Su'aalo Tusaale ah oo Ka Hadlaya Goobaha Birlabta
Goobta birlabta waa fikrad aasaasi ah oo ku jirta fiisikiska oo qeexaysa sida xoogagga birlabta ula falgalaan walxaha birlabta leh ama dallacaadaha korontada ee dhaqaaqaya. Barashada goobaha birlabta waa mid aad muhiim u ah sababtoo ah waxay leedahay codsiyo ballaaran, laga bilaabo aaladaha elektaroonigga ah ilaa caafimaadka ilaa duulista hawada. Maqaalkani wuxuu ka hadli doonaa dhowr tusaale oo ku saabsan barashada su'aalaha ku saabsan goobaha birlabta iyo sidoo kale dooddooda iyo xalalkooda, kuwaas oo aan rajeyneyno inay kaa caawin doonaan inaad si fiican u barato fikraddan.
Fahmidda Goobaha Birlabta
Guud ahaan, goob birlabeed waxaa soo saari kara birlab joogto ah ama koronto ku socota silig. Xoogga goobta birlabeed ee meel waxaa lagu xisaabiyaa iyadoo la adeegsanayo sharciga Biot-Savart ama sharciga Ampère, iyadoo ku xiran duruufaha gaarka ah. Goobta birlabeed waxaa lagu tilmaamaa vector B waxayna leedahay cutubyo Tesla (T).
Su'aalo iyo Doodo Tusaale ah
Su'aal 1: Goob birlab ah oo ku taal bartamaha goobada hadda socota
Su'aal: Xisaabi baaxadda goobta birlabta ee bartamaha wareegga silig wareegsan oo leh radius R iyo sidda hadda I.
Dood:
Goobta birlabta ee ku taal bartamaha wareegga silig wareegsan waxaa lagu xisaabin karaa iyadoo la adeegsanayo sharciga Biot-Savart kaas oo sheegaya:
\[ B = \frac{\mu_0 I}{2R} \]
Halkee:
– \( \mu_0 \) = marin u helidda faakuumka ( \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \) )
– I = koronto ku jirta wareegga
– R = gacanka wareegga
Ka soo qaad R = 0,1 m iyo I = 5 A, markaa baaxadda goobta birlabta ee bartamaha wareegga waa:
\[ B = \frac{4\pi \times 10^{-7} \times 5}{2 \times 0,1} = \frac{2\pi \times 10^{-6}}{0,1} = 2\pi \times 10^{-5} \, \text{T} \]
Markaa, baaxadda goobta birlabta ee bartamaha wareegga waa qiyaastii \( 6,28 \times 10^{-5} \, \text{T} \).
Su'aal 2: Goob Magnetic ah oo ku taal Silig Silig ah oo Si Toosan u Qaada Hadda
Su'aal: Go'aami goobta birlabta meel fog laga soo bilaabo silig dheer oo toosan oo sidda koronto I.
Dood:
Si loo xaqiijiyo goobta birlabta ee ku wareegsan silig sita hadda toosan, waxaan isticmaalnaa sharciga Ampere, kaas oo lagu sheegay sidan:
\[ B = \frac{\mu_0 I}{2\pi d} \]
Halkee:
– \( \mu_0 \) = marin u helidda faakuumka
– I = koronto ku jirta fiilada
– d = masaafada u jirta siligga
Ka soo qaad I = 10 A iyo d = 0,02 m, markaa:
\[ B = \frac{4\pi \times 10^{-7} \times 10}{2\pi \times 0,02} = \frac{4 \times 10^{-6} \times 10}{0,02} = 2 \times 10^{-4} \, \text{T} \]
Markaa, baaxadda goobta birlabta ee masaafada 0,02 mitir u jirta fiilada waa \( 2 \jeer 10^{-4} \, \text{T} \).
