Su'aalo Tusaale ah oo Ka Hadlaya Goobaha Korontada ee Taarikada Isbarbar socda
Goobta korontada ee saxanadaha barbar socda waa fikrad aasaasi ah oo ku saabsan fiisikiska korontada waxaana si joogto ah loogu tijaabiyaa heerar waxbarasho oo kala duwan, labadaba dugsiga sare iyo kulliyadda. Faham buuxa oo ku saabsan fikraddan waa muhiim, maadaama goobta korontada ee saxanadaha barbar socda ay si dhow ula xiriirto codsiyo kala duwan oo wax ku ool ah, oo ay ku jiraan naqshadeynta kaabsoodhada iyo aaladaha kale ee elektaroonigga ah. Maqaalkani wuxuu bixin doonaa tusaalooyin dhibaatooyin ah iyo dood faahfaahsan oo ku saabsan goobta korontada ee saxanadaha barbar socda si uu u caawiyo fahamka fikraddan.
Aragtida Aasaasiga ah ee Goobaha Korontada ee Taarikada Isbarbar socda
Saxannada is barbar socda waa laba saxan oo wax qabta oo qaada kharashyo koronto oo iska soo horjeeda waxaana loo habeeyay si is barbar socda masaafo cayiman. Saxannadan is barbar socda, kharashku wuxuu u janjeeraa inuu si siman ugu qaybsamo dusha sare ee saxannada. Sida ku cad sharciga Gauss, goobta korantada \(E \) ee u dhaxaysa laba saxan oo wax qabta oo is barbar socda oo leh kharashyo iska soo horjeeda waxaa lagu tilmaami karaa sidan:
\[ E = \frac{\sigma}{\epsilon_0} \]
Halkee:
– \( \sigma \) waa cufnaanta dusha sare ee saxanka,
– \( \epsilon_0 \) waa ogolaanshaha faakuumka \((8.85 \times 10^{-12} \, \text{F/m})\).
Xaaladaha ku habboon (cabbirka saxanka waa weyn yahay marka la barbar dhigo masaafada u dhaxaysa), goobta korantada ee u dhaxaysa saxanka waxaa loo arkaa mid isku mid ah.
Su'aalo iyo Doodo Tusaale ah
Su'aal 1aad:
Laba saxan oo is barbar socda oo leh aag A oo aad u weyn marka loo eego masaafada \(d \) ee u dhaxaysa ayaa loo habeeyey si saxanka sare uu u yeesho dallac \( +Q \) saxanka hoosena uu u leeyahay dallac \( -Q \). Haddii masaafada u dhaxaysa labada saxan ay tahay \( 2 \, \text{mm} \), bedka saxan kasta waa \( 1 \, \text{m}^2 \), dallacaadda \( Q \)na ay tahay \( 1 \, \mu \text{C} \), go'aami goobta korantada ee u dhaxaysa saxannada is barbar socda!
Tallaabooyinka Doodda:
1. Cufnaanta Dareeraha Dusha sare \( \sigma \):
Cufnaanta kharashka dusha sare waa xaddiga kharashka halkii cutub ee ku yaal saxanka. Waxaa lagu xisaabin karaa:
\[ \sigma = \frac{Q}{A} \]
Waa la ogyahay:
– \( Q = 1 \, \mu \text{C} = 1 \jeer 10^{-6} \text{C} \)
– \( A = 1 \, \qoraalka{m}^2 \)
Markaa:
\[ \sigma = \frac{1 \times 10^{-6} \text{C}}{1 \text{m}^2} = 1 \times 10^{-6} \text{C/m}^2 \]
2. Goobta Korontada \( E \):
Goobta korantada ee u dhaxaysa laba saxan oo is barbar socda oo leh dalac iska soo horjeeda waa \( E = \frac{\sigma}{\epsilon_0} \).
Marka la eego \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \), ka dibna:
\[ E = \frac{1 \times 10^{-6} \text{C/m}^2}{8.85 \times 10^{-12} \text{F/m}} \]
\[ E = 1.13 \times 10^5 \, \text{N/C} \]
Markaa, goobta korantada ee u dhaxaysa labada saxan waa \( 1.13 \times 10^5 \, \text{N/C} \).
Su'aal 2aad:
Kaaliyaha saxanka fidsan wuxuu ka kooban yahay laba saxan oo is barbar socda oo leh bedka \( 2 \, \text{m}^2 \) midkiiba waxaana kala fogeeya masaafada \( 1 \, \text{mm} \). Haddii awoodda saxanka sare ay tahay \( 200 \, \text{V} \) iyo saxanka hoose uu yahay 0 V, go'aami xoogga goobta korantada ee u dhexeeya labada saxan!
