Tusaalaha Su'aalaha Xoogga Goobta Korontada
Xoogga goobta korontada waa fikrad aasaasi ah oo ku jirta fiisikiska oo qeexaysa xoogga goobta korontada meel gaar ah oo hawada sare ah. Goobaha korontada waxaa soo saara kharashyada korontada waxayna saameyn karaan kharashyada kale ee gudaha goobtaas. Si aan si fiican u fahanno fikraddan, aan eegno tusaalooyin dhibaatooyin ah oo la xiriira xoogga goobta korontada iyo sida loo xalliyo.
Aasaaska Goobaha Korontada
Kahor inta aynaan guda gelin dhibaatooyinka tusaalaha ah, aan dib u eegno wax yar oo ku saabsan fikradda aasaasiga ah ee goobaha korontada. Xoogga goobta korontada (\(E\)) ee meel bannaan ah waxaa lagu qeexaa xoogga (\(F\)) halkii cutub ee dallacaadda (\(q\)) oo ay la kulmaan dallacaadda tijaabada yar ee meeshaas:
\[ E = \frac{F}{q} \]
Halkee:
– \(E\) waa xoogga goobta korantada (N/C ama V/m),
– \(F\) waa xoogga korontada ee ay la kulanto dallacaadda (N),
– \(q\) waa baaxadda kharashka tijaabada (C).
Haddii isha goobta korontadu ay tahay dallac dhibic \(Q\), markaa xoogga goobta korontadu ee masaafada \(r\) u jirta dallacaadda waxaa lagu bixiyaa isla'egta:
\[ E = \frac{k \cdot |Q|}{r^2} \]
Halkee:
– \(k\) waa joogtada Coulomb (\(8.99 \times 10^9 \, \text{N m}^2/\text{C}^2\)),
– \(Q\) waa kharashka isha (C),
– \(r\) waa masaafada u dhaxaysa lacagta laga soo qaado isha ilaa barta la socodka (m).
Su'aal Tusaale 1aad: Goobta Korontada iyadoo la adeegsanayo Lacag Dhibco ah
Su'aal: Dalac \(Q\) oo ah \(5 \jeer 10^{-6} \, \text{C}\) ayaa la dhigayaa asalka (0,0). Xisaabi xoogga goobta korantada masaafada 2 mitir u jirta dalacaadda.
Xalka:
Laga soo bilaabo isla'egta goobta korantada iyadoo la adeegsanayo dallacaadda dhibicda, waxaan u xisaabin karnaa xoogga goobta korantada sida soo socota:
\[ E = \frac{k \cdot |Q|}{r^2} \]
Geli qiimaha \(k\), \(Q\), iyo \(r\):
\[ E = \frac{8.99 \jeer 10^9 \jeer 5 \jeer 10^{-6}}{2^2} \]
\[ E = \frac{8.99 \jeer 10^9 \jeer 5 \jeer 10^{-6}}{4} \]
\[ E = \frac{44.95 \times 10^3}{4} \]
\[ E = 11.2375 \ jeer 10^3 \]
\[ E = 11,237.5 \, \ qoraal {N/C} \]
Markaa, xoogga goobta korantada ee masaafada 2 mitir u jirta dallacaadda waa \(11,237.5 \, \text{N/C}\).
Tusaale 2: Kordhinka Goobaha Korontada
Su'aal: Laba dallac, \(Q_1 = 4 \jeer 10^{-6} \, \text{C}\) iyo \(Q_2 = -3 \jeer 10^{-6} \, \text{C}\) ayaa la dhigayaa masaafo 3 mitir u jirta midba midka kale. Xisaabi xoogga goobta korantada ee bartamaha u dhexeeya labada dallac.
Xalka:
Marka hore, waxaan xisaabineynaa goobta korantada ee ay soo saarto dallac kasta oo ku yaal bartamaha.
