Tusaalaha Su'aalaha Doodda ee Magnetism-ka
Birlabnimadu waa dhacdo dabiici ah oo aad muhiim u ah oo xiiso leh oo lagu barto fiisikiska. Dhacdadani waxay la xiriirtaa awoodaha ka dhaca birlabyada iyo agabyada qaarkood. Guud ahaan, birlabnimadu waxaa lagu sharxi karaa fikradaha goobaha birlabyada, khadadka xoogga birlabyada, iyo isdhexgalka ka dhexeeya birlabyada iyo birlabyada oo leh walxaha ferromagnetic, paramagnetic, iyo diamagnetic. Maqaalkan, waxaan kaga hadli doonnaa dhowr dhibaato oo tusaale ah iyo doodahooda la xiriira mowduuca birlabnimada.
Su'aal 1aad: Aqoonsiga Tiirarka Birlabta ah
Su'aal: Birlab-jiidhku wuxuu leeyahay laba tiir, tiir waqooyi iyo tiir koonfureed. Sharax sida loo aqoonsado tiirarka birlab-jiidhku iyadoo la adeegsanayo kombas.
Dood:
Si aad u aqoonsato tiirarka birlabta, isticmaal kombas. Tallaabooyinkan waa kuwan:
1. Dhig kombaska meel u dhow hal dhinac oo ka mid ah birta birlabta.
2. Fiiri irbadda kombaska oo muujinaysa waqooyi iyo koonfur.
3. Tiirka birlabta ee soo jiidanaya dhammaadka waqooyi ee irbadda kombaska waa tiirka koonfureed ee birlabta, sababtoo ah tiirka waqooyi ee irbadda kombaska (oo dhab ahaantii ah tiirka koonfureed ee birlabta kombaska) waxaa soo jiidanaya tiirka koonfureed ee birlabta.
4. Sidoo kale, u dhaqaaji kombaska dhinaca kale ee birlabka baarka oo ku celi aragtida. Dhammaadka birlabka soo jiidanaya tiirka koonfureed ee irbadda kombaska waa tiirka waqooyi ee birlabka, sababtoo ah tiirka waqooyi ee irbadda kombaska waxaa soo jiidanaya tiirka koonfureed ee birlabka.
Su'aal 2: Goob birlab ah oo ku wareegsan silig sita hadda toosan
Su'aal: Silig dheer oo toosan ayaa sita koronto koronto oo ah 5 A. Go'aami jihada goobta birlabta ee ku wareegsan siligga meel 10 cm u jirta siligga.
Dood:
Goobta birlabta ee ku wareegsan silig toosan oo sidda hadda waxaa lagu go'aamin karaa iyadoo la adeegsanayo xeerka gacanta midig. Sidan ayaa loo sameeyaa:
1. Fiilada ku qabo gacantaada midig, iyadoo suulkaagu tilmaamayo jihada socodka hadda socda (laga bilaabo togan ilaa taban).
2. Jihada af-xidhka ku duuban siligga waxay tilmaamaysaa jihada goobta birlabta.
Tusaale ahaan, haddii qulqulka kor loo jeediyo (sida ku cad suulka), markaas meel 10 cm u jirta fiilada, goobta birlabta ayaa ku wareegsan doonta jihada dhaqdhaqaaqa farta gacanta midig:
– Haddii barta ay ku taal hore ee siligga, goobta birlabta ayaa u jeedda gudaha (dhinaca warqadda/shaashadda).
– Haddii barta ay ka dambeyso fiilada, goobta birlabta ayaa dibadda u tilmaamaysa (laga bilaabo warqadda/shaashadda).
Su'aal 3: Xoogga Lorentz ee Walxaha Hadda Xamuulka ah
Su'aal: Walax la dallacay (+1.6 × 10^-19 C) oo ku socota xawaare dhan 2 × 10^6 m/s ayaa gasha goob birlab ah oo ah 0.01 T oo laga soo toosiyay bogga. Go'aami baaxadda iyo jihada xoogga Lorentz ee uu la kulmay walaxda.
Dood:
Xoogga Lorentz ee ku yaal walax la dallacay oo ku jirta goob birlab ah waxaa lagu muujin karaa isle'egta \( \vec{F} = q \vec{v} \times \vec{B} \).
– Kharash qurub ah, \(q\) = +1.6 × 10^-19 C
– Xawaaraha walxaha, \( \vec{v} \) = 2 × 10^6 m/s (loo malaynayo inuu u jeedo dhidibka x)
– Goobta birlabta, \( \vec{B} \) = 0.01 T (laga soo bilaabo bogga, dhanka dhidibka z)
Jihada ciidanka:
1. Mar kale isticmaal xeerka gacanta midig si aad u marto vector-ka xawaaraha (\( \vec{v} \)) iyo goobta birlabta (\( \vec{B} \)).
