >
^ 3
%
>
[
%
\
. *
. ()
HN 3
h "
4 3
6Z
S X
d V% 8
$" #
%
3K
5
J
; λ
9
X
, 3
3
hS & % @
3~ . v3V
l−r
1
λ l −r 1
λ
[ln x − ln(l − x )] = λ ln l − r
+
dx =
2πεε 0 r x l − x
2πεε 0
r
πεε 0
r
U = − Edx =
πεε 0U
λ=
ln
"λ
$\
E=
l −r
r
5
1
6Z
l
l
2πεε 0 l
. l−
2
2
HM@
E=
BC 1
X
O@ 1
,
6Z
πεε 0U
.
ln
=
l−r
r
V . rB)
O@
2U
l−r
l. ln
r
2.1500
≈ 4.103 (V / m )
0,149
0,15. ln
0,001
, '
, &
G
X
< . B ( /1) \
'
\
,
( /1 S %
6Z
q
(
M
-
G
]J
q1
A = q2
HM@
[
A=
\
,
'
0(
, &
38
\
,
'
\
e "
e . i9 @
'
,
4πεε 0 r
(
−
q2
l.q1q2
=
4πεε 0 (l + r )
4πεε 0 r (l + r )
)
0,9. − 10 −6 .2.10 −6
≈ −0,162( J )
4π .1.8,86.10 −12.0,1.1
L
,
X
\ 6
V
,
'
<
\
! @
OV
BY
'
L
< > L
O
1
'
9
X
-
" \ 38
, $% &'
G
.
, &
38
X
\ h %
!" < > L
B
S σ . ( 1r
,
X , ' < . : rC? ( P1 [
X & > z. (
V
\
\
,
'
@
e . < :ie • i!?
i9 @
A = q.
=
HM@
A=
B* hX k
" @
B hX
1
3<
3
\
h
k
4πεε 0 R1
=
4πεε 0 R2
"3
(
)
k $% &'
Y
4
4πεε 0 R1
(do R2 = ∞)
2
k
'
,
3 ) %
h
4
k
W
-
T
;
k
b3
3 ) %
-
k
4πεε 0 R 2 + h 2
> k
h @
k
dq
2
4πεε 0 R + h
: .(?@
2
=
,
3
dq
V = dV =
"
10 −7.(1 / 3).10 −7. 10 −2
≈ 3,42.10 − 7 (J )
−12
−2
1.8,86.10 .11.10
dV =
p,
Q
3
\
p,
−
q.4π .r 2 .σ
σqr 2
=
4πεε 0 (r + R ) εε 0 (r + R )
3
k
Q
Q
4πεε 0 R 2 + h 2
,
3
'
s . : r0? ( +1
X
.C
'
3< p ,
X
"3
@
'
,
,
'
VO =
B p,
"
4πεε 0 R
=
h: .C
VH =
(1 / 9).10−8
4π .1.8,86.10 −12.4.10 − 2
?@
Q
4πεε 0 R 2 + h 2
(1 / 9).10−8
=
4π .1.8,86.10 −12
(4.10 ) + (3.10 )
−2 2
−2 2
= 200(V )
3
'
)
B
.B )&
- 3
,
,
W
'
O
X
38
,
3e . < 3i
dA = q.(− Edr ) = −q.
A = dA = −
λ=
i9 @
λ=
BP
X
:
= 250(V )
'
\ < . :BrC? ( 01 #
%
X HN 3
. Y R 36; % 34
,
6Z 3 HN 3
6;
6Z H5
, 6Z
" & >
%
P
9 X , 3
,
X
e . *( ( € '
B/ hX
,
& >
\
6Z
O@
Q
,
qλ
2πεε 0
λ
dr
2πεε 0 r
r2
r1
dr
qλ
=−
(ln r2 − ln r1 ) = qλ ln r1
2πεε 0 r2
r
2πεε 0
2πεε 0 A
r
q. ln 1
r2
2.π .1.8,86.10 −12.50.10 −7
≈ 6.10 − 7 (C / m )
4
−9
(2 / 3).10 . ln
2
&
, O \ O X
6Z
>& > &
n ) ' 34 6
n
? 6N &
•
6Z
= 67
G
O
,
,
= 67
- % f 7 6Z
6Z
&
n
6
% 8
O ; % f 7 ,
6Z
E
e
!
