Piv txwv cov lus nug thiab kev sib tham txog cov teb hluav taws xob
Lub zog hluav taws xob yog lub tswv yim tseem ceeb hauv kev kawm txog physics uas piav qhia txog qhov cuam tshuam ntawm ib yam khoom uas muaj hluav taws xob rau qhov chaw ib puag ncig. Lub zog hluav taws xob yog lub zog uas siv rau txhua qhov chaw hauv qhov chaw los ntawm qhov muaj lub zog ntawd. Yuav kom nkag siab lub tswv yim no kom tob dua, feem ntau yuav tsum tau xyaum ua. Hauv qab no yog cov qauv teeb meem thiab kev sib tham ntxaws txog lub zog hluav taws xob.
Piv txwv lus nug 1: Xam qhov loj ntawm lub zog hluav taws xob ntawm ib qho taw tes
Lo lus nug:
Ob lub ntsiab lus them nqi \( q_1 = +4 \mu C \) thiab \( q_2 = -8 \mu C \) raug muab tso rau ntawm qhov sib koom ua ke (0, 0) thiab (0, 2) meters. Xam qhov loj thiab kev coj ntawm lub teb hluav taws xob ntawm qhov chaw A uas yog ntawm (0, 1) meters.
Kev Sib Tham:
1. Txheeb xyuas qhov deb ntawm qhov chaw A thiab ob lub nqi:
– Qhov deb ntawm \( q_1 \) mus rau qhov A yog 1 meter.
– Qhov deb ntawm \( q_2 \) mus rau qhov A yog 1 meter.
2. Xam lub zog hluav taws xob vim yog txhua qhov them ntawm qhov chaw A:
Lub teb hluav taws xob vim yog ib qho chaw them nqi q ntawm qhov deb q yog:
\[ E = \frac{k\cdot |q|}{r^2} \]
rau q(1) thiab q(2):
\[ E_1 = \frac{9 \times 10^9 \cdot 4 \times 10^{-6}}{1^2} = 36 \times 10^3 \, \text{N/C} \]
\[ E_2 = \frac{9 \times 10^9 \cdot 8 \times 10^{-6}}{1^2} = 72 \times 10^3 \, \text{N/C} \]
3. Txheeb xyuas qhov kev taw qhia ntawm lub zog hluav taws xob:
Vim tias \( q_1 \) yog ib qho hluav taws xob zoo, nws lub zog hluav taws xob taw tes tawm ntawm qhov hluav taws xob, yog li \( E_1 \) nyob rau hauv qhov kev taw qhia y zoo (sab saud).
Vim tias \( q_2 \) yog tus nqi hluav taws xob tsis zoo, lub teb hluav taws xob yog mus rau tus nqi hluav taws xob, yog li \( E_2 \) yog nyob rau hauv qhov kev taw qhia y tsis zoo (downward).
4. Xam qhov hluav taws xob tshwm sim:
Vim tias \(E_1\) thiab \(E_2\) nyob rau tib txoj kab ncaj nraim, peb tuaj yeem rho tawm cov teb hluav taws xob:
\[ E_{\text{total}}} = E_2 – E_1 \]
\[ E_{\text{total}} = 72 \times 10^3 – 36 \times 10^3 \]
\[ E_{\text{total}} = 36 \times 10^3 \, \text{N/C} \]
Lub zog hluav taws xob ntawm lub zog hluav taws xob yog mus rau sab y-axis tsis zoo (down).
Piv Txwv Lo Lus Nug 2: Xam Lub Peev Xwm Hluav Taws Xob ntawm Ib Qho Chaw
Lo lus nug:
Ob lub ntsiab lus them nqi \( q_1 = +2 \mu C \) thiab \( q_2 = +3 \mu C \) raug muab tso rau ntawm qhov sib koom ua ke (0, 0) thiab (4, 0) meters. Xam lub zog hluav taws xob ntawm qhov chaw B uas yog ntawm (2, 0) meters.
