ʻO ke ʻano hana uila no nā uku ʻehā kiko
Pengantar
He manaʻo koʻikoʻi ka hiki ke uila i ka physics uila e kōkua iā mākou e hoʻomaopopo pehea e launa pū ai nā uku uila ma ka lewa. Ke kamaʻilio mākou e pili ana i kahi uku kiko, ke kuhikuhi nei mākou i kahi uku i manaʻo ʻia ua kau ʻia ma kahi kiko hoʻokahi ma ka lewa. Ma kēia ʻatikala, e kūkākūkā mākou i nā ʻano hana hiki ke uila no nā uku kiko ʻehā like ʻole, pehea e helu ai iā lākou, a me nā noi kūpono o kēia manaʻo.
Manaʻo Kumu o ka Hiki Uila
ʻO ka hiki ke uila ma kahi kiko ma ka lewa ka ikehu hiki ke uila no kēlā me kēia anakahi uku e ʻike ʻia e kahi uku hoʻāʻo maikaʻi i kau ʻia ma ia kiko. Hoʻohana pinepine ʻia ka hiki ke uila ma volts (V). Ma ke ʻano makemakika, ʻo ka hiki ke uila \( V \) ma muli o kahi uku \( q \) ma kahi mamao \( r \) mai kēlā uku ua hāʻawi ʻia e ke ʻano hana:
\[ V = \frac{kq}{r} \]
Ma hea:
– ʻO \( V \) ka hiki ke uila (volts),
– ʻO \( k \) ke kūpaʻa Coulomb (\( 8.99 \times 10^9 \, \text{N m}^2 \text{C}^{-2} \)),
– ʻO \( q \) ka uku (coulomb),
– ʻO \( r \) ka mamao mai ka hoʻopiʻi a i kahi i helu ʻia ai ka hiki ke hoʻoili ʻia (mika).
Ka Mana Uila o nā Uku ʻEhā Kiko
Inā loaʻa iā mākou nā helu uila ʻehā \( q_1 \), \( q_2 \), \( q_3 \), a me \( q_4 \) i loaʻa ma nā kūlana \( (x_1, y_1) \), \( (x_2, y_2) \), \( (x_3, y_3) \), a me \( (x_4, y_4) \) ma nā hoʻonohonoho Cartesian, hiki iā mākou ke helu i ka huina o ka hiki ke uila ma kahi kiko \( P(x, y) \) ma ka hoʻohui ʻana i nā hiki ke uila ma muli o kēlā me kēia helu uila ma ia wahi.
Ua hāʻawi ʻia ka huina o ka hiki uila \( V \) ma ke kiko \( P \) e:
\[ V = V_1 + V_2 + V_3 + V_4 \]
Ma hea:
– ʻO \( V_1 \) ka mana uila ma muli o \( q_1 \),
– ʻO \( V_2 \) ka mana uila ma muli o \( q_2 \),
– ʻO \( V_3 \) ka mana uila ma muli o \( q_3 \),
– ʻO \( V_4 \) ka mana uila ma muli o \( q_4 \).
Hiki ke kākau ʻia ka mana uila ma muli o kēlā me kēia hoʻopiʻi ma kahi \(P \) penei:
\[ V_1 = \frac{k q_1}{r_1}, \quad V_2 = \frac{k q_2}{r_2}, \quad V_3 = \frac{k q_3}{r_3}, \quad V_4 = \frac{k q_4}{r_4} \]
Ma hea:
– ʻO \( r_1 \) ka mamao ma waena o ka hoʻouku \( q_1 \) a me ke kiko \( P \),
– ʻO \( r_2 \) ka mamao ma waena o ka hoʻouku \( q_2 \) a me ke kiko \( P \),
– ʻO \( r_3 \) ka mamao ma waena o ka hoʻouku \( q_3 \) a me ke kiko \( P \),
– ʻO \( r_4 \) ka mamao ma waena o ka hoʻouku \( q_4 \) a me ke kiko \( P \).
Hiki ke helu ʻia ka mamao \( r \) ma waena o nā kiko ʻelua ma nā hoʻonohonoho Cartesian me ka hoʻohana ʻana i ke ʻano hana:
\[ r = \sqrt{(x – x_i)^2 + (y – y_i)^2} \]
Ma hea:
– ʻO \( (x, y) \) nā hoʻonohonoho o ke kiko \( P \),
– ʻO \( (x_i, y_i) \) nā hoʻonohonoho hoʻouku \( q_i \) (i = 1, 2, 3, 4).
