Cov Lus Nug Piv Txwv Sib Tham Txog Lub Zog Sib Nqus Ntawm Cov Xov Hlau Uas Nqa Tam Sim No
Lub zog sib nqus yog ib qho xwm txheej ntawm lub cev uas muaj kev sib cuam tshuam ntawm lub zog sib nqus thiab lub zog hluav taws xob. Qhov xwm txheej no tau piav qhia los ntawm Ampère txoj cai, uas hais tias lub zog hluav taws xob ntws los ntawm ib txoj hlua tuaj yeem tsim lub zog sib nqus. Tsab xov xwm no yuav piav qhia txog cov piv txwv thiab tham txog lub zog sib nqus hauv ib txoj hlua uas nqa tam sim no, uas tuaj yeem pab koj nkag siab lub tswv yim no tob dua.
Pendahuluuan
Qhov xwm txheej ntawm magnetism tau paub txij li thaum ub los, tab sis kev piav qhia txog kev tshawb fawb txog kev sib cuam tshuam ntawm cov hluav taws xob thiab cov teb magnetic tsis tau tshawb pom txog rau xyoo pua 19th. Hans Christian Ørsted yog thawj tus neeg tshawb pom tias cov hluav taws xob tuaj yeem tsim cov teb magnetic. Tom qab ntawd, André-Marie Ampère tau txhawb nqa qhov kev tshawb pom no los ntawm kev tsim qhov uas tam sim no hu ua Ampère's Law.
Cov Ntsiab Lus Tseem Ceeb
1. Txoj Cai Biot-Savart
Lub teb sib nqus uas tsim los ntawm ib qho khoom siv hluav taws xob me me tuaj yeem suav nrog siv txoj cai Biot-Savart:
\[
dB = \frac{\mu_0}{4\pi} \cdot \frac{I\cdot (d\mathbf{l} \times \mathbf{r})}{r^3}
\]
Qhov twg:
– \(dB\) = lub zog sib nqus
– \(\mu_0\) = permeability ntawm lub tshuab nqus tsev \((4\pi \times 10^{-7} \text{Tm/A})\)
- \(Kuv\) = Tam sim no hluav taws xob (A)
- \(d\mathbf{l}\) = hlau length element (m)
- \(\mathbf{r}\) = vector qhov chaw sib piv ntawm qhov tam sim no thiab qhov chaw soj ntsuam (m)
2. Lub zog Lorentz
Ib txoj xov hlau uas nqa ib qho tam sim no \(I\) thiab muab tso rau hauv ib lub teb sib nqus \(B\) yuav ntsib ib lub zog \(F\) uas muab los ntawm:
\[
\mathbf{F} = I(\mathbf{L} \times \mathbf{B})
\]
Qhov twg:
– \(\mathbf{F}\) = Lub zog sib nqus (N)
- \(Kuv\) = Tam sim no hluav taws xob (A)
- \(\mathbf{L}\) = Qhov ntev ntawm cov xov hlau hauv lub zog sib nqus (m)
– \(\mathbf{B}\) = Lub zog sib nqus (T)
Cov Lus Nug Piv Txwv thiab Kev Sib Tham
Lo lus nug thib 1:
Muab ib txoj hlua ncaj nraim uas ntev li 0.5 meters tso rau hauv ib lub zog sib nqus uas sib npaug zos li 0.2 Tesla. Yog tias txoj hlua nqa hluav taws xob ntawm 3 A thiab qhov kev coj ntawm qhov hluav taws xob yog perpendicular rau lub zog sib nqus, xam qhov loj ntawm lub zog Lorentz uas ua rau txoj hlua.
Kev daws teeb meem:
Siv cov qauv Lorentz force, peb tau txais:
\[
\mathbf{F} = I(\mathbf{L} \times \mathbf{B})
\]
Peb tuaj yeem txhais qhov kev taw qhia ntawm qhov tam sim no \(I\) sib luag rau \(\mathbf{L}\) thiab lub zog sib nqus \(B\) perpendicular rau \(\mathbf{L}\).
\[
|\mathbf{F}| = I \cdot L \cdot B \cdot \sin\theta
\]
Vim tias tam sim no thiab lub zog sib nqus yog perpendicular (\(\theta = 90^\circ\)), ces \(\sin 90^\circ = 1\), yog li:
\[
|\mathbf{F}| = 3 \, \text{A} \cdot 0.5 \, \text{m} \cdot 0.2 \, \text{T} \cdot 1 = 0.3 \, \text{N}
\]
Lo lus nug thib 2:
Ib txoj xov hlau puag ncig uas muaj lub vojvoog ntawm 0.1 meters nqa hluav taws xob ntawm 2 A. Txheeb xyuas lub zog sib nqus ntawm qhov chaw nruab nrab ntawm lub voj voog.
Kev daws teeb meem:
Siv cov mis ntawm lub zog magnetic hauv nruab nrab ntawm lub voj voog:
\[
B = \frac{\mu_0 I}{2R}
\]
nrog:
– \(\mu_0 = 4\pi \times 10^{-7} \, \text{Tm/A}\)
– \(Kuv = 2 \, \text{A}\)
– \(R = 0.1 \, \text{m}\)
Yog li ntawd:
\[
B = \frac{(4\pi \times 10^{-7} \, \text{Tm/A} \times 2 \, \text{A})}{2 \times 0.1 \, \text{m}}
= \frac{4\pi \times 10^{-7} \times 2}{0.2} \, \text{T}
= 4\pi \times 10^{-6} \, \text{T}
\kwv yees li 1.26 \times 10^{-5} \, \text{T}
\]
Lo lus nug thib 3:
Ob txoj hlua ncaj nraim uas ntev \(L\) raug muab tso rau ntawm qhov deb \(d\) ntawm ib leeg. Yog tias txhua txoj hlua nqa tam sim no \(I\) mus rau sab nraud, txiav txim siab lub zog ib chav ntev uas ua rau ntawm ob txoj hlua.
Kev daws teeb meem:
Lub zog ib chav ntev ntawm ob txoj xov hlau sib luag uas nqa tam sim no:
\[
f = \frac{\mu_0 I_1 I_2}{2\pi d}
\]
Vim tias cov dej ntws sib npaug thiab sib txawv hauv kev taw qhia:
\[
f = \frac{\mu_0 I^2}{2\pi d}
\]
Piv txwv li:
– \(\mu_0 = 4\pi \times 10^{-7} \, \text{Tm/A}\)
– \(I_1 = I_2 = Kuv\)
- \(d\) yog qhov deb ntawm cov xov hlau.
Hloov cov nqi rau hauv cov mis, peb tau txais:
\[
f = \frac{(4\pi \times 10^{-7})\, I^2}{2\pi d}
= \frac{2 \times 10^{-7} I^2}{d} \, \text{N/m}
\]
Xaus
Kev nkag siab txog kev sib cuam tshuam ntawm cov teb sib nqus thiab cov hluav taws xob tam sim no yog qhov tseem ceeb rau ntau yam thev naus laus zis niaj hnub no, txij li cov cav hluav taws xob mus rau cov generators. Los ntawm kev nkag siab txog lub ntsiab lus ntawm Lorentz lub zog, Biot-Savart txoj cai, thiab kev siv cov qauv teb sib nqus, peb tuaj yeem siv cov kev paub no rau ntau yam teeb meem thiab xwm txheej txhua hnub. Tsab xov xwm no yog los muab lub hauv paus ruaj khov rau kev nkag siab thiab daws cov teeb meem ntsig txog cov zog sib nqus hauv cov xov hlau uas nqa tam sim no.
