Cov Lus Nug Piv Txwv Sib Tham Txog Cov Nroj Tsuag Sib Nqus Uas Tau Txhaum Cai
Cov teb sib nqus uas raug induced yog ib qho tseem ceeb hauv physics, tshwj xeeb tshaj yog nyob rau hauv cov ntsiab lus ntawm electromagnetism. Qhov tshwm sim no tshwm sim thaum lub teb sib nqus hloov pauv tsim lub zog electromotive (EMF) lossis voltage hauv tus neeg coj hluav taws xob. Tsab xov xwm no yuav tshuaj xyuas ntau qhov teeb meem piv txwv thiab muab kev sib tham ntxaws ntxaws ntawm cov teb sib nqus uas raug induced kom peb nkag siab tob txog lub tswv yim no.
Kev Nkag Siab Txog Cov Nroj Tsuag Sib Nqus Uas Tau Ua Rau Muaj Zog
Ua ntej peb nkag siab txog qhov teeb meem piv txwv no, nws yog ib qho tseem ceeb uas yuav tsum nkag siab txog lub tswv yim yooj yim ntawm cov teb sib nqus uas raug tsim. Faraday txoj cai ntawm kev tsim hluav taws xob yog lub hauv paus rau qhov xwm txheej no. Txoj cai no hais tias kev hloov pauv ntawm cov hluav taws xob sib nqus hla lub voj voog hluav taws xob yuav tsim EMF. Cov mis lej rau Faraday txoj cai yog:
\[ \mathcal{E} = -\frac{d\Phi_B}{dt} \]
Qhov twg:
- \( \mathcal{E} \) yog lub zog electromotive (EMF).
- \( \Phi_B \) yog qhov sib nqus flux.
- \( t \) yog lub sijhawm.
Qhov tsis zoo hauv kab zauv saum toj no qhia txog kev coj ntawm EMF uas raug tsim raws li Lenz Txoj Cai, uas hais tias EMF uas raug tsim feem ntau tawm tsam qhov kev hloov pauv ntawm cov khoom sib nqus uas ua rau nws.
Cov Lus Nug thiab Kev Sib Tham Piv Txwv
Piv txwv 1: Solenoid uas nqa tam sim no
Lo lus nug:
Ib lub solenoid ntev muaj 500 tig thiab ntev 0,5 meters. Yog tias tam sim no los ntawm solenoid hloov ntawm 0 A mus rau 2 A hauv 0,2 vib nas this thiab thaj tsam ntawm lub solenoid yog \( 2 \times 10^{-4} \ \text{m}^2 \), xam qhov emf tsim tawm.
Kev Sib Tham:
Yuav kom daws tau qhov teeb meem no, peb xav tau cov mis magnetic flux ntawm solenoid thiab Faraday txoj cai.
Lub magnetic flux \( \Phi_B \) los ntawm ib lub solenoid yog:
\[ \Phi_B = B \cdot A \]
Qhov twg:
- \( B \) yog lub teb sib nqus hauv lub solenoid.
- \( A \) yog thaj tsam hla ntawm lub solenoid.
Lub teb sib nqus \(B \) hauv lub solenoid yog txhais los ntawm:
\[ B = \mu_0 \cdot n \cdot I \]
Qhov twg:
- \( \mu_0 \) yog qhov permeability ntawm lub tshuab nqus tsev \( (4\pi \times 10^{-7} \ \text{T}\cdot\text{m}/\text{A}) \).
- \( n \) yog tus naj npawb ntawm kev tig ib chav ntev, \( n = \frac{N}{l} \), qhov twg \( N \) yog tus naj npawb ntawm kev tig thiab \( l \) yog qhov ntev ntawm lub solenoid.
- \( Kuv \) yog qhov tam sim no hla lub solenoid.
Los ntawm cov lus nug:
– \( N = 500 \)
– \( l = 0,5 \ \text{m} \)
– \( A = 2 \times 10^{-4} \ \text{m}^2 \)
– \( \Delta I = 2 \ \text{A} \)
– \( \Delta t = 0,2 \ \text{s} \)
Ua ntej, xam \( n \):
\[ n = \frac{N}{l} = \frac{500}{0,5} = 1000 \ \text{turns/m} \]
Tom qab ntawd, xam qhov kev hloov pauv hauv lub teb sib nqus \(B\):
\[ \Delta B = \mu_0 \cdot n \cdot \Delta I = (4\pi \times 10^{-7}) \cdot 1000 \cdot 2 = 8\pi \times 10^{-4} \ \text{T} = 2,512 \times 10^{-3} \ \text{T} \]
Kev hloov pauv ntawm cov hluav taws xob sib nqus \( \Delta \Phi_B \):
\[ \Delta \Phi_B = \Delta B \cdot A = 2,512 \times 10^{-3} \cdot 2 \times 10^{-4} = 5,024 \times 10^{-7} \ \text{Wb} \]
Tam sim no, siv Faraday txoj cai los txiav txim siab qhov EMF uas tau tshwm sim:
\[ \mathcal{E} = -\frac{\Delta \Phi_B}{\Delta t} = -\frac{5,024 \times 10^{-7}}{0,2} = -2,512 \times 10^{-6} \ \text{V} = -2,512 \ \mu\text{V} \]
Yog li, qhov tshwm sim ntawm EMF yog \(-2,512 \ \mu\text{V}\).
