Mienzaniso yeMibvunzo Inokurukura nezveMagetsi Anokonzerwa Nesimba
Masimba emagineti anokonzerwa nemhepo (induced magnetic fields) inyaya inokosha mufizikisi, kunyanya panyaya yemagetsi. Izvi zvinoitika kana simba remagineti richichinja richiburitsa simba remagetsi (EMF) kana voltage muconductor. Chinyorwa chino chichaongorora matambudziko akati wandei uye chichapa hurukuro yakadzama yesimba remagineti rakakonzerwa nemhepo (induced magnetic fields) kuti tinzwisise pfungwa iyi zvakadzama.
Kunzwisisa Magnetic Fields Inokurudzirwa
Tisati tanyatsoongorora dambudziko remuenzaniso, zvinobatsira kutanga tanzwisisa pfungwa huru yesimba remagineti rakakonzereswa. Mutemo waFaraday we electromagnetic induction ndiwo hwaro hwechiitiko ichi. Mutemo uyu unoti shanduko mu magnetic flux mu conducting loop ichagadzira EMF. Fomura yemasvomhu yemutemo waFaraday ndeiyi:
\[ \masvomhu{E} = -\frac{d\Phi_B}{dt} \]
Di mana:
– \( \mathcal{E} \) isimba remagetsi rinokonzereswa (EMF).
– \( \Phi_B \) ndiyo magnetic flux.
– \(t \) inguva.
Chiratidzo chekuramba chiri muequation iri pamusoro apa chinoratidza divi reEMF inokonzerwa zvichienderana neMutemo waLenz, uyo unoti EMF inokonzerwa inowanzo pikisa shanduko yemagnetic flux inoikonzera.
Mibvunzo yemuenzaniso nehurukuro
Muenzaniso 1: Solenoid inotakura magetsi
Mubvunzo:
Solenoid refu ine matenderere mazana mashanu uye yakareba mamita 0,5. Kana magetsi ari musolenoid akachinja kubva pa0 A kuenda pa2 A mumasekonzi 0,2 uye nzvimbo ye solenoid iri \( 2 \times 10^{-4} \ \text{m}^2 \), verengai induced emf inogadzirwa.
Kukurukurirana:
Kuti tigadzirise dambudziko iri, tinoda fomura yemagnetic flux ye solenoid nemutemo waFaraday.
Kuyerera kwemagineti \( \Phi_B \) kuburikidza ne solenoid ndekwekuti:
\[ \Phi_B = B \cdot A \]
Di mana:
– \( B \) ndiyo simba remagineti riri mu solenoid.
– \( A \) inzvimbo ine chikamu chakasiyana che solenoid.
Simba remagineti \( B \) riri mu solenoid rinotsanangurwa ne:
\[ B = \mu_0 \cdot n \cdot I \]
Di mana:
– \( \mu_0 \) ndiyo nzira yekuvhenekesa vacuum \( (4\pi \times 10^{-7} \ \text{T}\cdot\text{m}/\text{A}) \).
– \( n \) ndiyo nhamba yekutenderera pahurefu hweyuniti, \( n = \frac{N}{l} \), apo \( N \) ndiyo nhamba yekutenderera uye \( l \) ndiyo urefu hwesolenoid.
– \( I \) ndiyo magetsi ari kuburikidza ne solenoid.
Kubva pamubvunzo:
– \( N = 500 \)
– \( l = 0,5 \ \mashoko{m} \)
– \( A = 2 \kawa 10^{-4} \ \text{m}^2 \)
– \( \Delta I = 2 \ \mashoko{A} \)
– \( \Delta t = 0,2 \ \text{s} \)
Kutanga, verenga \( n \):
\[ n = \frac{N}{l} = \frac{500}{0,5} = 1000 \ \text{turns/m} \]
Wobva waverenga shanduko mumunda wemagineti \( B \):
\[ \Delta B = \mu_0 \cdot n \cdot \Delta I = (4\pi \times 10^{-7}) \cdot 1000 \cdot 2 = 8\pi \times 10^{-4} \ \text{T} = 2,512 \times 10^{-3} \ \text{T} \]
Kuchinja kwe magnetic flux \( \Delta \Phi_B \):
\[ \Delta \Phi_B = \Delta B \cdot A = 2,512 \times 10^{-3} \cdot 2 \times 10^{-4} = 5,024 \times 10^{-7} \ \text{Wb} \]
Zvino, shandisa mutemo waFaraday kuti uone EMF inokonzerwa:
\[ \mathcal{E} = -\frac{\Delta \Phi_B}{\Delta t} = -\frac{5,024 \times 10^{-7}}{0,2} = -2,512 \times 10^{-6} \ \text{V} = -2,512 \ \mu\text{V} \]
Saka, EMF inokonzerwa nemhedzisiro ndeye \(-2,512 \ \mu\text{V}\).
