Nā nīnau hoʻohālike a me ke kūkākūkā ʻana o nā kahua uila
He manaʻo nui kahi kahua uila i ka physics e wehewehe ana i ka hopena o kahi mea i hoʻopiʻi ʻia i ka uila ma ka lewa a puni. ʻO ke kahua uila ka ikaika i hoʻokau ʻia ma kēlā me kēia wahi ma ka lewa e ke alo o kēlā hoʻopiʻi. No ka hoʻomaopopo hohonu ʻana i kēia manaʻo, pono ka hoʻomaʻamaʻa nui. Aia ma lalo nā pilikia hoʻohālike a me nā kūkākūkā kikoʻī e pili ana i nā kahua uila.
Laʻana Nīnau 1: Ke helu ʻana i ka nui o ke kahua uila ma kahi kiko
Nīnau:
Ua kau ʻia nā hoʻouku kiko ʻelua \( q_1 = +4 \mu C \) a me \( q_2 = -8 \mu C \) ma nā hoʻonohonoho (0, 0) a me (0, 2) mika. E helu i ka nui a me ke kuhikuhi o ke kahua uila ma ke kiko A aia ma (0, 1) mika.
Kūkākūkā:
1. E hoʻoholo i ka mamao ma waena o ke kiko A a me nā uku ʻelua:
– ʻO ka mamao mai \( q_1 \) a i ke kiko A he 1 mika.
– ʻO ka mamao mai \( q_2 \) a i ke kiko A he 1 mika.
2. E helu i ke kahua uila ma muli o kēlā me kēia hoʻopiʻi ma kahi A:
ʻO ke kahua uila ma muli o kahi hoʻouku kiko \( q \) ma kahi mamao \( r \) penei:
\[ E = \frac{k \cdot |q|}{r^2} \]
no \( q_1 \) a me \( q_2 \):
\[ E_1 = \frac{9 \times 10^9 \cdot 4 \times 10^{-6}}{1^2} = 36 \times 10^3 \, \text{N/C} \]
\[ E_2 = \frac{9 \times 10^9 \cdot 8 \times 10^{-6}}{1^2} = 72 \times 10^3 \, \text{N/C} \]
3. E hoʻoholo i ke kuhikuhi o ke kahua uila:
ʻOiai he uku maikaʻi ʻo \( q_1 \), kuhikuhi kona kahua uila mai ka uku mai, no laila aia ʻo \( E_1 \) ma ke kuhikuhi y maikaʻi (i luna).
ʻOiai he hoʻouku maikaʻi ʻole ʻo \( q_2 \), ke kuhikuhi nei ke kahua uila i ka hoʻouku, no laila aia ʻo \( E_2 \) ma ke kuhikuhi y maikaʻi ʻole (i lalo).
4. E helu i ke kahua uila i loaʻa:
ʻOiai ʻo \( E_1 \) a me \( E_2 \) ma ka laina pololei hoʻokahi, hiki iā mākou ke unuhi i nā kahua uila:
\[ E_{\text{total}} = E_2 – E_1 \]
\[ E_{\text{total}} = 72 \times 10^3 – 36 \times 10^3 \]
\[ E_{\text{total}} = 36 \times 10^3 \, \text{N/C} \]
ʻO ke kuhikuhi o ke kahua uila e kū pono ana i ka axis-y maikaʻi ʻole (i lalo).
Laʻana Nīnau 2: Ke Helu ʻana i ka Mana Uila ma kahi Kiko
Nīnau:
Ua kau ʻia nā hoʻouku kiko ʻelua \( q_1 = +2 \mu C \) a me \( q_2 = +3 \mu C \) ma nā hoʻonohonoho (0, 0) a me (4, 0) mika. E helu i ka hiki ke uila ma ke kiko B aia ma (2, 0) mika.
Kūkākūkā:
1. E hoʻoholo i ka mamao ma waena o ke kiko B a me nā uku ʻelua:
– ʻO ka mamao mai \( q_1 \) a i ke kiko B he 2 mika.
– ʻO ka mamao mai \( q_2 \) a i ke kiko B he 2 mika.
2. E helu i ka hiki ke uila ma muli o kēlā me kēia hoʻopiʻi ma kahi B:
ʻO ke kūlana uila ma muli o kahi hoʻopiʻi kiko \( q \) ma kahi mamao \( r \) penei:
\[ V = \frac{k \cdot q}{r} \]
no \( q_1 \) a me \( q_2 \):
\[ V_1 = \frac{9 \times 10^9 \cdot 2 \times 10^{-6}}{2} = 9 \times 10^3 \, \text{V} \]
\[ V_2 = \frac{9 \times 10^9 \cdot 3 \times 10^{-6}}{2} = 13.5 \times 10^3 \, \text{V} \]
3. E helu i ka huina o ka hiki ke uila ma ke kiko B:
He nui scalar ka hiki ke uila, no laila ʻo ka hiki holoʻokoʻa ka huina algebraic o kēia mau hiki:
\[ V_{\text{total}} = V_1 + V_2 \]
\[ V_{\text{total}} = 9 \times 10^3 + 13.5 \times 10^3 \]
\[ V_{\text{total}} = 22.5 \times 10^3 \, \text{V} \]
Laʻana 3: Kahua Uila i loko o kahi Mea Dielectric
Nīnau:
Inā kau ʻia kahi uku \( q = 5 \mu C \) ma ke kikowaena o kahi poepoe hakahaka me ka radius o 3 mika i hoʻopiha piha ʻia me kahi dielectric me kahi dielectric constant \( \kappa = 2 \). E helu i ke kahua uila ma kahi mamao o 2 mika mai ke kikowaena o ka poepoe.
Kūkākūkā:
1. ʻO ke ʻano hana no ke kahua uila i loko o kahi mea dielectric:
ʻO ke kahua uila \( E \) ma kahi mamao \( r \) i loko o kahi mea dielectric:
\[ E = \frac{q}{4 \pi \epsilon_0 \kappa r^2} \]
kahi \( \epsilon_0 = 8.85 \times 10^{-12} \) F/m.
2. E hoʻokomo i nā waiwai i hāʻawi ʻia:
\[ E = \frac{5 \times 10^{-6}}{4 \pi \cdot 8.85 \times 10^{-12} \cdot 2 \cdot (2)^2} \]
\[ E = \frac{5 \times 10^{-6}}{4 \pi \cdot 8.85 \times 10^{-12} \cdot 8} \]
\[ E = \frac{5 \times 10^{-6}}{8 \cdot 3.54 \times 10^{-10}} \]
\[ E = \frac{5 \times 10^{-6}}{28.32 \times 10^{-10}} \]
\[ E = 1.77 \times 10^4 \, \text{N/C} \]
Ka hopena
Ma o nā hiʻohiʻona ma luna, hiki iā kākou ke loaʻa kahi ʻike maopopo o ke kumumanaʻo o nā kahua uila. Hoʻokomo pū kēia me ka nui o ke kahua uila ma kahi kiko ma muli o nā uku he nui, ka helu ʻana o ka hiki ke uila, a me ke kahua uila i nā mea dielectric. He mea nui ka ʻike paʻa o kēia kumumanaʻo no ka mea hiki ke wehewehe ʻia nā hanana kino he nui e nā kahua uila, a me kā lākou noi ʻana i ka ʻenehana hou. E hoʻomau i ka hoʻomaʻamaʻa ʻana me nā pilikia like ʻole e hoʻopaʻa hohonu i kēia kumumanaʻo.
