Formula Mana Uila
Pendahuluan
ʻO ka hiki ke uila kahi manaʻo nui i ka physics uila e wehewehe ana i ka ikehu hiki ke uila no kēlā me kēia anakahi o ka hoʻopiʻi ma kahi kiko i loko o kahi kahua uila. He kuleana koʻikoʻi kona i nā ʻano noi like ʻole, me ka hoʻolālā ʻana i nā kaapuni uila, ka hoʻomaopopo ʻana i nā hanana uila a me ka magnetic, a me ka nānā ʻana i ke ʻano o nā ʻāpana i hoʻopiʻi ʻia. E kūkākūkā kēia ʻatikala i ka wehewehe ʻana o ka hiki ke uila, nā ʻano pili, ke kumumanaʻo o nā kahua uila, kāna mau noi i ke ola o kēlā me kēia lā, a me nā laʻana e hoʻoikaika i ka ʻike.
Ka Wehewehena o ka Mana Uila
Ua wehewehe ʻia ka mana uila ma kahi kiko i loko o kahi kahua uila ʻo ia ka nui o ka hana i hana ʻia e hoʻoneʻe i kahi uku hoʻokahi mai kahi kiko kuhikuhi (ʻo ka palena ʻole) a i kēlā kiko. Ma ke ʻano makemakika, ua hōʻike ʻia ka mana uila (\(V\)) ma nā ʻāpana o volts (V) a hiki ke hoʻohālikelike ʻia penei:
\[ V = \frac{W}{q} \]
Ma hea:
– ʻO \(V\) ka hiki ke uila,
– ʻO \(W\) ka hana i hana ʻia e hoʻoneʻe i ka uku,
– ʻO \(q\) ka nui o ka hoʻouku ʻana.
ʻO ke ʻano hana uila no nā kumu kiko
No kahi hoʻopiʻi kiko \(Q\) e hana ana i kahi kahua uila, ua hāʻawi ʻia ka hiki ke uila \(V\) ma kahi mamao \(r\) mai ka hoʻopiʻi e:
\[ V = \frac{kQ}{r} \]
Ma hea:
– ʻO \(V\) ka hiki ke uila,
– ʻO \(k\) ke kūpaʻa Coulomb (\(8.99 \times 10^9 \, \text{N m}^2/\text{C}^2\)),
– ʻO \(Q\) ka nui o ka uku,
– ʻO \(r\) ka mamao mai ka hoʻouku ʻana a i kahi i ana ʻia ai ka hiki.
Kahua Uila a me ka Mana Uila
ʻO ke kahua uila (\(E\)) he nui vector e wehewehe ana i ka ikaika no kēlā me kēia anakahi uku i ʻike ʻia e kahi uku hoʻāʻo ma kahi kiko ma ka lewa. Hiki ke hōʻike ʻia ka pilina ma waena o ke kahua uila a me ka hiki ke uila penei:
\[ \vec{E} = -\nabla V \]
Ma hea:
– ʻo \(\vec{E}\) ke kahua uila,
– ʻO \(\nabla V\) ka gradient hiki ke uila.
Ka Mana Uila no kekahi mau Uku
Inā he nui nā uku kiko, ʻo ka huina o ka hiki ke uila ma kahi kiko ka huina algebraic o nā hiki ke uila i hana ʻia e kēlā me kēia uku. Ma ke ʻano makemakika, no nā uku \(Q_1, Q_2, \ldots, Q_n\) i loaʻa ma kahi mamao \(r_1, r_2, \ldots, r_n\) mai ke kiko, ʻo ka huina o ka hiki ke uila \(V_{total}\) penei:
\[ V_{total} = \sum_{i=1}^{n} \frac{kQ_i}{r_i} \]
Ka Mana Uila i nā Alakaʻi
I loko o kahi alakaʻi uila, hiki i nā uku manuahi ke neʻe maʻalahi. ʻO ka hopena, ʻo ke kahua uila i loko o ke alakaʻi he ʻole, a ʻo ka hiki ke uila e mau ana ma loko o ke alakaʻi. ʻO ia hoʻi, inā mākou e hoʻohui i ʻelua mau kiko i loko o kahi alakaʻi, ʻaʻohe ʻokoʻa hiki ma waena o lākou.
