Piv txwv ntawm Cov Lus Nug Txog Lub Zog Hluav Taws Xob
Lub zog ntawm lub teb hluav taws xob yog lub tswv yim tseem ceeb hauv kev kawm txog physics uas piav qhia txog lub zog ntawm lub teb hluav taws xob ntawm ib qho chaw tshwj xeeb hauv qhov chaw. Lub teb hluav taws xob yog tsim los ntawm cov nqi hluav taws xob thiab tuaj yeem cuam tshuam rau lwm cov nqi hauv lub teb ntawd. Yuav kom nkag siab zoo dua txog lub tswv yim no, cia peb saib qee qhov piv txwv ntawm cov teeb meem cuam tshuam nrog lub zog ntawm lub teb hluav taws xob thiab yuav daws lawv li cas.
Cov Ntsiab Lus ntawm Cov Hluav Taws Xob
Ua ntej peb nkag mus rau hauv cov teeb meem piv txwv, cia peb rov xyuas me ntsis txog lub tswv yim yooj yim ntawm cov teb hluav taws xob. Lub zog hluav taws xob (\(E\)) ntawm ib qho chaw hauv qhov chaw yog txhais tias yog lub zog (\(F\)) ib chav tsev them (\(q\)) uas tau ntsib los ntawm kev sim them me me ntawm qhov ntawd:
\[ E = \frac{F}{q} \]
Qhov twg:
- \(E\) yog lub zog hluav taws xob (N/C lossis V/m),
- \(F\) yog lub zog hluav taws xob uas lub nqi (N) ntsib,
- \(q\) yog qhov loj ntawm qhov them sim (C).
Yog tias qhov chaw ntawm lub teb hluav taws xob yog ib qho chaw them nqi ^(Q\), ces lub zog hluav taws xob ntawm qhov deb ^(r\) ntawm tus nqi yog muab los ntawm cov qauv:
\[ E = \frac{k\cdot |Q|}{r^2} \]
Qhov twg:
- \(k\) yog Coulomb tas li (\(8.99 \times 10^9 \, \text{N m}^2/\text{C}^2\)),
- \(Q\) yog qhov them nqi (C),
- ρ yog qhov deb ntawm qhov chaw them mus rau qhov chaw soj ntsuam (m).
Piv txwv lus nug 1: Lub zog hluav taws xob los ntawm ib qho chaw them nqi
Lus Nug: Ib qho nqi hluav taws xob \(Q\) ntawm \(5 \times 10^{-6} \, \text{C}\) raug muab tso rau ntawm qhov pib (0,0). Xam lub zog hluav taws xob ntawm qhov deb ntawm 2 meters ntawm qhov nqi hluav taws xob.
Kev daws teeb meem:
Los ntawm cov qauv hluav taws xob los ntawm ib qho chaw them, peb tuaj yeem xam lub zog hluav taws xob raws li hauv qab no:
\[ E = \frac{k\cdot |Q|}{r^2} \]
Sau cov nqi ntawm \(k\), \(Q\), thiab \(r\):
\[ E = \frac{8.99 \times 10^9 \times 5 \times 10^{-6}}{2^2} \]
\[ E = \frac{8.99 \times 10^9 \times 5 \times 10^{-6}}{4} \]
\[ E = \frac{44.95 \times 10^3}{4} \]
\[ E = 11.2375 \times 10^3 \]
\[ E = 11,237.5 \, \text{N/C} \]
Yog li, lub zog hluav taws xob ntawm qhov deb ntawm 2 meters ntawm tus nqi yog \(11,237.5 \, \text{N/C}\).
Piv txwv 2: Kev sib tshooj ntawm cov teb hluav taws xob
Lus Nug: Ob lub nqi hluav taws xob, \(Q_1 = 4 \times 10^{-6} \, \text{C}\) thiab \(Q_2 = -3 \times 10^{-6} \, \text{C}\) raug muab tso rau ntawm qhov deb ntawm 3 meters ntawm ib leeg. Xam lub zog hluav taws xob ntawm qhov nruab nrab ntawm ob lub nqi hluav taws xob.
Kev daws teeb meem:
Ua ntej, peb xam lub teb hluav taws xob uas tsim los ntawm txhua tus nqi ntawm qhov nruab nrab.
