Piv txwv ntawm cov lus nug sib tham txog qhov loj ntawm EMF induced
Pendahuluuan
Lub zog hluav taws xob uas raug yuam (EMF) yog ib qho xwm txheej uas Michael Faraday tau tshawb pom hauv xyoo 1831. Faraday tau tshawb pom tias lub zog sib nqus uas hloov pauv hauv lub voj voog lossis lub kauj ntawm tus neeg coj hluav taws xob tuaj yeem ua rau muaj hluav taws xob. Qhov xwm txheej no hu ua electromagnetic induction thiab yog lub hauv paus rau ntau yam thev naus laus zis niaj hnub no, xws li cov generators, transformers, thiab cov motors hluav taws xob. Tsab xov xwm no yuav piav qhia txog ntau qhov teeb meem piv txwv thiab tham txog qhov loj ntawm EMF uas raug yuam, uas yuav muaj txiaj ntsig zoo rau cov tub ntxhais kawm uas kawm txog physics ntawm hluav taws xob thiab magnetism.
Lub Tswv Yim Tseem Ceeb ntawm EMF Uas Ua Rau Muaj Kev Cuam Tshuam
Ua ntej peb yuav tham txog qhov teeb meem piv txwv no, nws yog ib lub tswv yim zoo los saib xyuas lub tswv yim yooj yim ntawm induced emf. Faraday txoj cai hais tias induced emf hauv lub voj voog conducting yog ncaj qha proportional rau qhov kev hloov pauv ntawm magnetic flux los ntawm lub voj voog. Mathematically, Faraday txoj cai tuaj yeem tsim tau raws li hauv qab no:
\[ \mathcal{E} = – \frac{d\Phi}{dt} \]
Qhov twg:
- \( \mathcal{E} \) yog qhov EMF uas raug tsim (volts)
- \( \Phi \) yog lub zog sib nqus (Weber, Wb)
- \( t \) yog lub sijhawm (thib ob, s)
Lub cim tsis zoo hauv qhov sib npaug qhia txog Lenz Txoj Cai uas hais tias qhov kev taw qhia ntawm qhov tam sim no induced yuav tsim ib lub teb magnetic uas tawm tsam qhov kev hloov pauv ntawm magnetic flux uas ua rau nws.
Cov Lus Nug Piv Txwv thiab Kev Sib Tham
Lo lus nug 1: Ib lub kauj
Lo lus nug: Ib lub kauj uas muaj thaj tsam ntawm 0.02 m² raug muab tso rau hauv ib lub teb sib nqus sib npaug ntawm qhov loj 0.5 T, perpendicular rau qhov chaw ntawm lub kauj. Lub teb sib nqus tam sim ntawd xoom hauv 0.1 vib nas this. Xam qhov loj ntawm EMF uas tshwm sim hauv lub kauj.
Kev Sib Tham:
Nws paub tias:
- Thaj chaw ntawm lub kauj (A = 0.02 \, \text{m} ^ 2 \)
– Qhov loj ntawm lub teb sib nqus \( B = 0.5 \, \text{T} \)
- Lub sijhawm hloov pauv teb \( \Delta t = 0.1 \, \text{s} \)
Kev hloov pauv ntawm cov hluav taws xob sib nqus:
\[ \Delta \Phi = B \times A \]
\[ \Delta \Phi = 0.5 \, \text{T} \times 0.02 \, \text{m}^2 \]
\[ \Delta \Phi = 0.01 \, \text{Wb} \]
Qhov loj ntawm EMF induced:
\[ \mathcal{E} = – \frac{\Delta \Phi}{\Delta t} \]
\[ \mathcal{E} = – \frac{0.01 \, \text{Wb}}{0.1 \, \text{s}} \]
\[ \mathcal{E} = -0.1 \, \text{V} \]
Vim tias qhov uas raug nug yog qhov loj ntawm EMF (tsis tau them sai rau lub cim):
\[ |\mathcal{E}| = 0.1 \, \text{V} \]
Lo lus nug 2: Coil nrog N Tig
Lo lus nug: Ib lub kauj muaj 100 tig thiab nws thaj chaw yog 0.03 m². Lub kauj no nyob rau hauv ib lub teb sib nqus sib npaug ntawm 0.4 T perpendicular rau lub kauj. Yog tias lub teb sib nqus nce mus txog 1.2 T hauv 0.4 vib nas this, xam qhov nruab nrab induced emf tsim tawm hauv lub kauj.
