Su'aalo Tusaale ah oo Ka Hadlaya Xoogga Birlabta
Xoogga birlabta waa mid ka mid ah afarta awoodood ee aasaasiga ah ee fiisigiska waxayna door muhiim ah ka ciyaartaa dhacdooyinka dabiiciga ah ee kala duwan iyo tignoolajiyada casriga ah. Fahmidda fikraddan waxay u baahan tahay faham qoto dheer oo ku saabsan birlabta, goobaha birlabta, sharciyada electromagnetism-ka, iyo adeegsigeeda wax ku oolka ah ee nolol maalmeedka. Maqaalkani wuxuu ka hadli doonaa dhowr tusaale oo dhibaatooyin ah oo la xiriira xoogga birlabta, iyo doodo faahfaahsan si looga caawiyo akhristayaasha inay si fiican u fahmaan fikradda.
Fahmidda Xoogga Birlabta
Kahor inta aan laga hadlin dhibaatada, waa muhiim in la fahmo aasaaska xoogga birlabta. Xoogga birlabta waa xoog ay soo saarto goob birlabta waxayna ku shaqeysaa walxaha korontada ku shaqeeya ama walxaha birlabta. Goobta birlabta lafteedu waa meel lagu dareemi karo xoogga birlabta. Qofku wuxuu dareemi karaa xoogga birlabta marka laba birlab la isku soo dhawaado ama marka shay koronto ku shaqeeya la dhigo goob birlabta.
Goob birlabeed waxaa lagu tilmaamaa khadadka goobta birlabeed ee ka soo baxa tiirka waqooyi oo gala tiirka koonfureed. Intaa waxaa dheer, tiirarka birlabeed ee ku xiga ee leh tiirar iska soo horjeeda ayaa is soo jiidanaya, halka tiirarka oo kale ay is celinayaan.
Su'aalo iyo Doodo Tusaale ah
Su'aal 1: Goob birlab ah oo ku wareegsan silig toosan
Fiilo dheer oo toosan ayaa sidda hadda 5 A. Go'aami baaxadda goobta birlabta masaafada 0,2 m u jirta fiilada.
Dood:
Si loo helo baaxadda goobta birlabta ee ku wareegsan silig toosan oo sidda koronto, waxaan isticmaali karnaa sharciga Biot-Savart, laakiin kiiskan way fududahay in la isticmaalo sharciga Ampere:
Goobta birlabta \( B \) ee ku wareegsan silig dheer oo toosan waxaa lagu xisaabin karaa qaacidada:
\[ B = \frac{\mu_0 I}{2\pi r} \]
Halkee:
– \( \mu_0 \) waa marin-u-helidda faakuumka (\( 4\pi \times 10^{-7} \, T \cdot m/A \))
– \( I \) waa xoogga hadda jira (A)
– \( r \) waa masaafada fiilada (m)
Iyada oo la raacayo qiimayaasha la bixiyay:
– \( I = 5 \, A \)
– \( r = 0,2 \, m \)
Qiimahan ku beddel qaacidada:
\[
B = \frac{4\pi \times 10^{-7} \times 5}{2\pi \times 0,2}
\]
Fududee:
\[
B = \frac{4\pi \times 10^{-7} \times 5}{2\pi \times 0,2} \rightarrow
B = \frac{4 \jeer 5 \jeer 10^{-7}}{2 \jeer 0,2} \rightarrow
B = \frac{20 \times 10^{-7}}{0,4} = 5 \times 10^{-6} \, T \] ama \(5 \, \mu T\) (microtesla).
Su'aal 2: Xoogga Lorentz ee Walxaha la Dacweeyay
Walax si togan u dallacsan \(q = 1 \, \mu C\) (microCoulomb) oo ku socota xawaare \(v = 2 \times 10^4 \, m/s\) waxay gashaa goob birlabeed oo isku mid ah iyadoo la adeegsanayo soo-kicin birlabeed \(B = 0,5 \, T\) oo ku toosan jihada xawaaraha walaxda. Xisaabi xoogga birlabka ee ay la kulantay walaxda.
Dood:
Xoogga birlabta (xoogga Lorentz) ee ay la kulmaan walxaha la dallacay waxaa lagu xisaabin karaa qaacidada:
\[ F = q \cdot v \cdot B \cdot \sin(\theta) \]
Halkee:
– \( q \) waa korontada (C)
– \( v \) waa xawaaraha walxaha (m/s)
– \( B \) waa goobta birlabta (T)
– \( \theta \) waa xagasha u dhaxaysa xawaaraha iyo jihada goobta birlabta
Xaaladdan, goobta birlabta ayaa si toosan ugu toosan xawaaraha walxaha, sidaa darteed
\(\theta = 90^\circle\) iyo \(\sin(90^\circle) = 1\).
La bixiyay:
– \( q = 1 \, \mu C = 1 \jeer 10^{-6} \, C \)
– \( v = 2 \jeer 10^4 \, m/s \)
– \( B = 0,5 \, T \)
Qiimahan ku beddel qaacidada:
\[
F = 1 \jeer 10^{-6} \cdot 2 \jeer 10^4 \cdot 0,5 \cdot 1 \]
Fududee:
\[
F = 1 \jeer 10^{-6} \jeer 10^4 \jeer 1 = 10^{-6} \jeer 0,5 = 10^{-6} \jeer 0,5 = 1 \jeer 10^{-6} \, N
\]
Su'aal 3: Goob birlab ah oo ku taal bartamaha Wareegga Siligga
Anteeno wareegsan (wareeg) oo leh gacan 10 cm ah ayaa la socda hadda 3 A. Waa maxay baaxadda goobta birlabta ee bartamaha goobada?
Dood:
Goobta birlabta ee ku taal bartamaha wareegga siligga sidda hadda waxaa lagu xisaabin karaa qaacidada:
\[
B = \frac{\mu_0 I}{2r}
\]
Halkee:
– \( \mu_0 \) waa marin-u-helidda faakuumka (\( 4\pi \times 10^{-7} \, T \cdot m/A \))
– \( I \) waa xoogga hadda jira (3 A)
– \( r \) waa gacanka (10 cm = 0,1 m)
Qiimahan ku beddel qaacidada:
\[
B = \frac{4\pi \times 10^{-7} \times 3}{2 \times 0,1}
\]
Fududee:
\[
B = \frac{4\pi \times 10^{-7} \times 3}{0,2} = \frac{12\pi \times 10^{-7}}{0,2} = 60 \times 10^{-7} \, T \]
\[ B = 6 jeer 10^{-6} \, T \] ama \(6 \, \mu T\) (microtesla).
Gabagabo
Fahmidda awoodaha birlabta ayaa muhiim u ah fiisigiska iyo adeegsigiisa tignoolajiyada casriga ah ee kala duwan. Tusaalooyinka kor lagu soo sheegay, waxaan arki karnaa sida fikradaha aasaasiga ah sida goobaha birlabta, sharciga Ampère, iyo xoogga Lorentz loogu dabaqo xaaladaha dhabta ah ee adduunka. Ku celcelinta joogtada ah ee xallinta dhibaatooyinka sida kuwaan oo kale ah waxay si weyn uga caawin doontaa qoto dheereynta fahamkaaga iyo hagaajinta xirfadahaaga fiisigiska birlabta.
Maqaalkani waxaa la filayaa inuu bixiyo sawir cad oo ku saabsan sida xoogagga birlabta u shaqeeyaan iyo sida aan u falanqeyn karno dhibaatooyinka ku lug leh fikraddan si qoto dheer iyo faahfaahsan.
