pdf-ejercicios-de-electrostatica compress.pdf

Ioirmamab risuiktb G¿ 4
Fitirlagdr kd euirzd qui si ioirmi igtri kds mdrcds q 4 y q8 fastdgtis
ugd fi kd btrd 9 ml
Fdtbs?
J < 1 . 401 G . l8/M8 (ig ik vdmìb)
q4 < + 4. 40-5 M
q8 < + 8,9 . 40-5 M
r < 9 ml . 4 l/400ml < 0,09 l
Xisbkumaýg
Kds fbs mdrcds taigig ik laslb sacgb y pbr kb tdgtb si ripikiräg.
Muirpb 4
E84
Muirpb 8
+
E48
+
0,09 l
E48 is kd euirzd ripuksavd qui ioirmi ik muirpb
4 sbhri ik muirpb 8.
E84 is kd euirzd ripuksavd qui ioirmi ik muirpb
8 sbhri ik muirpb 4.
]i mulpki qui? |E48| < |E84|
Gbs vdlbs d kd imudmaýg fi Mbukblh y sustatualbs fdtbs?
8
E < J . |q4|. |q8| / r
1
8
8
-5
-5
E < 1 . 40 G . l /M . 4 . 40 M . 8,9 . 41 M/ (0,09 l)
1
-5
-5
8
8
8
8
8
E < 1 . 40 . 4 . 40 . 8,9 . 40 / 0,0089 G . l /M . M /l
E
1
-48
< 1000 . 40 . 40
G < 1000 . 40 G < 1 G
-=
G (Giwtbg) < Ygafdf fi Euirzdi ig ik ]astild Agtirgdmabgdk fi
ugafdfis
Dgtbgab _drdcbzd Kýpiz
Päcagd 4
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
Mbgmkusaýg? Kbs fbs muirpbs si ripikig mbg ugd euirzd fi agtigsafdf?
E
<
1G
Ioirmamab risuiktb G¿ 8
(Euigti Igugmadfb? Bsmdr Mbgtrirds. Xisbkumaýg? D. _drdcbzd)
Fitirlagdr
kd euirzd-9qui dmtÿd sbhri kds mdrcds ikámtramds q 4 < -4,89 .
-1
40 M. y q8 < +8 x 40 M. qui si igmuigtrdg ig ripbsb y ig ik vdmìb d
ugd fastdgmad fi 40 ml.
Fdtbs?
1
8
8
J < 1 . 40 G . l /M
-1
q4 < - 4,89 . 40 M
-9
q8 < 8 . 40 M
r < 40 ml . 4 l/ 400ml < 0,4 l
Muirpb 4
Muirpb 8
E84
E48
0,4 l
Ig isti mdsb, dk sir kds fbs mdrcds ikámtramds fi fastagtb sacgb si
DVX
D VX D I X Ä G , mbg ugd agtigsafdf fi euirzd qui gbs kd prbpbrmabgdrä kd
kiy fi Mbukblh?
E < J . |q
|q4| . |q8| / r 8
Kkivdgfb fdtbs?
1
8
8
-1
-9
8
E < 1 . 40 G . l /M . 4,89 . 40 M .8 . 40 M / (0,4 l)
E
-9
< 88,9/0,04 . 40 G.l /M . M / l < 889
88900 . 40
-9
8
8
8
8
G
Mbgmkusaýg? Kbs fbs muirpbs si dtrdig mbg ugd euirzd fi agtigsafdf
8890 . 40-9 G
8890
Päcagd 8
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
Ioirmamab risuiktb G¿ =
Euigti fi Igugmadfb? Prbeisbr ig Kìgid. Xisbkumaýg? D. _drdcbzd
Fbs mdrcds pugtudkis (q4 y q8) si dtrdig agamadkligti igtri sì mbg ugd
euirzd fi 500 G, sa kd sipdrdmaýg igtri ikkds si rifumi d ug tirmab fi su
vdkbr bracagdk ²muäk is kkd
d guivd euirzd fi dtrdmmaýg2 9600G
Xisbkumaýg
]icÿg kd kiy fi Mbukblh?
E < J . |q
|q4|. |q8|/
|/rr 8
pbfilbs quatdr kds hdrrds (vdkbris
dhsbkutbs)
y gbs quifdrìd?