Kev Sib Tham:
1. Txheeb xyuas qhov deb ntawm qhov chaw B thiab ob lub nqi:
– Qhov deb ntawm \( q_1 \) mus rau qhov chaw B yog 2 meters.
– Qhov deb ntawm \( q_2 \) mus rau qhov chaw B yog 2 meters.
2. Xam lub zog hluav taws xob vim yog txhua qhov them ntawm qhov chaw B:
Lub zog hluav taws xob vim yog ib qho chaw them nqi q ntawm qhov deb r yog:
\[ V = \frac{k^{q}}{r} \]
rau q(1) thiab q(2):
\[ V_1 = \frac{9 \times 10^9 \cdot 2 \times 10^{-6}}{2} = 9 \times 10^3 \, \text{V} \]
\[ V_2 = \frac{9 \times 10^9 \cdot 3 \times 10^{-6}}{2} = 13.5 \times 10^3 \, \text{V} \]
3. Xam tag nrho lub zog hluav taws xob ntawm qhov chaw B:
Lub zog hluav taws xob yog ib qho scalar quantity, yog li tag nrho cov peev xwm yog qhov algebraic sum ntawm cov peev xwm no:
\[ V_{\text{total}} = V_1 + V_2 \]
\[ V_{\text{total}} = 9 \times 10^3 + 13.5 \times 10^3 \]
\[ V_{\text{total}} = 22.5 \times 10^3 \, \text{V} \]
Piv txwv 3: Lub zog hluav taws xob hauv cov khoom siv dielectric
Lo lus nug:
Yog tias muaj ib qho nqi hluav taws xob \(q = 5 \mu C \) nyob hauv nruab nrab ntawm lub pob zeb uas muaj lub vojvoog ntawm 3 meters uas puv nrog lub dielectric nrog lub dielectric tas mus li \(\kappa = 2 \). Xam lub teb hluav taws xob ntawm qhov deb ntawm 2 meters ntawm qhov nruab nrab ntawm lub pob zeb.
Kev Sib Tham:
1. Cov mis rau lub teb hluav taws xob hauv cov khoom siv dielectric:
Lub teb hluav taws xob \(E \) ntawm qhov deb \(r \) hauv cov khoom siv dielectric yog:
\[ E = \frac{q}{4 \pi \epsilon_0 \kappa r^2} \]
qhov twg \( \epsilon_0 = 8.85 \times 10^{-12} \) F/m.
2. Sau cov nqi uas tau muab:
\[ E = \frac{5 \times 10^{-6}}{4 \pi \cdot 8.85 \times 10^{-12} \cdot 2 \cdot (2)^2} \]
\[ E = \frac{5 \times 10^{-6}}{4 \pi \cdot 8.85 \times 10^{-12} \cdot 8} \]
\[ E = \frac{5 \times 10^{-6}}{8 \cdot 3.54 \times 10^{-10}} \]
\[ E = \frac{5 \times 10^{-6}}{28.32 \times 10^{-10}} \]
\[ E = 1.77 \times 10^4 \, \text{N/C} \]
Xaus
Los ntawm cov piv txwv saum toj no, peb tuaj yeem nkag siab meej dua txog lub tswv yim ntawm cov teb hluav taws xob. Qhov no suav nrog qhov loj ntawm lub teb hluav taws xob ntawm ib qho chaw vim muaj ntau qhov nqi, kev suav ntawm lub zog hluav taws xob, thiab lub teb hluav taws xob hauv cov ntaub ntawv dielectric. Kev nkag siab zoo txog lub tswv yim no yog qhov tseem ceeb vim tias ntau yam xwm txheej lub cev tuaj yeem piav qhia los ntawm cov teb hluav taws xob, nrog rau lawv cov ntawv thov hauv cov thev naus laus zis niaj hnub. Txuas ntxiv xyaum nrog ntau yam teeb meem kom paub txog lub tswv yim no tob dua.
