Su'aalo Tusaale ah oo Ka Hadlaya Goobaha Birlabta ee Ku wareegsan Silig Toosan
Pengantar
Garoomada birlabta waxay had iyo jeer ahaayeen mowduuc xiiso leh oo ku jira fiisikiska, gaar ahaan doodda ku saabsan sida loo sameeyo iyo sida ay ula falgalaan qulqulka korontada. Mid ka mid ah dhinacyada muhiimka ah ee garoomada birlabta waa garoon birlabta ah oo ku wareegsan silig sita hadda toosan. Maqaalkan, waxaan ka hadli doonnaa fikradda aasaasiga ah ee garoon birlabta ah oo ku wareegsan silig toosan waxaanan bixin doonnaa dhowr dhibaato iyo xalal tusaale ah si aan u sii xoojinno fahamkeenna.
Aragtida Aasaasiga ah ee Goobaha Birlabta ee ku wareegsan Fiilooyinka Toosan
Kahor inta aynaan guda gelin dhibaatada tusaalaha ah, waxaa muhiim ah in marka hore la fahmo aragtida aasaasiga ah ee goobaha birlabta ee ku wareegsan silig toosan. Sida waafaqsan sharciga Biot-Savart iyo sharciga Ampère, goobta birlabta ee ku wareegsan silig toosan oo sidda koronto waxaa lagu muujin karaa isla'egta:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
Xaggee,
– \( B \) waa goobta birlabta (Tesla),
– \( \mu_0 \) waa marin-u-helidda faakuumka \( (4\pi \times 10^{-7} T \cdot m/A) \),
– \( I \) waa hadda socota ee ku jirta fiilada (Ampere), iyo
– \( r \) waa masaafada u dhaxaysa fiilada ilaa meesha lagu cabbiro goobta birlabta (mitir).
Goobtan birlabta ah waxay samaysaa goobo wareegsan oo ku wareegsan siligga iyadoo la raacayo xeerka midigta. Haddii suulka uu tilmaamayo jihada hadda jirta, markaa faraha haya siligga waxay tilmaamayaan jihada goobta birlabta.
Su'aalo iyo Doodo Tusaale ah
Su'aal 1aad:
Fiilo dheer oo toosan ayaa sidda koronto koronto oo ah 10 A. Xisaabi baaxadda goobta birlabta masaafada 0,2 mitir u jirta fiilada.
Dood:
Waxaan u isticmaalnaa isla'egta goobta birlabta ee ku wareegsan silig toosan:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
Waa la ogyahay:
\[ I = 10 \, A \]
\[ r = 0,2 \, m \]
\[ \mu_0 = 4 \pi \times 10^{-7} \, T \cdot m/A \]
Qiimahan ku beddel isla'egta:
\[ B = \frac{4 \pi \times 10^{-7} \times 10}{2 \pi \times 0,2} \]
\[ B = \frac{4 \pi \times 10^{-6}}{2 \pi \times 0,2} \]
\[ B = \frac{4 \jeer 10^{-6}}{0,2} \]
\[ B = 20 \ jeer 10^{-6} \]
\[ B = 2 \jeer 10^{-5} \, T \]
\[ B = 20 \, \mu T \]
Markaa, baaxadda goobta birlabta ee masaafada 0,2 mitir u jirta siligga waa 20 μT (microTesla).
Su'aal 2aad:
Laba fiilooyin oo toosan oo dheer ayaa sita isku mar koronto 5 A ah laakiin jihooyin iska soo horjeeda, masaafada u dhaxaysana waa 0,1 mitir. Xisaabi baaxadda goobta birlabta meel u dhaxaysa labada fiilooyin.
Dood:
Barta dhexe ee u dhaxaysa labada fiilooyin, masaafada waa \( r = 0,05 \, m \) laga bilaabo fiilooyin kasta. Waxaan marka hore xisaabinaynaa goobta birlabta ee ka dhalata hal fiilood.
