Zitsanzo za Mafunso Okhudza Maginito Oyambitsidwa
Maginito oyambitsidwa ndi mutu wofunikira mu fizikisi, makamaka pankhani ya maginito oyambitsidwa ndi magetsi. Chochitika ichi chimachitika pamene mphamvu ya maginito yosinthika imapanga mphamvu yamagetsi (EMF) kapena magetsi mu kondakitala. Nkhaniyi iwunikanso mavuto angapo a zitsanzo ndikupereka kukambirana mwatsatanetsatane za mphamvu yamagetsi oyambitsidwa kuti timvetsetse bwino lingaliro ili.
Kumvetsetsa Maginito Oyambitsidwa
Tisanafufuze bwino nkhaniyi, ndikofunikira kumvetsetsa kaye mfundo yoyambira ya mphamvu zamaginito zomwe zayambitsidwa. Lamulo la Faraday la kulowetsa mphamvu zamaginito ndiye maziko a izi. Lamuloli limati kusintha kwa magnetic flux kudutsa mu conducting loop kudzapanga EMF. Fomula ya masamu ya lamulo la Faraday ndi iyi:
\[ \masamu{E} = -\frac{d\Phi_B}{dt} \]
Kumene:
– \( \mathcal{E} \) ndi mphamvu yamagetsi yopangidwa (EMF).
– \( \Phi_B \) ndi maginito othamanga.
– \(t \) ndi nthawi.
Choyipa chomwe chili pamwambapa chikuwonetsa komwe EMF yoyambitsidwa ikupita malinga ndi Lamulo la Lenz, lomwe limati EMF yoyambitsidwa imakonda kutsutsa kusintha kwa maginito komwe kumayambitsa.
Mafunso ndi Zokambirana za Zitsanzo
Chitsanzo 1: Solenoid yonyamula magetsi
Funso:
Solenoid yayitali imakhala ndi ma turn 500 ndipo ndi yayitali mamita 0,5. Ngati mphamvu yodutsa mu solenoid yasintha kuchoka pa 0 A kufika pa 2 A mu masekondi 0,2 ndipo dera lodutsa la solenoid ndi \( 2 \times 10^{-4} \ \text{m}^2 \), werengani emf yomwe yapangidwa.
Kukambirana:
Kuti tithetse vutoli, tikufunika njira ya magnetic flux ya solenoid ndi lamulo la Faraday.
Kutuluka kwa maginito \( \Phi_B \) kudzera mu solenoid ndi:
\[ \Phi_B = B \cdot A \]
Kumene:
– \( B \) ndi mphamvu ya maginito mu solenoid.
– \( A \) ndi dera lozungulira la solenoid.
Mphamvu ya maginito \( B \) mu solenoid imafotokozedwa ndi:
\[ B = \mu_0 \cdot n \cdot I \]
Kumene:
– \( \mu_0 \) ndi vacuum permeability \( (4\pi \times 10^{-7} \ \text{T}\cdot\text{m}/\text{A}) \).
– \( n \) ndi chiwerengero cha ma turns pa unit length, \( n = \frac{N}{l} \), pomwe \( N \) ndi chiwerengero cha ma turns ndipo \( l \) ndi kutalika kwa solenoid.
– \( I \) ndi mphamvu yamagetsi kudzera mu solenoid.
Kuchokera pa funso:
– \( N = 500 \)
– \( l = 0,5 \ \malemba{m} \)
– \( A = 2 \nthawi 10^{-4} \ \malemba{m}^2 \)
– \( \Delta I = 2 \ \malemba{A} \)
– \( \Delta t = 0,2 \ \text{s} \)
Choyamba, werengerani \( n \):
\[ n = \frac{N}{l} = \frac{500}{0,5} = 1000 \ \text{turns/m} \]
Kenako, werengerani kusintha kwa mphamvu ya maginito \( B \):
\[ \Delta B = \mu_0 \cdot n \cdot \Delta I = (4\pi \times 10^{-7}) \cdot 1000 \cdot 2 = 8\pi \times 10^{-4} \ \text{T} = 2,512 \times 10^{-3} \ \text{T} \]
Kusintha kwa maginito \( \Delta \Phi_B \):
\[ \Delta \Phi_B = \Delta B \cdot A = 2,512 \times 10^{-3} \cdot 2 \times 10^{-4} = 5,024 \times 10^{-7} \ \text{Wb} \]
Tsopano, gwiritsani ntchito lamulo la Faraday kuti mudziwe EMF yomwe yayambitsidwa:
\[ \mathcal{E} = -\frac{\Delta \Phi_B}{\Delta t} = -\frac{5,024 \times 10^{-7}}{0,2} = -2,512 \times 10^{-6} \ \text{V} = -2,512 \ \mu\text{V} \]
Kotero, EMF yomwe imabwera chifukwa chake ndi \(-2,512 \ \mu\text{V}\).