Kev Sib Tham:
Nws paub tias:
- Tus naj npawb ntawm kev tig \( N = 100 \)
- Thaj chaw ntawm lub kauj (A = 0.03 \, \text{m} ^ 2 \)
– Kev hloov pauv ntawm lub zog sib nqus \( \Delta B = 1.2 \, \text{T} – 0.4 \, \text{T} \)
- Lub sijhawm hloov pauv teb \( \Delta t = 0.4 \, \text{s} \)
Kev hloov pauv ntawm magnetic flux ib zaug tig:
\[ \Delta \Phi = A \times \Delta B \]
\[ \Delta \Phi = 0.03 \, \text{m}^2 \times (1.2 \, \text{T} – 0.4 \, \text{T}) \]
\[ \Delta \Phi = 0.03 \, \text{m}^2 \times 0.8 \, \text{T} \]
\[ \Delta \Phi = 0.024 \, \text{Wb} \]
Tag nrho cov kev hloov pauv ntawm cov dej ntws rau N tig:
\[ \Delta \Phi_{\text{total}} = N \times \Delta \Phi \]
\[ \Delta \Phi_{\text{total}} = 100 \times 0.024 \, \text{Wb} \]
\[ \Delta \Phi_{\text{total}} = 2.4 \, \text{Wb} \]
Qhov loj ntawm EMF induced:
\[ \mathcal{E} = – \frac{\Delta \Phi_{\text{total}}}{\Delta t} \]
\[ \mathcal{E} = – \frac{2.4 \, \text{Wb}}{0.4 \, \text{s}} \]
\[ \mathcal{E} = -6 \, \text{V} \]
Vim tias qhov uas raug nug yog qhov loj ntawm EMF (tsis tau them sai rau lub cim):
\[ |\mathcal{E}| = 6 \, \text{V} \]
Lo lus nug 3: Kev txav mus los hauv lub zog sib nqus
Lo lus nug: Ib lub kauj plaub fab uas muaj 50 lub voj voog, ntev 4 cm, thiab dav 2 cm, raug muab tso rau hauv ib lub zog sib nqus sib npaug ntawm 0.3 T sib luag rau qhov ntev ntawm lub kauj. Yog tias lub kauj txav tawm ntawm lub zog sib nqus ntawm qhov ceev tas li ntawm 5 cm / s, qhov EMF induced hauv lub kauj yog dab tsi?
Kev Sib Tham:
Nws paub tias:
- Tus naj npawb ntawm kev tig \( N = 50 \)
– Ntev (l = 0.04), qhov ntev (m)
– Dav \( w = 0.02 \, \text{m} \)
– Qhov loj ntawm lub teb sib nqus \( B = 0.3 \, \text{T} \)
- Qhov ceev tawm ntawm lub teb sib nqus \( v = 0.05 \, \text{m/s} \)
Lub zog electromotive ntawm lub kauj txav mus rau hauv lub teb magnetic yog muab los ntawm:
\[ \mathcal{E} = B lv \]
Vim tias lub kauj muaj N tig, tag nrho cov EMF uas raug cuam tshuam yog:
\[ \mathcal{E}_{\text{total}} = NB lv \]
\[ \mathcal{E}_{\text{total}} = 50 \times 0.3 \, \text{T} \times 0.04 \, \text{m} \times 0.05 \, \text{m/s} \]
\[ \mathcal{E}_{\text{total}} = 50 \times 0.0006 \, \text{V} \]
\[ \mathcal{E}_{\text{total}} = 0.03 \, \text{V} \]
Xaus
Cov kev sib tham txog cov teeb meem piv txwv saum toj no qhia tau tias yuav ua li cas xam tau emf uas raug tsim los ntawm kev hloov pauv ntawm cov hluav taws xob sib nqus lossis los ntawm kev txav ntawm lub kauj hauv lub teb sib nqus. Lub tswv yim no yog qhov tseem ceeb rau electromagnetism thiab muaj ntau daim ntawv thov hauv thev naus laus zis. Kev nkag siab txog yuav ua li cas xam tau emf uas raug tsim los ntawm cov teeb meem ua tau zoo yuav pab cov tub ntxhais kawm kom paub txog cov ntaub ntawv no thiab siv nws hauv ntau qhov chaw.