E < J . q4 . q8 /r 8
Kkdlilbs d kd kbgcatuf fi sipdrdmaýg agamadk
1
8
500 < 1 . 40 q4 . q8/(^b) :
^b, kuicb?
1
8
500 < 1 . 40 q4 . q8 /^b (4)
Dk rifumar kd fastdgmad agamadk ig 4/=, kd fastdgmad fi sipdrdmaýg sirä
^b
^b//= y gbs dpdrimirä ugd guivd euirzd qui ki vdlbs d kkdldr E 8?
1
8
1
E8 < 1 . 40 . q4 . q8/r :
8
E8 < 1 . 40 q4 .q8 / (^b/=)
1
8
E8 < 1 . 40 q4 . q8 / ^b /1
1
8
E8 < 1 . 40 . 1 . q4 . q8/^b (8)
Fi kd imudmaýg (4) puifb bhtigir?
8
1
q4 . q8 / ^b < 500/1 . 40
Fi kd imudmaýg (8) pbfilbs bhtigir?
8
1
q4 . q8 / ^b < E8 / 1 . 40 . 1
]a kbs fbs lailhrbs fi kd azquairfd fi kds fbs ÿktalds imudmabgis sbg
acudkis tdlhaág kb siräg kbs fbs lailhrbs fi kd firimnd, is fimar?
1
1
500/1.40 < E8 / 1 . 40 . 1 : 500 < E8 / 1 :
E 8 < 500 . 1 < 96
9600
00 G
Päcagd =
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
Ioirmamab risuiktb G¿6
Euigti Igugmadfb? Prbeisbr ig Kìgid. Xisbkumaýg? D. _drdcbzd
²Muäk fihi sir kd sipdrdmaýg igtri fbs mdrcds fi +9 ¹M pdrd qui kd
euirzd fi ripuksaýg sid 6 G2
Xisbkumaýg
FDVB]?
Dpdrimi ug suhlÿktapkb fik Mbulbhab, ik lamrbMbukblhab (λM)
-5
]dhilbs qui 4λM < 40 M
-5
q4 < + 9 λM < +9 . 40 M
-5
q8 < +9 λM < + 9 . 40 M
E<6G
]icÿg kd imudmaýg fi Mbukblh?
E < J . q4 . q8 / r 8
]ustatualbs kbs fdtbs?
1
8
8
-5
-5
8
6 G < 1 . 40 G . l /M . 9 . 40 M . 9 . 40 M / r
-=
8
8
8
8
6 G < 889 . 40 G . l /M . M /r
-=
8
6 G < 889 . 40 G / r
Kd agmýcgatd is ‛r“?
8
-=
8
-=
8
6 G . r < 889 . 40 G : r < 889 . 40 G . l /6 G
8
-=
8
-=
8 4/8
r < 95,89 . 40 l : r < ( 95,89 . 40 l )
r < 0,8=,3 l
Ioirmamab risuiktb G¿ 9
-5
-5
Fbs mrdcds pugtudkis q4< =.40 M y q8< 6.40 M istdg sipdrdfds 0,9 l
y uhamdfds ig ik vdmab. Mdkmuki ik vdkbr fi kd euirzd igtri kds mdrcds.
Xisbkumaýg
Päcagd 6
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
-5
q4 < = . 40 M
-5
q8 < 6 . 40 M
X < 0,9 l
Mblb kds fbs mdrcds sbg fik laslb sacgb (+) ixastarä
ugd euirzd fi XIPYK]AÝG
]icÿg kd imudmaýg fi Mbukblh?
E < J . q4. q8 / X 8
Kkivdgfb fdtbs? Istdlbs ig ].A
1
8
8
-5
-5
E < 1 . 40 G . l /M . = . 40 M . 6 . 40 M/(0,9 l)
E < 6=8 . 40
E
-=
8
8
8
8
8
G . l /M . M /l
< 6=8 . 40 G < 0,6=8 G
-=
Ioirmamab risuiktb G¿ 5
Euigti fi igugmadfb? Easamdgit
Mdkmukdr kd mdrcd fi fbs pdrtìmukds acudkligti mdrcdfds, qui si
ripikig mbg ugd euirzd fi 0,4 G, mudgfb istäg sipdrdfds pbr ugd
fastdgmad fi 90 ml ig ik vdmìb.