Chitsanzo Chachiwiri: Dera Lozungulira mu Mphamvu Yosintha ya Maginito
Funso:
Chizunguliro chozungulira chokhala ndi utali wa mita 0,1 chimayikidwa mu mphamvu ya maginito yofanana yomwe imasintha kuchoka pa 0,5 T kufika pa 0 mu sekondi 0,1. Werengani emf yomwe yayambitsidwa mu chizungulirocho.
Kukambirana:
Mofanana ndi vuto lapitalo, tigwiritsa ntchito lamulo la Faraday. Choyamba, timawerengera kusintha kwa magnetic flux.
Malo ozungulira \( A \):
\[ A = \pi r^2 = \pi (0,1)^2 = \pi \nthawi 10^{-2} \ \text{m}^2 = \pi \nthawi 10^{-2} \pafupifupi 3,14 \nthawi 10^{-2} \ \text{m}^2 \]
Kusintha kwa maginito \( \Delta \Phi_B \):
\[ \Delta \Phi_B = \Delta B \cdot A = (0 – 0,5) \cdot 3,14 \times 10^{-2} = -0,5 \cdot 3,14 \times 10^{-2} = -1,57 \times 10^{-2} \ \text{Wb} \]
EMF Yoyambitsidwa \( \mathcal{E} \):
\[ \mathcal{E} = -\frac{\Delta \Phi_B}{\Delta t} = -\frac{-1,57 \times 10^{-2}}{0,1} = 1,57 \times 10^{-1} \ \text{V} = 0,157 \ \text{V} \]
Chitsanzo 3: Disiki Yozungulira mu Magnetic Field
Funso:
Disiki yokhala ndi utali wa mamita 0,2 imazungulira molunjika ndi liwiro la angular la 10 rad/s mu mphamvu ya maginito yopingasa ya 0,3 T. Werengani EMF yomwe yachitika pakati pa pakati ndi m'mphepete mwa diski.
Kukambirana:
Pachifukwa ichi, timagwiritsa ntchito lingaliro la electromagnetic induction pa rotating disk, lotchedwa Faraday's induced EMF.
EMF yomwe imapangidwa pa disk yozungulira imaperekedwa ndi:
\[ \masamu{E} = \frac{1}{2} B \omega r^2 \]
Kumene:
– \( B \) ndi mphamvu ya maginito.
– \( \omega \) ndi liwiro la angular.
– \(r \) ndi utali wa diski.
Sinthani mfundo kuchokera ku vuto:
\[ B = 0,3 \ \malemba{T} \]
\[ \omega = 10 \ \text{rad/s} \]
\[r = 0,2 \ \malemba{m} \]
Kuwerengera EMF yoyambitsidwa:
\[ \mathcal{E} = \frac{1}{2} \cdot 0,3 \cdot 10 \cdot (0,2)^2 = \frac{1}{2} \cdot 0,3 \cdot 10 \cdot 0,04 = 0,6 \times 0,04 = 0,024 \ \text{V} \]
Motero, EMF yomwe imayambitsa pakati pa pakati ndi m'mphepete mwa diski ndi 0,024 V kapena 24 mV.
Mapeto
Maginito oyambitsidwa ndi nkhani yofunika kwambiri yomwe imafuna kumvetsetsa mfundo zoyambira za fizikisi ndi momwe zimagwiritsidwira ntchito masamu. Kudzera mu zitsanzo za mavuto monga omwe ali pamwambapa, titha kuwona momwe malamulo monga Faraday's Law ndi Lenz's Law amagwirira ntchito m'mikhalidwe yosiyanasiyana. Kumvetsetsa mfundozo ndi mavuto ochita masewera olimbitsa thupi kumathandiza kulimbikitsa luso la nkhaniyi ndikukulitsa kugwiritsa ntchito kwake m'malo osiyanasiyana.