Silig kasta:
\[ B_1 = \frac{\mu_0 I}{2 \pi r} \]
Waa la ogyahay:
\[ I = 5 \, A \]
\[ r = 0,05 \, m \]
\[ \mu_0 = 4 \pi \times 10^{-7} \, T \cdot m/A \]
Qiimahan ku beddel isla'egta:
\[ B_1 = \frac{4 \pi \times 10^{-7} \times 5}{2 \pi \times 0,05} \]
\[ B_1 = \frac{4 \pi \times 10^{-7} \times 5}{\pi \times 0,1} \]
\[ B_1 = \frac{20 \pi \times 10^{-7}}{\pi \times 0,1} \]
\[ B_1 = \frac{20 \jeer 10^{-7}}{0,1} \]
\[ B_1 = 200 \jeer 10^{-7} \]
\[ B_1 = 2 \jeer 10^{-5} \, T \]
Maadaama labada fiilooyin ay sitaan hirar jihooyin iska soo horjeeda, goobaha birlabta ayaa is baabi'iya waqtigaas. Goobta birlabta guud ee meeshaas waa eber.
Su'aal 3aad:
Fiilo dheer oo toosan A waxay siddaa hadda 12 A waxayna la siman tahay silig dheer oo toosan B ah oo wata hadda 8 A oo isku jiho ah. Xisaabi wadarta goobta birlabta meel 0,15 mitir u jirta silig A iyo 0,1 mitir u jirta silig B.
Dood:
Xisaabi goobta birlabta ee fiilada kasta meeshaas.
Silig A:
\[ B_A = \frac{\mu_0 I_A}{2 \pi r_A} \]
Waa la ogyahay:
\[ I_A = 12 \, A \]
\[ r_A = 0,15 \, m \]
Beddelka qiimaha:
\[ B_A = \frac{4 \pi \times 10^{-7} \times 12}{2 \pi \times 0,15} \]
\[ B_A = \frac{48 \pi \times 10^{-7}}{\pi \times 0,3} \]
\[ B_A = \frac{48 \jeer 10^{-7}}{0,3} \]
\[ B_A = 160 \jeer 10^{-7} \]
\[ B_A = 1,6 \jeer 10^{-5} \, T \]
Silig B:
\[ B_B = \frac{\mu_0 I_B}{2 \pi r_B} \]
Waa la ogyahay:
\[I_B = 8 \, A \]
\[ r_B = 0,1 \, m \]
Beddelka qiimaha:
\[ B_B = \frac{4 \pi \times 10^{-7} \times 8}{2 \pi \times 0,1} \]
\[ B_B = \frac{32 \pi \times 10^{-7}}{\pi \times 0,2} \]
\[ B_B = \frac{32 \jeer 10^{-7}}{0,2} \]
\[ B_B = 160 \jeer 10^{-7} \]
\[ B_B = 1,6 \ jeer 10^{-5} \, T \]
Maadaama hirarka labada fiilooyin ay ku socdaan jiho isku mid ah, dhibcahana ay ka fog yihiin fiilo kasta, goobta birlabta ee ka dhalata waxay ku jiri doontaa jiho isku mid ah. Sidaa darteed, wadarta guud ee goobta birlabta waa wadarta labada goobood ee birlabta.
\[ B_{wadarta} = B_A + B_B \]
\[ B_{wadarta} = 1,6 \jeer 10^{-5} + 1,6 \jeer 10^{-5} \]
\[ B_{wadarta} = 3,2 \jeer 10^{-5} \, T \]
Markaa, wadarta guud ee goobta birlabta ee bartaas waa 32 μT (microTesla).
Gabagabo
Fahmidda fikradda goob birlabeed oo ku wareegsan silig toosan ayaa muhiim u ah fiisikiska sababtoo ah waxay leedahay codsiyo badan oo wax ku ool ah. Annagoo adeegsanayna tusaalooyin iyo doodo sida kan kor ku xusan, waxaan xoojin karnaa fikradda aasaasiga ah oo aan qoto dheereyn karnaa fahamkeenna ku saabsan sida goobaha birlabeedku uga shaqeeyaan silig sidda hadda socda. Had iyo jeer xasuuso, joogtaynta falanqaynta iyo fahamka sharciyada aasaasiga ah ayaa muhiim u ah xallinta dhibaatooyinka fiisikiska ee kala duwan.