Su'aal 3: Goob birlab ah oo u dhaxaysa laba fiilooyin oo sidda hadda socda
Su'aal: Laba fiilooyin oo sidda hadda oo is barbar socda ayaa lagu kala saaraa masaafo d mid walbana wuxuu sitaa hadda oo I1 iyo I2 ah. Go'aami goobta birlabta ee bartamaha u dhaxaysa labada fiilooyin.
Dood:
Si loo xisaabiyo goobta birlabta ee bartamaha u dhaxaysa laba fiilo, waa in aan tixgelinnaa jihada iyo baaxadda goobta birlabta ee ay soo saarto silig kasta.
Bal qiyaas I1 = 5 A iyo I2 = 10 A, masaafada u dhaxaysa labada fiilooyinna waa 0,1 m. Markaa masaafada u dhaxaysa barta dhexe ilaa fiilooyin kasta waa 0,05 m. Iyada oo ku saleysan sharciga Ampere:
Goobta birlabta ee fiilada 1 (B1) ee bartamaha:
\[ B_1 = \frac{\mu_0 I_1}{2\pi (d/2)} = \frac{4\pi \times 10^{-7} \times 5}{2\pi \times 0,05} = 2 \times 10^{-5} \, \text{T} \]
Goobta birlabta ee fiilada 2 (B2) ee bartamaha:
\[ B_2 = \frac{\mu_0 I_2}{2\pi (d/2)} = \frac{4\pi \times 10^{-7} \times 10}{2\pi \times 0,05} = 4 \times 10^{-5} \, \text{T} \]
Maadaama labada goobood ee birlabta ay ku yaalliin jihooyin iska soo horjeeda bartamaha, baaxadda guud ee goobta birlabta ee bartamaha waa farqiga u dhexeeya B2 iyo B1:
\[ B_{\text{total}} = B_2 – B_1 = 4 \jeer 10^{-5} – 2 \jeer 10^{-5} = 2 \jeer 10^{-5} \, \text{T} \]
Markaa, baaxadda goobta birlabta ee bartamaha u dhaxaysa labada fiilooyin waa \( 2 \times 10^{-5} \, \text{T} \).
Su'aal 4: Goob birlab ah oo ku taal xudunta Solenoid-ka
Su'aal: Xisaabi goobta birlabta ee ku jirta solenoid-ka dheer kaas oo leh wareeg n ah halkii cutubba dhererkiisa oo sita hadda I.
Dood:
Solenoid-ka dheer, goobta birlabta ee solenoid-ka waa mid ku dhawaad joogto ah waxaana lagu xisaabiyaa iyadoo la adeegsanayo isla'egta:
\[ B = \mu_0 n I \]
Halkee:
– \( \mu_0 \) = marin u helidda faakuumka
– n = tirada wareegyada mitirkiiba
– I = koronto koronto
Ka soo qaad in solenoid-ku uu leeyahay 1000 wareeg halkii mitir iyo hadda oo ah 2 A, markaa:
\[ B = 4\pi \times 10^{-7} \times 1000 \times 2 = 8\pi \times 10^{-4} \, \text{T} \]
\[ B = 8 \jeer 3.14 \jeer 10^{-4} = 25.12 \jeer 10^{-4} \, \qoraal{T} \]
Markaa, goobta birlabta ee ku jirta solenoid-ka waa qiyaastii \( 2.51 \times 10^{-3} \, \text{T} \).
Gabagabo
Fahmidda goobaha birlabta ayaa fure u ah codsiyada tignoolajiyada casriga ah ee badan. Tusaalooyinkan, akhristayaashu waxay rajeynayaan inay si fiican u fahmaan sida goobaha birlabta ay u shaqeeyaan xaalado kala duwan, sida wareegga siligga wareegsan, silig toosan, laba fiilo oo is barbar socda, iyo solenoid. Ku celcelinta joogtada ah ee leh dhibaatooyin iyo xaalado kala duwan ayaa sii xoojin doonta fikraddan.