Ka Hoʻohana ʻana o ka Mana Uila i ke Ola o kēlā me kēia Lā
Nā Pākahi a me nā Kaapuni Uila
ʻO ka pila kahi kumu o ka hiki ke uila e hana ai i kahi ʻokoʻa hiki ke hana ma waena o kona mau kikowaena maikaʻi a me nā kikowaena maikaʻi ʻole. ʻO kēia ʻokoʻa hiki ke hana i kahi au uila e kahe i loko o kahi kaapuni pani, e hāʻawi ana i ka mana i nā mea uila like ʻole.
Kapasitor
He mea hana ka capacitor e mālama i ka ikehu ma ke ʻano o kahi kahua uila ma waena o ʻelua mau papa conductive i hoʻokaʻawale ʻia e kahi dielectric. ʻO ka mana uila ma waena o nā papa e hoʻoholo ai i ka nui o ka uku hiki iā ia ke mālama.
Uila
Hiki mai ka uila i ka wā e hōʻiliʻili ʻia ai nā uku uila i loko o nā ao e hana ai i kahi ʻokoʻa nui ma waena o ke ao a me ka ʻili o ka Honua. Ke lawa ka nui o kēia ʻokoʻa, hoʻokuʻu ʻia ka ikehu uila ma ke ʻano o ka uila.
Nā nīnau a me nā pane hoʻohālike
Laʻana Nīnau 1
Ua kau ʻia kahi uku kiko \(Q = 2 \, \mu \text{C}\) ma kekahi kiko. E helu i ka hiki ke uila ma kahi mamao o 0,5 mika mai ka uku.
Hoʻonā:
Ke hoʻohana nei i ke ʻano hana uila no kahi hoʻopiʻi kiko:
\[ V = \frac{kQ}{r} \]
E hoʻokomo i nā waiwai i hāʻawi ʻia:
\[ V = \frac{8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \times 2 \times 10^{-6} \, \text{C}}{0,5 \, \text{m}} \]
\[ V = \frac{17.98 \times 10^3 \, \text{N m/C}}{0,5} \]
\[ V = 35.96 \times 10^3 \, \text{V} \]
\[ V = 35.96 \, \text{kV} \]
No laila, ʻo ka mana uila ma kahi mamao o 0,5 mika mai ka hoʻopiʻi he 35,96 kV.
Laʻana Nīnau 2
Ua kau ʻia nā helu uila ʻelua \(Q_1 = 3 \, \mu \text{C}\) a me \(Q_2 = -2 \, \mu \text{C}\) ma kahi mamao o 1 mika a me 0,5 mika mai kahi kiko P. E helu i ka huina o ka hiki ke uila ma kahi kiko P.
Hoʻonā:
Ke hoʻohana nei i ke ʻano hana uila no kekahi mau uku:
\[ V_{total} = \frac{kQ_1}{r_1} + \frac{kQ_2}{r_2} \]
E hoʻokomo i nā waiwai i hāʻawi ʻia:
\[ V_{huina} = \frac{8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \times 3 \times 10^{-6} \, \text{C}}{1 \, \text{m}} + \frac{8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \times (-2) \times 10^{-6} \, \text{C}}{0,5 \, \text{m}} \]
\[ V_{total} = 26.97 \times 10^3 \, \text{V} – 35.96 \times 10^3 \, \text{V} \]
\[ V_{total} = -8.99 \times 10^3 \, \text{V} \]
No laila, ʻo ka huina o ka hiki ke uila ma ke kiko P he -8.99 kV.
Ka hopena
He manaʻo koʻikoʻi ka hiki ke uila e wehewehe ana i ka ikehu hiki no kēlā me kēia anakahi o ka hoʻopiʻi ma kahi kiko i loko o kahi kahua uila. Ma ka hoʻomaopopo ʻana i nā haʻilula e pili ana i ka hiki ke uila, e like me \( V = \frac{W}{q} \) a me \( V = \frac{kQ}{r} \), a me kā lākou noi ʻana ma nā ʻano like ʻole, hiki iā mākou ke hoʻomaopopo maikaʻi i nā hanana uila i ke ola o kēlā me kēia lā. He nui nā noi kūpono o ka hiki ke uila, mai ka hoʻolālā kaapuni uila a hiki i nā hanana kūlohelohe e like me ka uila. Ma o nā pilikia hoʻohālike i hoʻokomo ʻia, ua manaʻolana ʻia e ʻoi aku ka hohonu a me ka pili o ka hoʻomaopopo ʻana i kēia manaʻo.