Xisbkumaýg
]a kds mdrcds si ripikig is pbrqui taigig ik
gicdtavds).
la sl
slb
b sasa cgb ( pbsatavds b
90 ml < 0,9 l
Dfiläs si mulpki qui |q4| < |q8| < q
q4
q8
0,9 l
E
q
q
E
Päcagd 9
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
]icÿg Mbukblh?
8
8
E < J . q4 . q8 / X : q4 < q8
8
8
E < J . q . q /X
8
8
E < J . q /X : q < E . X / J
8
1
8
8 4/8
q < Z0,4 G . (0,9 l) / 1 . 40 G . l /M \
q < Z0,008> . 40
-=
-1
8
8
8 4/8
G . l . M /G . l \
8 4/8
q < Z8,> . 40 M \
-=
: q < 0,091 . 40 M
q4 < q8 < q <9,1 . 40-8 . 40-= M < 9,1 . 40-9 M
Ioirmamab risuiktb G¿ 3
Euigti Igugmadfb? Easamdgit
Ndkkdr ik vdkbr fi kd mdrcd T fi ugd pdrtìmukd tdk qui mbkbmdfd d 4 l
->
fi btrd, muyd mdrcd is fi 8.40 M, kd dtrdi mbg ugd euirzd fi 8 G.
Xidkazd ug mrbquas fi kd dmmaýg igtri kds fbs mdrcds
Xisbkumaýg
q
T
4l
->
q < 8 . 40 M
X<4l
E<8G
Kd mdrcd T fihi sir GICDVAUD puistb qui dtrdi d q qui is
PB]AVAUD . Ik lýfukb fi T kb bhtigfrilbs lifadgti kd imudmaýg fi
Mbukblh?
8
8
E < J . T . q /X : T < E . X / J . q
8
1
8
8
->

T < 8 G . (4 l) / Z1 . 40 G . l /M \ . 8 . 40 M

T < 0,444 G . 40 l . M / G . l . M < 0,0444 M

-4
8
8
8
T < - 4,4 . 40-8 M
Päcagd 5
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
Ioirmamab risuiktb G¿ >
Euigti fi Igugmadfb? Easamdgit
Mdkmukdr kd fastdgmad ‛r“ qui sipdrd fbs pdrtìmukds mdrcdfds mbg
-8
8.40 M mdfd ugd, sdhaigfb qui kd euirzd fi agtirdmmaýg igtri dlhds is
9
fi 1.40 G.
Xisbkumaýg
-8
q4 < q8 < 8 . 40 M
9
E < 1 . 40 G
]icÿg kd imudmaýg fi Mbukblh?
8
8
4/8
E < J . q4 . q8 / r : E . r < J . q4 . q8 : r < ( J . q4 . q8 / E )
1
8
8
-8
-8
9
4/8
r < Z 1 . 40 G . l /M . 8 . 40 M . 8 . 40 M / 1 . 40 G\
r < (6 . 401 . 40-8 . 40-8 . 40-9 l8)4/8 : r < 8 l
Ioirmamab risuiktb G¿ 1
-5
Fitirlagdr kd euirzd qui si ioirmi igtri kds mdrcds q 4 < +4 . 40 M y
-5
q8 < + 8,9 . 40 M fastdgtis ugd fi kd btrd 9 ml. Kd pirlatavafdf rikdtavd
fik lifab is fi 6
Xisbkumaýg
9 ml . 4 l / 400 Ml < 0,09 l
]icÿg kd Kiy fi Mbukblh?
E < J/ιr . q4 . q8 / X 8
1
8
8
-5
-5
E < 1 . 40 G . l /M / 6 . 4 . 40 M . 8,9 . 40 M / (0,09 l)
E
< 8890 . 40
-=
8
G . l . M /M . l < 8,8
8,890
90 G
8
8
8
8
Päcagd 3
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
Ioirmamab risuiktb G¿ 40
²Fitirlagdr kd pirlatavafdf rikdstavd fik lifab ig fbgfi si
igmuigtrdg fbs muirpbs mdrcdfbs ikámtramdligti mbg ik laslb sacgb y
vdkbr fi +9 ¹M, sipdrdfds ugd fastdgmad fi 4,9 l pdrd qui kd euirzd fi
ripuksaýg sid > G2
Xisbkumaýg
-5
q4 < q8 < + 9 λM < + 9 . 40 M
X < 4,9 l
Guistrb dlacb Mbukblh gbs fami qui?
