ر ا
ا ول :
),-
ا ؤوس AوBوCوD
لا
ا )
آ
و
(' $%& a = 20cmآ
آ 67ا 45$ ا لا 23(1-1 (1د " .ات " آ 67ا 45$ ا لا 23 ( 2-1د " .ات " (- (2ض ا ! $%ا ? د 67ا أ Aو $%! ، C آ 67ا 45$ ا لا 23 (1-2د " .ات " آ (2-2ا 67 H 3ا 2& C 45$ة ا ل ا ا ! $%ا ? دة 67ا .C 45$ آ $ا 5I4 ا
آ ر !" #
مر
par SBIRO Abdelkrim
. q = +1µC :
" Oآ .ا ). :; $" Mا .CD (45 q ' = −1µC "! :; $" Mا .CD (45 ا 2%ث " Gف ا ! %ا ? دة 67ا ؤوس AوBوCD . D
2& B $ة ا 5ة
************************************************************************************************************
ا
ا : 6- K
************************************************************************************************************
ا
ا:L K
.q # l = 10cmوآ ' P % ، m = 10 gن MN-ا ! $%ا آ $ن " PKن OAو ’ G ،O’Aل آ Qوا$" 23 ا نآ ) .ا S-ا ! .( Q 2 Iآ ر6ا $ا - ، D = 7cm 5 ( 6 45- H 5 2$ب TUV ، d = 5cmا AA' 7ا 5
" Y
ا ! q $%؟
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ا
ا ا ): Q %آ -اس آ ا ;% N \I4-
و" از AوBرأ [. 7 % N آ & 2? ،q $%ا $اس " ) از. '-او ا %$ 7 U AB = V A − VB = 500Vف ا $اس
$ Q;Nا . d = 10cm : 7 . α = 10°ا S-ا ! . Q
ا ;% N آ ا 2%ث (1أ ] " .ات ا ل ا . ا آ $ا 5I4 23 (2د " .ات ا 5ة ا آ ا $اس. 23 (3د Yوإ& رة ا ! q $%ا % 6 (4ا Y G H 3ا ) ا وا Y 4 (? " M 45$ا
آ$ )ا
2$ا آ. $
ا
( : 64آ Aو.B
g = 10 N / kg ، l = 30cm ، m = 1g :
). N
************************************************************************************************************
ا
ا : M" a d=10cm 7 K" $ Q;Nا . UAB D [A % Nو "Bاز \I4r r r -27 ا ; " % Nا O 45$ا[ Qا ( (0, i , j ) C آ Eا 2%ث QU2و ن آ ' m=1,76.10 kgا ل ا " a Vo = 10m / s S$ج " ا S 45$ذات ا ;Nل ). YSا S-ا ! .( Q
UAB؟ " (1إ& رة ا ا Iو ن PUل ا 5 -dل " ا O 45$إ ا . S 45$ آ $ا 5I4 (2ا Qe& H 3ا 5ة ا ( $%& ، YS = 5cm ، U AB = 100V : 64ا Iو ن. q = +e = +1,6.10 −19 C :آ . $ا Y G Y B $ا ) ا ى ا 657dا ر " ا O 45$آ ?) Y 4ا ) ا a-(3ر ا ا Iو ن 2$ا Q - .S 45$وزن ا Iو ن وا 3dآ ت. (4اH 3
أ57
r Vo
آ I $و ن 2$ا . S 45$
************************************************************************************************************
**************************************************************************************************************
ا
ا
):
آ - d=5cm 7 " $ Q;N ،ا و" از [A % Nو Bرأ ), ' Yا " %آ %$ 7 E ' = 100Vف ا $اس ا 2 ; Qا ;% N؟ ? Qا .g ا ;% N U ABا \I4 " (1إ& رة ا (2إ ] " .ات " (3ا2& H 3ة ا 5ة ا (4أو? I( 2آ
آ
(5ا Qe& H 3ا 5ة ا
r
ا لا آ E $ا 2%ث r . ا آ Fe $ا 5I4 ا $اس d2 m
ا ;% N
.
α ، Feو CD. gاY H 3
r آ Fe $أ $Dء ا 5 -ل ا $اس " ا
آ Q % L=10cm ' G $آ ' &. q = −0,5µC $% " ) از '-ا أ . 6او . α = 10°
. g = 10 N / kg : 64(- .