Muenzaniso Dambudziko rechipiri: Dunhu reLoop muMunda weMagineti Unochinja
Mubvunzo:
Chitenderedzwa chakatenderera chine radius ye 0,1 metres chinoiswa mumunda wemagineti wakafanana unoshanduka kubva pa 0,5 T kuenda pa 0 mumasekondi 0,1. Verengai emf induced iri murobho.
Kukurukurirana:
Kufanana nedambudziko rekare, tichashandisa mutemo waFaraday. Kutanga, tinoverenga shanduko mu magnetic flux.
Nzvimbo yedenderedzwa \( A \):
\[ A = \pi r^2 = \pi (0,1)^2 = \pi \nguva 10^{-2} \ \text{m}^2 = \pi \nguva 10^{-2} \inenge 3,14 \nguva 10^{-2} \ \text{m}^2 \]
Kuchinja kwe magnetic flux \( \Delta \Phi_B \):
\[ \Delta \Phi_B = \Delta B \cdot A = (0 – 0,5) \cdot 3,14 \times 10^{-2} = -0,5 \cdot 3,14 \times 10^{-2} = -1,57 \times 10^{-2} \ \text{Wb} \]
EMF Yakakonzerwa \( \mathcal{E} \):
\[ \mathcal{E} = -\frac{\Delta \Phi_B}{\Delta t} = -\frac{-1,57 \times 10^{-2}}{0,1} = 1,57 \times 10^{-1} \ \text{V} = 0,157 \ \text{V} \]
Muenzaniso 3: Kutenderera Disk muMagnetic Field
Mubvunzo:
Dhisiki ine radius ye 0,2 metres inotenderera mundege yakatwasuka ine angular velocity ye 10 rad/s mumunda wemagineti wakatwasuka we 0,3 T. Verenga EMF inokonzerwa pakati pepakati nemucheto wedhisiki.
Kukurukurirana:
Panyaya iyi, tinoshandisa pfungwa ye electromagnetic induction pa rotating disk, inozivikanwa se Faraday's induced EMF.
EMF inokonzerwa padiski inotenderera inopiwa ne:
\[ \masvomhu{E} = \frac{1}{2} B \omega r^2 \]
Di mana:
– \( B \) ndiyo simba remagineti.
– \( \omega \) ndiyo kasi yekona.
– \( r \) ndiyo radius yedhisiki.
Tsiva kukosha kubva padambudziko:
\[ B = 0,3 \ \mashoko{T} \]
\[ \omega = 10 \ \text{rad/s} \]
\[r = 0,2 \ \mashoko{m} \]
Verenga EMF inokonzerwa:
\[ \mathcal{E} = \frac{1}{2} \cdot 0,3 \cdot 10 \cdot (0,2)^2 = \frac{1}{2} \cdot 0,3 \cdot 10 \cdot 0,04 = 0,6 \times 0,04 = 0,024 \ \text{V} \]
Saka, EMF inokonzerwa pakati pepakati nemucheto wedhisiki i0,024 V kana 24 mV.
Mhedziso
Masimba emagineti anokurudzirwa inyaya yakadzama inoda kunzwisisa pfungwa dzefizikisi dzakakosha uye mashandisirwo adzo emasvomhu. Kuburikidza nemibvunzo yakaita seiri pamusoro apa, tinogona kuona kuti mitemo yakaita seMutemo waFaraday neMutemo waLenz inoshanda sei mumamiriro akasiyana. Kunzwisisa pfungwa idzi nematambudziko ekudzidzira kunobatsira kusimbisa kugona kwechinhu ichi uye kuwedzera mashandisirwo acho mumamiriro akasiyana-siyana.