Rau qhov them nqi \(Q_1\):
\[ r_1 = \frac{3}{2} = 1.5 \, \text{m} \]
\[ E_1 = \frac{k\cdot |Q_1|}{r_1^2} \]
\[ E_1 = \frac{8.99 \times 10^9 \times 4 \times 10^{-6}}{1.5^2} \]
\[ E_1 = \frac{35.96 \times 10^3}{2.25} \]
\[ E_1 = 15.9822 \times 10^3 \]
\[ E_1 = 15,982.2 \, \text{N/C} \]
Rau qhov them nqi \(Q_2\):
\[ r_2 = 1.5 \, \text{m} \]
\[ E_2 = \frac{k\cdot |Q_2|}{r_2^2} \]
\[ E_2 = \frac{8.99 \times 10^9 \times 3 \times 10^{-6}}{1.5^2} \]
\[ E_2 = \frac{26.97 \times 10^3}{2.25} \]
\[ E_2 = 11.9822 \times 10^3 \]
\[ E_2 = 11,982.2 \, \text{N/C} \]
Vim tias \(Q_1\) yog qhov zoo thiab \(Q_2\) yog qhov tsis zoo, lawv cov teb hluav taws xob ntawm qhov nruab nrab yuav thim rov qab los ntawm ib leeg. Yog li, peb ntxiv ob lub teb hluav taws xob:
\[ E = E_1 + E_2 \]
\[ E = 15,982.2 + 11,982.2 \]
\[ E = 27,964.4 \, \text{N/C} \]
Yog li, lub zog hluav taws xob ntawm qhov nruab nrab ntawm ob qho nqi yog \(27,964.4 \, \text{N/C}\).
Piv txwv 3: Lub zog hluav taws xob los ntawm Dipole
Lus Nug: Ib lub dipole hluav taws xob muaj ob lub nqi \(\pm 4 \times 10^{-6} \, \text{C}\) uas yog 1 cm sib nrug. Xam lub zog hluav taws xob ntawm ib qho chaw 1 meter ntawm qhov chaw nruab nrab ntawm lub dipole ntawm lub axis ntawm lub dipole.
Kev daws teeb meem:
Lub zog hluav taws xob raws txoj kab ntawm dipole (rau qhov deb loj txaus piv rau qhov deb ntawm cov nqi dipole) yog muab los ntawm:
\[ E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{2p}{r^3} \]
Qhov twg \(p\) yog lub zog hluav taws xob dipole (\(p = q \cdot d\)), \(d\) yog qhov deb ntawm cov nqi dipole, thiab \(r\) yog qhov deb ntawm qhov chaw nruab nrab ntawm dipole mus rau qhov chaw soj ntsuam.
Ua ntej, xam lub sijhawm dipole:
\[ p = q \cdot d \]
\[ p = 4 \times 10^{-6} \cdot 0.01 \]
\[ p = 4 \times 10^{-8} \, \text{C m} \]
Tom qab ntawd, xam lub zog ntawm lub zog hluav taws xob:
\[ E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{2p}{r^3} \]
\[ E = \frac{8.99 \times 10^9}{1} \cdot \frac{2 \times 4 \times 10^{-8}}{1^3} \]
\[ E = 8.99 \times 10^9 \cdot 8 \times 10^{-8} \]
\[ E = 7.192 \times 10^2 \]
\[ E = 719.2 \, \text{N/C} \]
Yog li, lub zog hluav taws xob ntawm qhov chaw 1 'meter' ntawm qhov chaw nruab nrab ntawm dipole ntawm lub dipole axis yog \(719.2 \, \text{N/C}\).
Xaus
Kev nkag siab txog lub zog ntawm lub zog hluav taws xob yog qhov tseem ceeb hauv kev kawm txog physics thiab nws cov kev siv. Cov teeb meem piv txwv saum toj no qhia tau hais tias cov ntsiab cai yooj yim ntawm cov teb hluav taws xob tuaj yeem siv los xam lub zog ntawm lub teb hauv ntau yam kev teeb tsa nqi. Cov teeb meem xyaum zoo li no pab tau zoo heev rau kev nkag siab txog lub tswv yim thiab kev siv Coulomb txoj cai thiab kev sib tshooj ntawm lub teb hluav taws xob. Los ntawm kev nkag siab thiab xyaum ntau cov teeb meem, peb tuaj yeem nkag siab tob txog kev sib cuam tshuam hluav taws xob hauv ntau lub cev.