) ا 6#2Iإ
ا
) ا . 6# $
************************************************************************************************************
. d = 1m 7 " 6 $ C 45- 67 5
أن
إAB
:
$ Q;N و (45 ل اG
"Kا
ا
" L K" رؤوس
),-
45- $%& ),q 2 = +2nC : وq1 = +0,5nC ةU اkT ك ه% 7 q 3 = q1 L % q3 # آ$%& AB (45 إ ا6 $ 45- 67 ),. AB 45 . Y H 3 اCD d وq 2 ، q1 d2 AC 7 اI( 2?(أو1 DBوA
. q = +10 −8 C
45- 67 6 ا ا
! " 45- %& ثPD a = 5cm '( .
Y H 3 اCD $%& Qآ
، عP
5I4 اo7
وي ا
ا$آ
ة ا5 ة ا2& Fe I( 23(2
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: ) . #$ ا%& ا. AB
. d = 20cm ' ) لا ك%
و !ا
C
BوA + % q3 , % آ
:
ت ا0 ا
q 2 = 2 q :و q 2 = 3q
ا ا AB
q 2 وq1 ' إ ا
آ
AB ' ا q1 = q 2 = q 3 = q q1 = q 3 = q : وq1 = q3 = q
ا
C
C
ا !" !"
! ا2
د45 (1 (2 (3
************************************************************************************************************
: p %; ا ************************************************************************************************************
: ا ول . DوCوBوA %! ف اG " ث2% ) وي " ع " ت ا ل ا r r r r ا ا. ا ةو E A وE B , EC , E D ت نا
اp %; (1
ا. " آO 45$ ا67 آ ا لا " (1-1 (1 r r r r r q = +1µC > 0 أن EO = E A + E B + EC + E D
a2 :ن 2 q 10 −6 E A = E B = EC = E D = K . 2 = 9.10 9. = 45.10 6 V / m −4 a /2 2.10
. رسq
$ هI" OA 2 = OB 2 = OC 2 = OD 2 =
r r r r r E A + EC = 0 إذن، ن " ( آ ن%$" وCS$ اMNE A وEC r r r r r r r r r r r EO = E A + E B + EC + E D = 0 : 6 وE B + E D = 0 إذن، ن " ( آ ن%$" وCS$ اMNEB وED -----------------------------------------------------------------------------------------------------------------------------------. .CD (45 ا:; $" M 45$ ا67 آ ا لا " (2-1 r r r r r r r r r ا ا. ا ةو E A وE B , EC , E D ت نا q = +1µC > 0 أن E M = E A + E B + EC + E D
r r r E D + EC = 0 إذن، ن# آ% & و& (' ن 2
a AM 2 = a 2 + : )& 2
E A = EB = K.
q AM
2
= 9.10 9.
10 −6 1 0,2 2 × (1 + ) 4
= 18.10 4 V / m ة
ا
r r E D وEC
ا
r r E A وEB
-----------------------------------------------------------------------------------------------------------------------------------(1-2 (2 . .CD (45 ا:; $" M 45$ ا67 آ ا لا " r r r r r r r ا ا. ا '* و+, E B وE D *' نا q > 0 أن E M = E A + E B + EC + E D r r . ا ا. ا ا ' '* و, اE A وEC '
tan α ' =
a =2 a/2
α ' = tan −1 (2) = 63,4° E1 = E C + E D = 2.K
q ( a / 2)
E2 = 2.E A . cosα ' = 2 × K.
2
= 2 × 9.10 9.
q' a a2 + 2
10 −6 = 18.10 5 V / m : إذن 2 0,1
. cosα ' = 2 × 9.109. 2
10−6 . cos63,4 ≈ 1,6.105 V / m : $ 2 2 0,2 .1,25 : إذن
"(آ ن
r r r وE1 = EC + E D
r r %$ اMN- وE B وE D
%$" وk
d اMN-
E M = E1 − E 2 = (18 − 1,6)10 5 = 164.10 4 V / M
( اC
r r r E2 = EA + EB
و
واE1 > E 2 CS$ اL 3 " r r r r r E M = E A + E B + EC + E D r r ...... = E 2 + E1
(
) (
:
)
S$"
--------------------------------------------------------------------------------------------------------------------------------.DوBوA ا ؤوس67 ا ? دة%! ف اG " C 45$ ا67 ث2% آ ا ة ا ل ا2& د2%$ (2-2
E A = K.