Lacag ahaan \(Q_1\):
\[ r_1 = \frac{3}{2} = 1.5 \, \text{m} \]
\[ E_1 = \frac{k \cdot |Q_1|}{r_1^2} \]
\[ E_1 = \frac{8.99 \jeer 10^9 \jeer 4 \jeer 10^{-6}}{1.5^2} \]
\[ E_1 = \frac{35.96 \jeer 10^3}{2.25} \]
\[ E_1 = 15.9822 \ jeer 10^3 \]
\[ E_1 = 15,982.2 \, qoraal{N/C} \]
Lacag ahaan \(Q_2\):
\[ r_2 = 1.5 \, \qoraalka{m} \]
\[ E_2 = \frac{k \cdot |Q_2|}{r_2^2} \]
\[ E_2 = \frac{8.99 \jeer 10^9 \jeer 3 \jeer 10^{-6}}{1.5^2} \]
\[ E_2 = \frac{26.97 \jeer 10^3}{2.25} \]
\[ E_2 = 11.9822 \ jeer 10^3 \]
\[ E_2 = 11,982.2 \, qoraal{N/C} \]
Maadaama \(Q_1\) uu yahay mid togan oo \(Q_2\) uu yahay mid taban, goobahooda korontada ee bartamaha ayaa iska sii fogaan doona. Markaa, waxaan ku dareynaa labada goobood ee korontada:
\[ E = E_1 + E_2 \]
\[ E = 15,982.2 + 11,982.2 \]
\[ E = 27,964.4 \, \ qoraal {N/C} \]
Markaa, xoogga goobta korantada ee bartamaha u dhexeeya labada dallacaad waa \(27,964.4 \, \text{N/C}\).
Tusaale 3: Goobta Korontada ee Dipole
Su'aal: Diidoole koronto wuxuu ka kooban yahay laba dallacaad \(\pm 4 \times 10^{-6} \, \text{C}\) oo 1 cm u jira. Xisaabi xoogga goobta korontada meel 1 mitir u jirta bartamaha dipole-ka ee dhidibka dipole-ka.
Xalka:
Xoogga goobta korantada ee ku teedsan dhidibka dipole (masaafadaha ku filan ee ka weyn masaafada u dhaxaysa dallacaadaha dipole) waxaa lagu bixiyaa:
\[ E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{2p}{r^3} \]
Halka \(p\) uu yahay daqiiqadda dipole-ka korontada (\(p = q \cdot d\)), \(d\) uu yahay masaafada u dhaxaysa dallacaadaha dipole-ka, iyo \(r\) uu yahay masaafada u dhaxaysa bartamaha dipole-ka ilaa barta la socodka.
Marka hore, xisaabi daqiiqadda dipole:
\[ p = q \cdot d \]
\[ p = 4 \ jeer 10^{-6} \cdot 0.01 \]
\[ p = 4 \ jeer 10^{-8} \, \qoraalka{C m} \]
Kadib, xisaabi xoogga goobta korantada:
\[ E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{2p}{r^3} \]
\[ E = \frac{8.99 \times 10^9}{1} \cdot \frac{2 \times 4 \times 10^{-8}}{1^3} \]
\[ E = 8.99 \jeer 10^9 \cdot 8 \jeer 10^{-8} \]
\[ E = 7.192 \ jeer 10^2 \]
\[ E = 719.2 \, \ qoraal {N/C} \]
Markaa, xoogga goobta korantada ee barta 1 mitir u jirta bartamaha dipole-ka ee dhidibka dipole waa \(719.2 \, \text{N/C}\).
Gabagabo
Fahmidda xoogga goobta korontada ayaa muhiim u ah fiisigiska iyo adeegsigeeda. Dhibaatooyinka tusaalaha ah ee kor ku xusan waxay muujinayaan sida mabaadi'da aasaasiga ah ee goobaha korontada loo isticmaali karo si loo xisaabiyo xoogga goobta ee qaabab kala duwan oo dallacaad ah. Dhibaatooyinka ku dhaqanka sida kuwaan ayaa aad waxtar ugu leh fahamka fikradda iyo adeegsiga sharciga Coulomb iyo superposition-ka goobta korontada. Adigoo fahmaya oo ku dhaqmaya dhibaatooyin badan, waxaan si qoto dheer u fahmi karnaa isdhexgalka korontada ee nidaamyada kala duwan.