E < J/ιr . q4 . q8 / X 8
8
8
E . ιr . X < J . q4 . q8 : ιr < J . q4 . q8 / E . X
ιr < 1 . 401 G . l8/M8 . 9 . 40-5 M . 9 . 40-5 M / > G . (4,9 l)8
ιr < 48,9 G . l8/M8 . M8/G . l8 < 48,9 (dfaligsabgdk)
Ioirmamab risuiktb G¿ 44
Fdfb ik isquild sacuaigti?
q4 < 8 λM
+
480 ml
q8 < 6 . 40-5 M
─
400 ml
q= < 5 λM
─
Fitirlagdr cräeamd y mudgtatdtavdligti?
d) Kd euirzd qui si ioirmi sbhri q 8
h) Kd euirzd qui si ioirmi sbhri q =
m) Kd euirzd qui si ioirmi sbhri q 4
Xisbkumaýg
Dgtbgab _drdcbzd Kýpiz
Päcagd >
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
-5
q4 < 8 . 40 M
-5
q8 < 6 . 40 M
-5
q= < 5 . 40 M
r4 < 4,80 l
r8 < 4 l
]bhri kd mdrcd q8 dmtudräg fbs euirzds ioirmafds pbr kds btrds fbs
mdrcds.
Ximbrfdr qui mdrcds fik laslb sacgb si ripikig y mdrcds fi fastagtb
sacgb si dtrig.
Kd q4 pbr tigir fastagtb sacgb dtrdirä d q8 mbg ugd euirzd E48 qui taigi
ik pugtb fi dpkamdmaýg ig ik muirpb qui sbpbrtd kd mdrcd q8. Kd mdrcd q=
taigi ik laslb sagb qui q8 y pbr kb tdgtb ripikirä d q8 ndmaigfb qui ik
muirpb qui sbpbrtd kd q8 si fispkdmi ndmad kd azquairfd sacuaigfb kd
farimmaýg fi kds mdrcds. Bhtigilbs ug fadcrdld fi euirzds?
E=4
E48
─
+
─
Bhtigilbs fbs euirzds fi kd lasld farimmaýg y sigtafb. ]us vdkbris
sbg?
8
E48 < J . q4 . q8 /r4
1
8
8
-5
-5
E48 < 1 . 40 G . l /M . 8 . 40 M . 6 . 40 M / (4,80 l)
-=
8
8
8
8
8
-=
E48 < 38/4,66 . 40 G . l . M / M . l < 90 . 40 G < 0,090 G
E=8 < J . q8 . q= / r8
1
8
8
-5
8
-5
E=8 < 1 . 40 G . l /M . 6 . 40 M . 5 . 40 M / (4 l)
-=
8
8
8
8
8
-=
E=8 < 845 . 40 G . l . M /M . l < 845 . 40 G < 0,849 G
Dgtbgab _drdcbzd Kýpiz
Päcagd 1
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
Kd euirzd risuktdgti sbhri kd q 8 tigfrä ik vdkbr?
EX < E48 + E=8
E X < 0,090 G + 0,849 G < 0,859 G
d) ]bhri kd mdrcd q=
]bhri kd q= dmtÿdg fbs euirzds, mridfds pbr q4 y q8.
Kd mdrcd q8 ripiki d kd q= pbr tigir ik laslb sacgb laigtrds qui
kd q4 dtrdirä d kd q= pbr sacgbs mbgtrdrabs. Kd dtrdmmaýg b
ripuksaýg fi mdrcds si ridkazdrd lifadgti kds E 4= y E 8=. Ik
fadcrdld fi euirzds risuktdgti is?
E=4
E48
E4=
E8=
─
+
─
400 ml
880 ml
]i bhtaigig fbs euirzds fi kd lasld farimmaýg pirb fi sigtafb
mbgtrdrab?
EX < Eldybr - Eligbr
Mäkmukb fi E4=?