q' AM 2
10 −6 = 9.10 = 18.10 4 V / m : - و 2 0,2 × 1,25 9
r r r r EC = E1 − EC = 138198V / m : CS$ ا E1 k وا%$" MN- EC = E A + E1 : إذن r r r r r v (o, i , j ) C ( ا67 EC = E A + E B + E D YP( ] ا5 - : ىU ا5 4 أو EC =
( E C x )2 + ( E C y )2
E x = − E A . sin 45 + 0 + E D = −18.104 sin 45 + 225.103 = 97720,8V / m = 138198V / m : و C EC y = − E A . cos 45 + E B + 0 = −18.104 cos 45 + 225.103 = 97720,8V / m q 10 −6 E D = E B = K . 2 = 9.10 9. 2 = 225.10 3 V / m : ن a 0,2 :C 45$ ا67 ا ? دةq ' $%! ا 5I4 ا$آ ة ا5 ة ا2&و r r r F = q ' .EC = 10 −6.138198 = 0,14 N : 2& وq '. < 0 نd EC ا%$" M F = q'.EC
************************************************************************************************************
: 6- K ا q A . qB
اp %; (2
−7 2
(1,6.10 ) = 5,76.10 −3 N : q B $%! ا q A $%! ف اG " 5I4 ا$آ ة ا5 ة ا2& (1 2 d 0,2 ---------------------------------------------------------------------------------------------------------------------------------------r r r EC = E A + E B : $%! ف اG "C 45$ ا67 ث2% آ ا ا لا " (2 r r . Q ! اS- ا، T - E A وEB ⇐ اqB > 0 وq A > 0 FA / B = K .
2
= 9.10 9.
E C = E A − E B = 576000 − 64000 = 5,12.10 5 V / m
: ه
r r r EC = E A + E B
اCS$" . ن " ( آ ن%$" وk
d اMN-
r r E A وEB
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
. $آ
r ة ا5 ا: Fe ] a ا
r :T
r وزن اP : ىY ثPD D L% ازن67 اس$ ا r r r r P + T + Fe = 0 : إذن
.\ e" ثPK ى ا5 6( , ] أa ") آ ن اV7
آ-2-3
. 6( , ] أa ا ( ل ا r r r r P + T + Fe = 0 : YP( ن ا
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
q o = +3,1.10 −8 C : إذنq o > 0 : نr7 %$ اMN-
r r EO وFe أن
qo =
Fe 3,17.10 −3 = ≈ 3,1.10 −8 C ⇐ Fe = q o .E O $ 2 (3-3 EO 101823
************************************************************************************************************
:L Kا
اp %;
2
.
q . F = FA / A' = FA'/ A = k . 2 :s(I ا,( $%! ف اG " 5I4 ا$آ D r r r وزن ا: P ] a ا : T $آ ة ا5 اFe : ىY ثPD DV t% ازن- 3 67
α = 5,74° ⇐
sin α =
ة ا5 ة ا2& " اQآ
(D − d ) / 2 D − d 7 − 5 = = = 0,1 : $ 2 Q ! ل اPU " l 2l 2 × 10
m.g.D2 . tanα 10 ×10 ×10−3.0,072. tan5,74 q= = = 7,4.10−8 C 9 K 9.10
: '$"و
k.
