Tusaale Su'aal Dood ah oo ku saabsan Fiilo Wareegan oo sidda Koronto
Pendahuluan
Fiilo duuban oo sidda koronto waa qayb muhiim ah oo ka mid ah codsiyada badan ee fiisigiska iyo injineernimada korontada. Fahmidda mabaadi'da aasaasiga ah iyo xisaabinta goobaha birlabta ee ay soo saarto fiiladani waa lama huraan meelo kala duwan, laga bilaabo naqshadeynta matoorka korontada ilaa dareemayaasha goobta birlabta. Maqaalkani wuxuu sahaminayaa dhowr dhibaato oo tusaale ah iyo xalalkooda si uu akhristayaasha uga caawiyo inay fahmaan mabaadi'da aasaasiga ah ee fiilada duuban ee sidda koronto.
Goob Magnetic ah oo ay ku jirto Silig La Duubay
Sharciga Biot-Savart
Sharciga Biot-Savart wuxuu saldhig u yahay xisaabinta goobta birlabta ee ku wareegsan fiilada sidda hadda jirta. Qaabaynta aasaasiga ah ee sharciga Biot-Savart waa sidan soo socota:
\[
d\mathbf{B} = \frac{\mu_0}{4\pi} \cdot \frac{I d\mathbf{l} \times \mathbf{\hat{r}}}{r^2}
\]
Halkee:
– \( \mathbf{B} \) waa goobta birlabta
– \( \mu_0 \) waa marin-u-helidda faakuumka (\( 4\pi \times 10^{-7} \ \text{H/m} \))
– \(I \) waa qulqulka korantada
– \( d\mathbf{l} \) waa walax yar oo ka mid ah fiilada
– \( \mathbf{\hat{r}} \) waa vector cutub oo jihada ka imanaya curiyaha siligga ilaa barta la socodka
– \( r \) waa masaafada u dhaxaysa curiyaha siligga iyo barta la socodka
Silig Hal-la-duuban
Goobta birlabta ee ku taal bartamaha wareegga silig wareegsan oo leh radius \( R \) iyo current \( I \) waa:
\[
B = \frac{\mu_0 I}{2R}
\]
Su'aal Tusaale 1aad
Su'aal: Xisaabi goobta birlabta ee ku taal bartamaha wareegga siligga oo leh gacan 10 cm ah oo sidda hadda 5 A ah.
Dood:
Isticmaal qaacidada goobta birlabta ee hal wareeg,
\[
B = \frac{\mu_0 I}{2R}
\]
Halkee:
– \( \mu_0 = 4\pi \times 10^{-7} \ \text{H/m} \)
– \( I = 5 \ \qoraal{A} \)
– \( R = 0.1 \ \text{m} \) (sababtoo ah 10 cm = 0.1 m)
Adigoo beddelaya qiimayaashan,
\[
B = \frac{4\pi \times 10^{-7} \times 5}{2 \times 0.1}
\]
\[
B = \frac{20\pi \times 10^{-7}}{0.2}
\]
\[
B = 2\pi \jeer 10^{-6} \ \qoraal{T}
\]
\[
B = 6.28 \jeer 10^{-6} \ \qoraal{T}
\]
Markaa, goobta birlabta ee ku taal bartamaha wareegga siligga waa \( 6.28 \ \mu T \).
Su'aal Tusaale 2aad
Su'aal: Gariir ka kooban 20 wareeg oo leh gacan 10 cm ah wuxuu sitaa hadda 5 A. Xisaabi goobta birlabta ee bartamaha gariiradda.
Dood:
Goobta birlabta ee gariiradda N-rogidda waa:
\[
B = \frac{\mu_0 NI}{2R}
\]
Halkee:
– \( N = 20 \)
– \( I = 5 \ \qoraal{A} \)
– \( R = 0.1 \ \qoraalka{m} \)
– \( \mu_0 = 4\pi \times 10^{-7} \ \text{H/m} \)
Adigoo beddelaya qiimayaashan,
\[
B = \frac{4\pi \times 10^{-7} \times 20 \times 5}{2 \times 0.1}
\]
\[
B = \frac{400\pi \times 10^{-7}}{0.2}
\]
\[
B = 20\pi \jeer 10^{-6} \ \qoraal{T}
\]
\[
B = 62.8 \jeer 10^{-6} \ \qoraal{T}
\]
Markaa, goobta birlabta ee ku taal bartamaha gariiradda waa \( 62.8 \ \mu T \).
Silig Wareeg ah oo ku yaal xagal gaar ah
Haddii silig side ah oo hadda la jaro xagal, markaas qaybtaas wareegga ah waxay soo saari doontaa goob birlabeed oo ka duwan. Tusaale ahaan, goob wareeg ah, goob birlabeedku waa kala bar goob birlabeed oo buuxda, taasoo u baahan is-dhexgal dheeraad ah oo loogu talagalay xalalka adag.
Su'aal Tusaale 3aad
Su'aal: Xisaabi goobta birlabta ee bartamaha silig wareegsan oo wareegta badhkeed (180 darajo) oo keliya, oo leh gacan 10 cm ah iyo hadda 5 A ah.
Dood:
Goobo nus-goob ah, goobta birlabta ee bartamaha ku taal waa kala bar goobta birlabta oo buuxda:
\[
B = \frac{1}{2} \cdot \frac{\mu_0 I}{2R}
\]
Halkee:
– \( \mu_0 = 4\pi \times 10^{-7} \ \text{H/m} \)
– \( I = 5 \ \qoraal{A} \)
– \( R = 0.1 \ \qoraalka{m} \)
Adigoo beddelaya qiimayaashan,
\[
B = \frac{1}{2} \cdot \frac{4\pi \times 10^{-7} \times 5}{2 \times 0.1}
\]
\[
B = \frac{1}{2} \times 2\pi \times 10^{-6} \ \text{T}
\]
\[
B = \pi \times 10^{-6} \ \text{T}
\]
\[
B = 3.14 \jeer 10^{-6} \ \qoraal{T}
\]
Markaa, goobta birlabta ee ku taal bartamaha siligga wareega ah waa \( 3.14 \ \mu T \).
Xiritaanka
Tusaalooyinka kor ku xusan, waxaa la rajeynayaa in akhristayaashu ay si fiican u fahmi doonaan sida loo xisaabiyo goobta birlabta ee ay soo saarto silig duuban oo sita koronto. Fahamkan aad ayuu waxtar ugu leeyahay codsiyada tignoolajiyada kala duwan iyo cilmi-baarista sayniska, gaar ahaan meelaha electromagnetism-ka iyo injineernimada korontada.
