Su'aalo Tusaale ah oo Ka Hadlaya Sharciga Coulomb
Sharciga Coulomb waa mabda' aasaasi ah oo ku saabsan fiisikiska kaas oo sharraxaya xoogga u dhexeeya laba dallacaad koronto. Sharcigan oo lagu bartay qaybta hoose ee electrostatics, wuxuu sharxayaa sida dallacaadyada korontadu isu soo jiitaan ama isu celiyaan. Sharcigan waxaa markii ugu horreysay soo jeediyay fiisikisyahan Faransiis ah Charles-Augustin de Coulomb qarnigii 18aad. Maqaalkani wuxuu ka hadli doonaa Sharciga Coulomb isagoo baaraya tusaalooyinka iyo xalalkooda, sidaas darteed wuxuu ka caawinayaa akhristayaasha inay fahmaan codsiyada wax ku oolka ah ee mabda'an aasaasiga ah.
Aasaaska Aragtida: Waa maxay Sharciga Coulomb?
Sharciga Coulomb wuxuu sheegayaa in baaxadda xoogga korontada ku shaqeeya ee \( F \) ee u dhexeeya laba dallacaad oo dhibic ah \( q_1 \) iyo \( q_2 \) ay si toos ah ugu dhigantaa wax soo saarka baaxadda labada dallacaad oo ay si liddi ku ah ugu dhigantaa labajibbaaranaha masaafada \( r \) ee u dhaxaysa. Xisaab ahaan, qaacidada Sharciga Coulomb waxaa lagu qeexi karaa sidan:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Halkee:
– \( F \) waa baaxadda xoogga korontada ku shaqeeya
– \( k_e \) waa joogtada Coulomb (\( 8.9875 \times 10^9 \, N \cdot m^2 \cdot C^{-2} \))
– \( q_1 \) iyo \( q_2 \) waa baaxadda dallacaadda korantada
– \( r \) waa masaafada u dhaxaysa labada dallacaad
Su'aal Tusaale 1aad
Su'aal:
Waxaa jira laba dalac oo dhibco ah: \( q_1 = 2 \jeer 10^{-6} \, C \) iyo \( q_2 = -3 \jeer 10^{-6} \, C \). Waxay u dhexeeyaan 0,05 mitir. Xisaabi baaxadda xoogga korontada ku shaqeeya ee u dhexeeya labada dalac.
Dood:
Tallaabada ugu horreysa waa in dib loo qoro qaacidada Sharciga Coulomb:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Hadda waxaan ku beddeleynaa qiimayaasha la yaqaan qaacidada:
\[ k_e = 8.9875 \jeer 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[ q_1 = 2 \jeer 10^{-6} \, C \]
\[ q_2 = -3 \jeer 10^{-6} \, C \]
\[ r = 0,05 \, m \]
Waxaan qiimahan ku dhejineynaa qaacidada:
\[ F = 8.9875 \jeer 10^9 \, \frac{|2 \jeer 10^{-6} \cdot -3 \jeer 10^{-6}|}{(0,05)^2} \]
\[ F = 8.9875 \ jeer 10^9 \, \frac{6 \ jeer 10^{-12}}{0,0025} \]
\[ F = 8.9875 \jeer 10^9 \, \frac{6 \jeer 10^{-12}}{2,5 \jeer 10^{-3}} \]
\[ F = 8.9875 \ jeer 10^9 \, \ jeer 2,4 \ jeer 10^{-9} \]
\[ F = 21.57 \, N \]
Maadaama dallacaadda \( q_2 \) ay tahay mid taban, xoogga korontada ku shaqeeya waa xoog soo jiidasho leh, sababtoo ah dallacaadaha togan iyo kuwa taban ayaa is soo jiita.
Su'aal Tusaale 2aad
Su'aal:
Laba dallacaad koronto \( q_1 = 5 \jeer 10^{-9} \, C \) iyo \( q_2 = 10 \jeer 10^{-9} \, C \) waxaa kala sooca masaafo dhan 0,1 mitir. Xisaabi baaxadda xoogga korontada ku shaqeeya \( q_1 \).
Dood:
Mar kale isticmaal qaacidada Sharciga Coulomb:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Ku beddel qiimayaasha la yaqaan:
\[ k_e = 8.9875 \jeer 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[ q_1 = 5 \jeer 10^{-9} \, C \]
\[ q_2 = 10 \jeer 10^{-9} \, C \]
\[ r = 0,1 \, m \]
\[ F = 8.9875 \ jeer 10^9 \, \frac{(5 \ jeer 10^{-9}) (10 \ jeer 10^{-9})}{(0,1)^2} \]
\[ F = 8.9875 \ jeer 10^9 \, \frac{50 \ jeer 10^{-18}}{0,01} \]
\[ F = 8.9875 \ jeer 10^9 \, \ jeer 5 \ jeer 10^{-15} \]
\[ F = 44.9375 \, N \]
Xoogga shaqeeya waa xoog diidmo ah, sababtoo ah labada dallac \( q_1 \) iyo \( q_2 \) labaduba waxay leeyihiin calaamad isku mid ah, taas oo ah togan.