Piv Txwv Teeb Meem 2: Lub voj voog voj voog hauv lub zog sib nqus hloov pauv
Lo lus nug:
Ib lub voj voog uas muaj lub vojvoog ntawm 0,1 'meter' raug muab tso rau hauv ib lub teb sib nqus sib npaug uas hloov ntawm 0,5 T mus rau 0 hauv 0,1 vib nas this. Xam qhov emf induced hauv lub voj voog.
Kev Sib Tham:
Zoo li qhov teeb meem dhau los, peb yuav siv Faraday txoj cai. Ua ntej, peb yuav xam qhov kev hloov pauv ntawm cov hlau nplaum sib nqus.
Thaj chaw ntawm lub voj voog \( A \):
\[ A = \pi r^2 = \pi (0,1)^2 = \pi \times 10^{-2} \ \text{m}^2 = \pi \times 10^{-2} \approx 3,14 \times 10^{-2} \ \text{m}^2 \]
Kev hloov pauv ntawm cov hluav taws xob sib nqus \( \Delta \Phi_B \):
\[ \Delta \Phi_B = \Delta B \cdot A = (0 – 0,5) \cdot 3,14 \times 10^{-2} = -0,5 \cdot 3,14 \times 10^{-2} = -1,57 \times 10^{-2} \ \text{Wb} \]
EMF uas raug cuam tshuam \( \mathcal{E} \):
\[ \mathcal{E} = -\frac{\Delta \Phi_B}{\Delta t} = -\frac{-1,57 \times 10^{-2}}{0,1} = 1,57 \times 10^{-1} \ \text{V} = 0,157 \ \text{V} \]
Piv txwv 3: Lub Disc Tig Hauv Lub Zog Sib Nqus
Lo lus nug:
Ib lub disc uas muaj lub vojvoog ntawm 0,2 meters tig rau hauv ib lub dav hlau ntsug nrog lub angular velocity ntawm 10 rad/s hauv ib lub magnetic field kab rov tav ntawm 0,3 T. Xam qhov induced EMF ntawm qhov chaw nruab nrab thiab ntug ntawm lub disk.
Kev Sib Tham:
Rau qhov xwm txheej no, peb siv lub tswv yim ntawm electromagnetic induction ntawm lub disk tig, hu ua Faraday's induced EMF.
Cov EMF uas raug tsim los ntawm lub disk tig yog muab los ntawm:
\[ \mathcal{E} = \frac{1}{2} B \omega r^2 \]
Qhov twg:
- \( B \) yog lub teb sib nqus.
- \( \omega \) yog qhov ceev ntawm lub kaum sab xis.
-\( r\) yog lub vojvoog ntawm lub disk.
Hloov cov nqi ntawm qhov teeb meem:
\[ B = 0,3 \ \text{T} \]
\[ \omega = 10 \ \text{rad/s} \]
\[ r = 0,2 \ \text{m} \]
Xam qhov EMF uas raug cuam tshuam:
\[ \mathcal{E} = \frac{1}{2} \cdot 0,3 \cdot 10 \cdot (0,2)^2 = \frac{1}{2} \cdot 0,3 \cdot 10 \cdot 0,04 = 0,6 \times 0,04 = 0,024 \ \text{V} \]
Yog li, qhov EMF induced ntawm qhov chaw thiab ntug ntawm lub disk yog 0,024 V lossis 24 mV.
Xaus
Cov teb sib nqus uas raug tsim los ntawm lub zog yog ib qho kev kawm tob uas yuav tsum nkag siab txog ob qho tib si lub ntsiab lus tseem ceeb ntawm physics thiab lawv cov kev siv lej. Los ntawm cov teeb meem piv txwv zoo li qhov saum toj no, peb tuaj yeem pom tias cov kev cai lij choj zoo li Faraday's Law thiab Lenz's Law siv li cas rau ntau qhov xwm txheej. Kev nkag siab txog cov ntsiab lus thiab kev xyaum cov teeb meem pab txhawb kev paub txog cov ntaub ntawv no thiab nthuav nws daim ntawv thov hauv ntau qhov xwm txheej.