2. Faraha gacanta midig waxay raacaan jihada xawaaraha (dhidibka x), farahana waxay u laabaan dibadda warqadda (sida waafaqsan goobta birlabta ee dhidibka z), ka dibna suulka ayaa bixiya jihada xoogga Lorentz (dhidibka y).
Baaxadda xoogga Lorentz \( F \) waxaa loo xisaabin karaa sidan:
\[ F = q \cdot v \cdot B \cdot \sin \theta \]
Tan iyo \( \theta \) = 90° (xawaaraha ku toosan goobta birlabta),
\[ F = (1.6 \ jeer 10^{-19} C) \cdot (2 \ jeer 10^6 m/s) \cdot (0.01 T) \sin (90°) \]
\[ F = 3.2 \ jeer 10^{-21} N \]
Jihada xoogga waxay la mid tahay laabista faraha (dhinaca midig = dhidibka y-togan).
Su'aal 4: Goob birlab ah oo ku taal bartamaha Solenoid-ka
Su'aal: Waxaa la ogyahay in solenoid-ka dheer uu leeyahay 500 oo wareeg oo dhererkiisu yahay 0.5 m oo wata hadda 2 A. Xisaabi baaxadda goobta birlabta ee bartamaha solenoid-ka.
Dood:
Beerta birlabta ee ku jirta solenoid-ka dheer waxaa lagu xisaabin karaa qaacidada:
\[ B = \mu_0 n I \]
Halkee:
– \( B \): baaxadda goobta birlabta ee ku jirta solenoid-ka (Tesla)
– \( \mu_0 \): isku-darka faakuumka ee marin-u-helka (\(4 \pi \times 10^{-7} \: T \cdot m/A\))
– \( n \): tirada wareegyada dhererka cutubkiiba (leexasho/mitir), oo loo qaabeeyey \( n = \frac{N}{L} \)
– \( I \): xaddiga hadda socda ee dhex mara solenoid-ka (Amperes)
Markaa,
– \( N = 500 \)
– \( L = 0.5 m \)
– \( n = \frac{500}{0.5} = 1000 \: wareegyo/m \)
– \( I = 2 A \)
Haddaba,
\[ B = \mu_0 \cdot n \cdot I \]
\[ B = (4 \pi \times 10^{-7} T \cdot m/A) \cdot (1000 \: rogrogmada/m) \cdot 2 A \]
\[ B = 8 \pi \times 10^{-4} T \]
\[ B \qiyaastii 2.51 \jeer 10^{-3} T \]
Su'aal 5: Koronto-kicinta
Su'aal: Gariirku wuxuu ka kooban yahay 200 oo wareeg waxaana la dhigaa goob birlab ah oo ka beddesha 0.1 T ilaa 0.5 T 0.25 ilbiriqsi gudahood. Xisaabi danabka la kiciyay ee lagu soo saaray gariiradda.
Dood:
Soo-saarista elektromagnetka waxaa lagu xisaabin karaa iyadoo la adeegsanayo Sharciga Faraday:
\[ \mathcal{E} = -N \frac{\Delta \Phi_B}{\Delta t} \]
Dimana,
– \( \mathcal{E} \): danab la kiciyey (Volts)
– \( N \): tirada wareegyada
– \( \Delta \Phi_B \): isbeddelka qulqulka birlabta (Wb)
– \( \Delta t \): isbeddelka waqtiga (yada)
Iyadoo \(\Delta \Phi_B = B \cdot A \); halkaas oo A ay tahay bedka gariiradda. Si kastaba ha ahaatee, haddii aaggu uusan isbeddelin
\[ \mathcal{E} = -N \cdot \frac{\Delta B \cdot A}{\Delta t} \]
Tan iyo \(\Delta B = 0.5 T – 0.1 T = 0.4 T \),
bur
\[ \mathcal{E} = -200 \cdot \frac{0.4 T \cdot A}{0.25 s} \]
\[ \mathcal{E} = -320 \cdot A \]
Haddii aan la bixin meel gaar ah (loo malaynayo inay isku mid tahay),
Qiimaha soo-kicinta ayaa si toos ah ugu tiirsan A.
Waxaan rajeyneynaa, tusaalooyinkan dhibaatooyinka birlabta inay kaa caawin doonaan inaad fahamto fikradaha iyo codsiyada wax ku oolka ah ee birlabta. Aragtiyahaan iyo mabaadi'dan waxaa si joogto ah loogu isticmaalaa heerar waxbarasho oo kala duwan iyo cilmi baaris qoto dheer.