Su'aal Tusaale 3aad
Su'aal:
Saddexda dhibcood ee dallacaadda waxay ku jiraan xariiq toosan. Dallaca koowaad waa \( q_1 = 2 \mu C \), dallaca labaad waa \( q_2 = -1 \mu C \), dallaca saddexaadna waa \( q_3 = 3 \mu C \). Masaafada u dhaxaysa \( q_1 \) iyo \( q_2 \) waa 0,1 m, halka masaafada u dhaxaysa \( q_2 \) iyo \( q_3 \) ay tahay 0,2 m. Xisaabi baaxadda iyo jihada guud ee xoogga korantada ee ku shaqeeya \( q_2 \).
Dood:
Marka hore, waxaan xisaabineynaa xoogga korontada ku shaqeeya ee u dhexeeya \( q_1 \) iyo \( q_2 \):
\[ F_{12} = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
\[ k_e = 8.9875 \jeer 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[ q_1 = 2 \jeer 10^{-6} \, C \]
\[ q_2 = -1 \jeer 10^{-6} \, C \]
\[ r = 0,1 \, m \]
\[ F_{12} = 8.9875 \jeer 10^9 \, \frac{(2 \jeer 10^{-6}) (-1 \jeer 10^{-6})}{(0,1)^2} \]
\[ F_{12} = 8.9875 \jeer 10^9 \, \frac{2 \jeer 10^{-12}}{0,01} \]
\[ F_{12} = 8.9875 \jeer 10^9 \, \jeer 2 \jeer 10^{-10} \]
\[ F_{12} = 1.7975 \, N \]
Maadaama \( q_1 \) uu yahay togan iyo \( q_2 \) uu yahay taban, xoogga \( F_{12} \) waa xoog soo jiidasho leh oo loo jiheeyay \( q_1 \).
Marka labaad, waxaan xisaabineynaa xoogga korontada ku shaqeeya ee u dhexeeya \( q_2 \) iyo \( q_3 \):
\[ F_{23} = k_e \frac{|q_2 \cdot q_3|}{r^2} \]
\[ q_2 = -1 \jeer 10^{-6} \, C \]
\[ q_3 = 3 \jeer 10^{-6} \, C \]
\[ r = 0,2 \, m \]
\[ F_{23} = 8.9875 \jeer 10^9 \, \frac{(-1 \jeer 10^{-6}) (3 \jeer 10^{-6})}{(0,2)^2} \]
\[ F_{23} = 8.9875 \jeer 10^9 \, \frac{3 \jeer 10^{-12}}{0,04} \]
\[ F_{23} = 8.9875 \jeer 10^9 \, \jeer 7.5 \jeer 10^{-11} \]
\[ F_{23} = 0.67406 \, N \]
Maadaama \( q_2 \) uu yahay taban oo \( q_3 \) uu yahay togan, xoogga \( F_{23} \) waa xoog soo jiidasho leh oo loo jiheeyay \( q_3 \).
Ugu dambeyntii, waxaan isku dareynaa labada awoodood si aan u helno natiijada kama dambaysta ah:
Wadarta xoogga saaran \( q_2 \):
\[ F_{\text{total}} = F_{12} – F_{23} \]
\[ F_{\text{wadarta}} = 1.7975 \, N – 0.67406\, N \]
\[ F_{\text{wadarta}} = 1.12344 \, N \]
Jihada guud ee xoogga waxay u socotaa dhanka \( q_1 \) sababtoo ah xoogga \( F_{12} \) wuxuu ka weyn yahay \( F_{23} \).
Gabagabo
Sharciga Coulomb wuxuu bixiyaa aragtiyo muhiim ah oo ku saabsan isdhexgalka u dhexeeya dallacaadaha korontada, kuwa soo jiidashada leh iyo kuwa aan la jeclayn labadaba. Tusaalooyinka laga wada hadlay waxay muujinayaan hirgelinta sharcigan marka la xisaabinayo awoodaha korontada iyadoo la tixgelinayo baaxadda dallacaadaha iyo masaafada u dhaxaysa. Faham buuxa oo ku saabsan Sharciga Coulomb wuxuu naga caawin karaa inaan fahanno dhacdooyinka kala duwan ee korontada iyo birlabta ee nagu xeeran.