No laila, hiki iā mākou ke helu i ka mamao \(r \) no kēlā me kēia hoʻopiʻi a laila e hoʻohana i ke ʻano hana uila e ʻike ai i ka mana ma kahi \(P \).
Laʻana Heluhelu
E lawe kākou i kahi laʻana paʻa me nā uku helu ʻehā penei:
– \( q_1 = 2 \, \mu \text{C} \) ma (0, 0),
– \( q_2 = -3 \, \mu \text{C} \) ma (1, 0),
– \( q_3 = 4 \, \mu \text{C} \) ma (0, 1),
– \( q_4 = -1 \, \mu \text{C} \) ma (1, 1).
Makemake mākou e helu i ka hiki ke uila ma ke kiko \(P \) i loaʻa ma (2, 2).
ʻO ka mea mua, helu mākou i ka mamao ma waena o ke kiko \(P \) a me kēlā me kēia uku:
\[ r_1 = \sqrt{(2-0)^2 + (2-0)^2} = \sqrt{8} = 2\sqrt{2} \]
\[ r_2 = \sqrt{(2-1)^2 + (2-0)^2} = \sqrt{5} \]
\[ r_3 = \sqrt{(2-0)^2 + (2-1)^2} = \sqrt{5} \]
\[ r_4 = \sqrt{(2-1)^2 + (2-1)^2} = \sqrt{2} \]
A laila, hoʻohana mākou i kēia waiwai mamao e helu i ka hiki ke uila ma muli o kēlā me kēia uku ma kahi \( P \):
\[ V_1 = \frac{8.99 \times 10^9 \times 2 \times 10^{-6}}{2\sqrt{2}} \approx 3.18 \times 10^3 \, \text{V} \]
\[ V_2 = \frac{8.99 \times 10^9 \times (-3) \times 10^{-6}}{\sqrt{5}} \approx -3.81 \times 10^3 \, \text{V} \]
\[ V_3 = \frac{8.99 \times 10^9 \times 4 \times 10^{-6}}{\sqrt{5}} \approx 7.62 \times 10^3 \, \text{V} \]
\[ V_4 = \frac{8.99 \times 10^9 \times (-1) \times 10^{-6}}{\sqrt{2}} \approx -6.36 \times 10^3 \, \text{V} \]
ʻO ka huina o ka hiki ke uila ma kahi \( P \) ka huina o kēia mau hiki āpau:
\[ V = 3.18 \times 10^3 – 3.81 \times 10^3 + 7.62 \times 10^3 – 6.36 \times 10^3 \approx 0.63 \times 10^3 \, \text{V} \]
Nā Hoʻohana o ka Mana Uila
He mea nui ka hoʻomaopopo ʻana i ka hiki ke uila o kekahi uku kiko i nā ʻano hana like ʻole, e like me:
– Hoʻolālā kaapuni uila: Pono nā ʻenekinia e hoʻomaopopo i ka hoʻolaha hiki i loko o kahi kaapuni e hōʻoia i ka hana pono ʻana o nā ʻāpana.
– Nā kahua uila i loko o ka biology: He kuleana ko ka mana uila i ka hana o nā cell nerve a me ka hoʻoili ʻana i nā hōʻailona i loko o ke kino.
– Ka hana ʻana i nā mea: Hoʻohana ʻia ka mana uila i nā ʻano hana electrostatic e like me ka waiho ʻana o ka electrostatic a me ka hoʻomaʻemaʻe ʻana i nā mea.
Ka hopena
ʻO ka helu ʻana i ka hiki ke uila o kekahi mau uku kiko e pono ai ka ʻike kumu o ka hana ʻana o ka hiki ke uila a pehea ka hopena o ka mamao ma waena o nā uku. Me kēia manaʻo, hiki iā mākou ke wehewehe pono a hoʻolālā i nā ʻōnaehana e pili ana i nā pilina uila. ʻO ka hiki ke uila kahi mea hana koʻikoʻi e kōkua iā mākou e hoʻomaopopo i ke ao o ka physics ma nā pae microscopic a me macroscopic.