2
q D
2
= mg tan α : أيF = mg. tanα ⇐ tan α =
F P
************************************************************************************************************
% N; ى ا
:
"
دي : k d ا: ات ا. .( - ا د2 ذات ا% N; ا%-
S$"و. B % N; ا%-A % N; " ا
E=
r ? " E
ا ا2
:) ا ا
r Eل
ا " و، CS $" % N; ا ذات ا% N; ; ) أي " اY $ د ا
اp %;
آ ا%-
( ا ل ا1 ? " : %$ ا
⇐ V A > VB : نr7 U AB = V A − VB = 500V > 0 أن
U AB 500 = = 5000V / m d 0,1 ازن ا
را2 (2
F ⇐ tan α = P r . ا. " آ: D ا45- - F : $آ ة ا5 ات ا. " إذن . % N; ا دي : DV ] اU . B %- A " : %$ ا−3 : ة2! اF = 1,76.10 N r r = 3,52.10 − 7 C : '$" وF = q .E : CS$ ذات اF = q.E : $آ ة ا5 اI( لPU " (3 r r q = +3,52.10 −7 C : 6 وq > 0 : نr7 %$ اMNFو.E أن F = mg. tan α = 10−3.10. tan10 = 1,76.10−3 N
q =
F 1,76.10 −3 = E 5000
C = −q.E.x M ⇐
0 = q.E.x M + C : $ 2 وE pe = q.E.x + C : $ 2 E pe = q.E.x − qE.x M
: إذن : N 45$ ا2$ )
اYG
************************************************************************************************************
: M" a ا . A %- B " أي r r . Q ! اS- ا. F %$" MNE
ذات% N; " ا
ا%- $آ إذن ا
اp %;
ة ا5 ا%$" نr7 A % N; ا%- t7 %-" ا.% ( أن ا1 r r F = qE : $ 2 ⇐ و q > 0 و نI ا$%&
r ? " ) أي. ;Y $ د ا ا%$" MN% N; ا ث2% اE آ ا لا " أنC (- ىU" ? أ U AB < 0 : أيV A − VB > 0 ⇐ VB > V A :إذن .( - ا د2 ذات ا% N; ا%ا2 ا
.
% N; ا
r 0 x S − xO = E .( y S − y O ) × U OS = VO − V S = E .OS = :ن + E y S − yO ا ) اY G e ) د " ا2% يT ا ل وه ا ر ا ازي% ه اoy ر% ا% اkT ه67 (3 C = 0 ⇐ 0 = q.E × 0 + C $آ ا ) اY 4 )? " O : $ 2 وE pe = q.E. y + C : $ 2
$آ
E pe = q.E. y
E pe S
r WFO→ S = 8.10 −18 J $ 2 (2 CY\ ر E peS = 8.10
−18
.? ,وا@; آ ت آ
r ال اu ل اPU " وWFO→ S = − ∆EpeO→ S
& زن0 ن ا
: $ 2 : ىU ا5 4 أو
−18
: $ 2 وE peS − E peO = 8.10 : ∆ أيEpeO→ S = −8.10 −18 J إذن : S وO*' ن0+ و1 ا234 5' ا ( آ56 7 ا5 1& 8'17 (4 r 9 + : ;' ة ا0 ا: ه5 ة ا = آ0> ا ∆EcO →S = WFO→ S r Ecs − EcO = WFO→ S
: إذنE peO = 0
r 2.WFO →S 2 + VO m
.V S =
: إذن : S 45$ ا2$ ) اY G 100 = q.E. y S = 1,6.10 −19 5.10 − 2 = 8.10 −18 J 0,1
⇐
.VS =
r 1 1 2 2 m.VS − m.VO = WFO→ S 2 2
2 × (8.10 −18 ) + 10 2 ≈ 9,8.10 3 m / s − 27 1,67.10
:ع.ت
************************************************************************************************************
:دس .
:
ات ا.
وذات ا
ا
اp %;
" إذنq A < 0 (1 r .C 45$ ا: Q[ اEA . AC: k d ا. A %- C " : %$ ا-
اT - اC 45$ ا67 'D2% يT ل ا
ا
−8
− 10 qA 9 = 9 . 10 . = 2250V / m :CS$ اAC 2 0,2 2 .................................................................................................................................................................................... (( أ2 EA = K.
.................................................................................................................................................................................... E E E × BC 2250 × 60 AC AC EB = A = = 6750V / m : إذنA = : '$" وtan α = : g T آ$ 2 وtan α = A لQ ! ل اPU " (ب AC 20 E B BC BC EB qB E B .BC 2 6750 × 0,6 2 = = 2,7.10 −7 C ⇐ : $ 2 ىUو" ? أ qB = EB = K. 9 K 9.10 BC 2 q B = +2,7.10 −7 C : نr7 q A = −10 −8 C $%! ذات اq A $%! إ& رة اM q B $%! أن ا .................................................................................................................................................................................... F = q C .E c = q c × E A + E B = 10 −6 × 2250 2 + 6750 2 ≈ 7,1.10 −3 N : q C $%! ا 2
2
5I4 ا$آ
ة ا5 ة ا2& (ج
....................................................................................................................................................................................