E
]
lf
6Z
&'
9
1
6
I)
O@
dV = − E.dl
VA − VA = −
E.dl
ABCDA
=−
E.dl + E.dl + E.dl + E.dl
AB
BC
CD
DA
= −(E1 .AB + 0 − E 2 .CD + 0)
= (E 2 − E1 )l = 0
i9 @ A" = 67
&
n
B+
'
X
6Z
- f 7 6Z
$X &
,
"
\ e
N= H @
$U
O $#
X
`
,
6Z
O ,
X < > L 3K
n
%
,
X
\
#
B
X
\
#
< > L
C
X
\
#
< > L
&
6Z
n
% 8 6
,
"3
[
S -
O
, < $#
%
, '
\
< > L
%
$W
X
$#
O w
W$
,
)
= >
"
%
z
V
x
1
< > L
k
6N '
r = R2 − h2
,
;
dq = σ .dS = σ .
;
O
S
cos α =
'
67
6
r
R
$
I @
,
"3
3
B*)
X
4
,
"3
,
S σ=
-
k
4πεε 0 r 2 + (h + x )
>
,
O ]a
2
S L
=
2
#
V=
=2
q
+ x + 2 hx
< > L :V . (?
\
k
3
@
=
x
X & >
qdh
8πεε 0 R R 2 + x 2 + 2hx
@
( R + x − R − x ) = 4πεεq 0 R
=
8πεε 0 xR
4πεε 0 x
"
e %
8πεε 0 R r 2 + h 2 + x 2 + 2hx
q
B p,
-
b $% &'
J @
\
q.dh
V=
T
'
q.dh
2
2
t=R
− R8πεε 0 R R + x + 2hx
"
W 3L 3
q
p,
4πR 2
3
q
p,
O
q
q.dh
.2πR.dh =
2
4πR
2R
dq
R
V = dV =
9
'
2πr.dh
cos α
dq =
dV =
i9 )
k
3
e
(R+ x)2
16πεε 0 xR ( R − x ) 2
( R + x) 2
dt
q
=
.2 t
t 16πεε 0 xR
(R − x )2
[ ]
(x ≤ R )
(x > R )
S L :V . z?@
q
4πεε 0 R
< > L ) %
q
4πεε 0 (R + a )
S L
X & >
:V . z o ?@
V
B0
1
'
,
"
X
\
G
X &
>
pG
O $% &'
G
,
'
dq
"3
4πεε 0 x 2 + h 2
> G
V = dV =
0
σ
2εε 0
C( ` >
&
$>
X
9
X
G
k
,
& { $% &'
$
B*) ,
2πσxdx
4πεε 0 x 2 + h 2
=
,
-
V) $W X
"3
3V _ L
& {
%
& {
@
σxdx
2εε 0 x 2 + h 2
σxdx
2εε 0 x 2 + h 2
(R
%
2
+ h2 − h
=2
t = x +h2
σ
4εε 0
R2 +h2
h
2
R 2 + h2
dt
σ
2 t
=
t 4εε 0
h2
[ ]
)
$> 4 ,
3 . * ) 6Z
X ,
6Z
$>
$ 3g
6Z H5 - , 6Z
[
$# / ( ir hX
$> &
- 4 , ; 9 M $
L $# &
9 M O$
; $>
5
- 4 , Q > " $b < >
6U
- g
Y
n
H
&
,
6Z
M
@ e . ~ . v3
hS & % @
A=
v2 =
W
S σ
6Z
1
'
@
R
i9 @ V =
=
z)
= L
dq = σ .dS = σ .2πxdx
dV =
p,
4
1
1
1
mv 22 − mv12 = mv 22
2
2
2
( 3 v1 = 0)
2A
2eEd
2.1,6.10 −19.6.10 4.5.10 −2
=
=
≈ 3,26.107 (m / s )
−31
m
m
9,1.10