Tallaabooyinka Doodda:
1. Xisaabinta Farqiga Suurtagalka ah \( V \):
Waa la ogyahay in saxanka sare uu leeyahay awood \( V_{\text{top}} = 200 \, \text{V} \) iyo saxanka hoose \( V_{\text{bottom}} = 0 \, \text{V} \). Sidaa darteed, farqiga suurtagalka ah \( V \) ee u dhexeeya labada saxan waa:
\[ V = V_{\text{top}} – V_{\text{bottom}} = 200 \, \text{V} – 0 \, \text{V} = 200 \, \text{V} \]
2. Xoogga Goobta Korontada \( E \):
Goobta korantada ee ku jirta capacitor-ka saxanka barbar socda waxaa lagu xisaabin karaa iyadoo farqiga suurtagalka ah \( V \) loo qaybinayo masaafada \( d \):
\[ E = \frac{V}{d} \]
Marka la eego masaafada \( d = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} \), markaa:
\[ E = \frac{200 \, \text{V}}{1 \times 10^{-3} \, \text{m}} = 2 \times 10^5 \, \text{V/m} \]
Markaa, xoogga goobta korantada ee u dhaxaysa labada saxan waa \( 2 \times 10^5 \, \text{V/m} \).
Su'aal 3aad:
Kaaliyaha saxanka barbar socda wuxuu leeyahay saxanno leh bedka \( 0.5 \, \text{m}^2 \) iyo masaafada u dhaxaysa saxannada \( 0.5 \, \text{cm} \). Haddii kaaliyahan lagu dallaco kharash ah \( 2 \, \mu \text{C} \), xisaabi kartidiisa iyo goobta korantada ee u dhaxaysa saxannada!
Tallaabooyinka Doodda:
1. Awoodda \( C \):
Awoodda capacitor-ka saxanka barbar socda waxaa lagu xisaabin karaa qaacidada:
\[ C = \epsilon_0 \frac{A}{d} \]
Waa la ogyahay:
– \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \)
– \( A = 0.5 \, \qoraalka{m}^2 \)
– \( d = 0.5 \, \qoraalka{cm} = 0.5 \jeer 10^{-2} \, \qoraalka{m} \)
Markaa:
\[ C = 8.85 \jeer 10^{-12} \, \qoraalka{F/m} \times \frac{0.5 \, \qoraalka{m}^2}{0.5 \jeer 10^{-2} \, \qoraalka{m}} \]
\[ C = 8.85 \jeer 10^{-12} \jeer 10 \, \qoraal{F} \]
\[ C = 88.5 \jeer 10^{-12} \, \qoraalka{F} \]
\[ C = 88.5 \, \qoraalka{pF} \]
2. Goobta Korontada \( E \):
Si loo xisaabiyo goobta korantada, waa inaan marka hore ogaano farqiga suurtagalka ah \( V \). Farqiga suurtagalka ah \( V \) waxaa loo xisaabin karaa sidan:
\[ V = \frac{Q}{C} \]
Waa la ogyahay:
– \( Q = 2 \, \mu \text{C} = 2 \jeer 10^{-6} \text{C} \)
– \( C = 88.5 \jeer 10^{-12} \qoraalka{F} \)
Markaa:
\[ V = \frac{2 \times 10^{-6} \, \text{C}}{88.5 \times 10^{-12} \, \text{F}} \]
\[ V = 22.6 \ jeer 10^3 \, \qoraal{V} \]
\[ V = 22.6 \, \qoraal{kV} \]
Marka xigta, adoo isticmaalaya qaacidada \( E = \frac{V}{d} \), goobta korantada waa:
\[ E = \frac{22.6 \, \text{kV}}{0.5 \times 10^{-2} \, \text{m}} \]
\[ E = 22.6 \jeer 10^3 \, \frac{\text{V}}{0.5 \jeer 10^{-2} \, \text{m}} \]
\[ E = 4.52 \ jeer 10^6 \, \qoraal{V/m} \]
Markaa, awoodda kaabsooshadu waa \( 88.5 \, \text{pF} \) goobta korontada ee u dhaxaysa taarikadana waa \( 4.52 \times 10^6 \, \text{V/m} \).
Gabagabo
Fahmidda goobta korantada ee taarikada is barbar socda waa muhiim maaha oo keliya imtixaannada tacliinta laakiin sidoo kale codsiyada wax ku oolka ah ee qaybaha kala duwan ee injineernimada iyo fiisigiska. Iyadoo la adeegsanayo dhibaatooyinka iyo doodaha tusaalaha ah ee kor ku xusan, waxaa la rajeynayaa in akhristayaashu ay si fiican u fahmi doonaan fikradda iyo codsigeeda, taasoo u suurtagelinaysa inay si kalsooni leh ugu wajahaan xaaladaha iyo imtixaannada dhabta ah.