.C 45 ا67 آ
لا
ة ا2& م2($ L % 2 2 ي اT ) ا
E 'c = K
qc MC
2
: )"
MC =
ا67 ? دة
اq c $%! ف اG " ث2% آ ا
r r E ' c = E c : CS$ اL 3 " وE 'C = − EC : أي K . qc E A + EB 2
2
=
9.10 9.10 −6 2250 2 + 6750 2 . ةT -
. Q ! اS-' ا$"
N ا
r ا67 وE c k \ ") اI4$ اC 5
لا
ا
r
" E'C
(3
r r r EC + E 'C = 0 : $ 2 إذن
≈ 1,125m = 112,5cm : 2 - '$"و
r E' c
ن اr7 q c > 0
6 $ M 45- 67 2?
q c $%! ا
************************************************************************************************************
r .F
%$" M
r E : أنB $
r r q < 0 : )" F = q.E YP( ل اP هC-( وQ ! اS-)ا
:) $آ
ة ا5 ا%$"
ا
اp %;
$ 2 اس$ اف ا%- ا%$" (1
r
. U AB < 0 : أيV A − V B < 0 : إذنV B > V A ⇐ . ;Y $ د ا ا%$" MNE أنC (-و ........................................................................................................................................................................................................ r . % N; ى " ى اQ د: k d ا-: E ا ل " ات. " و. CS $" % N; ا آ ( ا ل ا2 .A % 5; ا%- B % N; ; أي " اY $ د ا ا%$" MN- : %$ ا-
E=
U AB d
=
100 = 2000V / m CS$ ا 0,05
........................................................................................................................................................................................................ Fe = q. E = 0,5.10 −6 × 2.10 3 = 10 −3 N (3 ........................................................................................................................................................................................................ (4
tan α =
Fe : '$"و P
m=
Fe 10 −3 = = 0,567.10 −3 kg g. tan α 10. tan 10
Fe = mg . tan α
⇐
........................................................................................................................................................................................................
************************************************************************************************************
: "Kا .( Q ! اS- اk
FB / C = K .
q B . qC BC
=K
2
q 2 × q3 (d − AC ) 2
FA / C = FB / C ⇐
⇐
q (d − AC ) = 2 2 q1 AC 2
1+
: أي
q2 q1 AC =
d
:و
5ا
q A × qC
=K
هDV t% q3
q2 q1 = : أي 2 AC (d − AC ) 2 q2 d = 1+ : '$"و AC q1
AC
2
d −1 = AC
K
q1 × q3 AC 2
$%! ا5
: ة2! ا "2$
q1 × q3 q 2 × q3 =K 2 (d − AC ) 2 AC
q2 : أي q1
d − AC = AC
q2 q1
1
≈ 0,33m = 33cm : دي2 \ I4 2 × 10 −9 1+ 0,5 × 10 −9 ....................................................................................................................................................................................... . 60° ث " وPK وا ا. ا، ) " وي اABCL K ( ا2
q2 1+ q1
=
FA / C = K .
r r r FA / C + FB / C = 0 :
⇐
d
AC =
r r 5I4 اFB / C وFA / C ة5 C $%! ) ا,a (1
$%! ف اG "
d و ا%$ ) اq 2 ، q1
اp %;
F = 2.FA / C × cos α q2 .... = 2 × .K × 2 × cos 30 a ..... = 2. × 9.10
(10 ) ×
−8 2
9
0,05 2
. cos 30 ≈ 6,2.10 − 4 N
************************************************************************************************************
:)
AC =
AC =
d
=
20
≈ 8,3cm 2q 1 + 2 1+ q d 20 AC = = ≈ 7,3cm 3q 1 + 3 1+ q
d q 1+ q
=
d = 10cm 2
q 2 = 2 q :و
q 2 = 3q
q1 = q 2 = q 3 = q
q1 = q 3 = q
: وq1 = q3 = q
:
ا
و:ا
:
اp %;
ا
;ا
: ; ;ا
(1
ا
(2
ا
(3
************************************************************************************************************
SBIRO Abdelkrim Lycée agricole d’Oulad-Taima région d’Agadir royaume du Maroc Pour toute observation contactez moi Sbiabdou@yahoo.fr .\ 7 ا ( ن واC v ل ا- وC # دp [ " - $ d