E < J . q4 . q= / X 8
1
8
8
-5
-5
8
E < 1 . 40 G . l /M . 8 . 40 M . 5 . 40 M / (8,80 l)
-=
8
8
8
E < =6,>5 . 40 G . l . M / M
E < =6,>5 . 40-= G
Dgtbgab _drdcbzd Kýpiz
Päcagd 40
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
h) ]bhri kd q4?
─
+
─
480 ml
400 ml
880 ml
Pbr kd rdzbgis ixpkamdfds pdrd q8 y q= bhtigilbs ug fadcrdld fi
euirzds?
q4
E84
E=4
q8
q=
─
+
─
480 ml
400 ml
880 ml
Kd euirzd risuktdgti sbhri q 4 si bhtigfrä lifadgti kd imudmaýg?
EX < E84 + E=4
Mäkmukb fi E84?
E 84 < 1 . 401 G . l8/M8 . 6 . 40-5 M . 8 . 40-5 M / (4,80 l)8
E 84 < 90 . 40-= G . l8/M8 . M8/l8 < 90 . 40-= G
Mäkmukb fi E=4?
8
8
-5
-5
E=4 < 1 . 401 G . l /M . 5 . 40 M . 8 . 40 M / (8,80 l)
8
E =4 < 88
88,=4
,=4 . 40-= G
Euirzd risuktdgti sbhri q4?
E X < E 84 + E =4
Dgtbgab _drdcbzd Kýpiz
Päcagd 44
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
E X < 90 . 40-= G + 88,=4 . 40-= G < 38,=4 . 40-= G
Ioirmamab risuiktb G¿ 48
Ig kbs vártamis fi ug trägcukb iquakätirb fi 90 ml fi kdfb ixastig tris
mdrcds fi? q4 < - 8,9 λM : q8 < - 4,9 λM y q= < = . 40-> M, sicÿg ik
isquild?
q4
90 ml
q8
q=
Fitirlagdr kd euirzd risuktdgti qui si ioirmi sbhri kd mdrcd q 4.
ALPBXVDGVI? Mudgfb gb ispimaeamdg ik lifab mbgsafirdrilbs
sailpri ik vdmìb b ik dari.
Xisbkumaýg
-5
q4 < - 8,9 . 40 M
-5
q8 < - 4,9 . 40 M
->
q= < = . 40 M
X < 90 ml . 4 l / 400 ml < 0,9 l
q4 (-)
90 ml
q8 (+)
q= (-)
Ik fadcrdld fi euirzds sirä?
90 ml
q8 (+)
Dgtbgab _drdcbzd Kýpiz
q= (-)
Päcagd 48
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
Pbr kd rickd fik pdrdkikbcrdlb, kd euirzd risuktdgti sirä?
δ < 10b
E=4
E84
90 ml
q= (-)
q8 (+)
Mäkmukb fi E=4?
]icÿg kd kiy fi Mbukblh?
8
E=4 < J . q= . q4 / X
1
8
8
->
-5
8
E=4 < 1 . 40 G . l /M . = . 40 M . 8,9 . 40 M / (0,9 l)
E =4 < 830 . 40-9 G
Mdkmukb fi kd E84?
1
8
8
-5
-5
E84 < 1 . 40 G . l /M . 4,9 . 40 M . 8,9 . 40 M / (0,9 l)
8
E 84 < 4=9 . 40-9 G
Vigilbs fbs euirzds rimtdgcukdris muyb lýfukb, pbr ik tibrild fik
mbsigb vdki?
8
8
EX < Z( E=4) + (E84) + 8 . E=4 . E84 mbs δ)\
b
b
δ < 10
8
4/8
mbs 10 < 0
8
4/8
EX < Z(E=4) + (E84) + 8 . E=4 . E84 . 0\
Dgtbgab _drdcbzd Kýpiz
Päcagd 4=
Ioirmambs y prbhkilds risuiktbs sbhri kd kiy fi mbukblh
4/88
E X < Z(Z(EE =4) 8 + (E 84) 8\4/
-9
8
-9
8 4/8
EX < Z(830 . 40 G) + (4=9 . 40 G) \
EX < (38100 . 40-40 G8 + 4>889 . 40-9 G8)4/8
E X < =0
=04,>
4,>33 . 40-9 G
Dgtbgab _drdcbzd Kýpiz
Päcagd 46