Nā nīnau hoʻohālike e kūkākūkā ana i nā kahua uila ma nā papa like
ʻO ke kahua uila i loko o nā papa like he manaʻo nui ia i ka physics uila a hoʻāʻo pinepine ʻia ma nā pae hoʻonaʻauao like ʻole, ma ke kula kiʻekiʻe a me ke kulanui. He mea nui ka hoʻomaopopo piha ʻana i kēia manaʻo, ʻoiai ke kahua uila i loko o nā papa like e pili pono ana i nā noi hana like ʻole, me ka hoʻolālā ʻana o nā capacitors a me nā mea uila ʻē aʻe. E hāʻawi kēia ʻatikala i nā pilikia hoʻohālike a me kahi kūkākūkā kikoʻī o ke kahua uila i loko o nā papa like e kōkua i ka hoʻomaopopo ʻana i kēia manaʻo.
Ke Kumumanaʻo Kumu o nā Kahua Uila ma nā Papa Hoʻohālikelike
ʻO nā papa like ʻelua he mau papa alakaʻi e lawe ana i nā uku uila kū'ē a ua hoʻonohonoho like ʻia ma kahi mamao. Ma kēia mau papa like, e hoʻolaha like ʻia ka uku ma luna o ka ʻili o nā papa. Ma muli o ke kānāwai o Gauss, hiki ke hōʻike ʻia ke kahua uila \(E \) ma waena o ʻelua mau papa alakaʻi like me nā uku kū'ē penei:
\[ E = \frac{\sigma}{\epsilon_0} \]
Ma hea:
– ʻO \( \sigma \) ka nui o ka hoʻouka ʻana o ka ʻili ma luna o ka pā,
– ʻO \( \epsilon_0 \) ka permittivity vacuum \((8.85 \times 10^{-12} \, \text{F/m})\).
Ma lalo o nā kūlana kūpono (nui ka nui o nā ana o ka pā i hoʻohālikelike ʻia me ka mamao ma waena o lākou), ua manaʻo ʻia ke kahua uila ma waena o nā pā he like.
Nā nīnau hoʻohālike a me nā kūkākūkā
Nīnau 1:
Ua hoʻonohonoho ʻia ʻelua mau papa like me kahi ʻāpana A i nui loa i ka hoʻohālikelike ʻia me ka mamao \( d \) ma waena o lākou i loaʻa i ka papa o luna kahi uku \( +Q \) a me ka papa o lalo kahi uku \( -Q \). Inā ʻo ka mamao ma waena o nā papa ʻelua he \( 2 \, \text{mm} \), ʻo ka ʻāpana o kēlā me kēia papa he \( 1 \, \text{m}^2 \), a ʻo ka uku \( Q \) he \( 1 \, \mu \text{C} \), e hoʻoholo i ke kahua uila ma waena o nā papa like!
Nā Kaʻina Kūkākūkā:
1. Ka nui o ka hoʻouku ʻili \( \sigma \) :
ʻO ka nui o ka hoʻouku ʻili ka nui o ka hoʻouku no kēlā me kēia ʻāpana ma ka pā. Hiki ke helu ʻia ma o:
\[ \sigma = \frac{Q}{A} \]
Ua ʻike ʻia:
– \( Q = 1 \, \mu \text{C} = 1 \times 10^{-6} \text{C} \)
– \( A = 1 \, \text{m}^2 \)
No laila:
\[ \sigma = \frac{1 \times 10^{-6} \text{C}}{1 \text{m}^2} = 1 \times 10^{-6} \text{C/m}^2 \]
2. Kahua Uila \( E \) :
ʻO ke kahua uila ma waena o ʻelua mau papa like o ka uku kū'ē ʻo \( E = \frac{\sigma}{\epsilon_0} \).
Hāʻawi ʻia \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \), a laila:
\[ E = \frac{1 \times 10^{-6} \text{C/m}^2}{8.85 \times 10^{-12} \text{F/m}} \]
\[ E = 1.13 \times 10^5 \, \text{N/C} \]
No laila, ʻo ke kahua uila ma waena o nā papa ʻelua he \( 1.13 \times 10^5 \, \text{N/C} \).
Nīnau 2:
ʻO kahi capacitor pālahalaha he ʻelua mau papa like me ka ʻāpana o \( 2 \, \text{m}^2 \) kēlā me kēia a hoʻokaʻawale ʻia e kahi mamao o \( 1 \, \text{mm} \). Inā ʻo ka hiki ma ka papa luna he \( 200 \, \text{V} \) a ma ka papa lalo he 0 V, e hoʻoholo i ka ikaika o ke kahua uila ma waena o nā papa ʻelua!
Nā Kaʻina Kūkākūkā:
1. Ka helu ʻana o ka ʻokoʻa hiki \( V \):
Ua ʻike ʻia he hiki ke hoʻololi ʻia ka papa luna \( V_{\text{top}} = 200 \, \text{V} \) a ʻo ka papa lalo \( V_{\text{bottom}} = 0 \, \text{V} \). No laila, ʻo ka ʻokoʻa hiki ke hoʻololi ʻia \( V \) ma waena o nā papa ʻelua:
\[ V = V_{\text{luna}} – V_{\text{lalo}} = 200 \, \text{V} – 0 \, \text{V} = 200 \, \text{V} \]
2. Ikaika o ke Kahua Uila \( E \):
Hiki ke helu ʻia ke kahua uila i loko o kahi capacitor pā like ma ka puʻunaue ʻana i ka ʻokoʻa hiki \( V \) ma ka mamao \( d \):
\[ E = \frac{V}{d} \]
Hāʻawi ʻia ka mamao \( d = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} \), a laila:
\[ E = \frac{200 \, \text{V}}{1 \times 10^{-3} \, \text{m}} = 2 \times 10^5 \, \text{V/m} \]
No laila, ʻo ka ikaika o ke kahua uila ma waena o nā papa ʻelua he \( 2 \times 10^5 \, \text{V/m} \).
Nīnau 3:
Loaʻa i kahi capacitor pā like nā pā me ka ʻāpana o \( 0.5 \, \text{m}^2 \) a me ka mamao ma waena o nā pā o \( 0.5 \, \text{cm} \). Inā hoʻopiʻi ʻia kēia capacitor me ka hoʻopiʻi o \( 2 \, \mu \text{C} \), e helu i kona capacitance a me ke kahua uila ma waena o nā pā!
Nā Kaʻina Kūkākūkā:
1. Ka hiki ke hoʻohana ʻia (C):
Hiki ke helu ʻia ka capacitance o kahi capacitor pā like me ka hoʻohana ʻana i ke ʻano hana:
\[ C = \epsilon_0 \frac{A}{d} \]
Ua ʻike ʻia:
– \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \)
– \( A = 0.5 \, \text{m}^2 \)
– \( d = 0.5 \, \kikokikona{cm} = 0.5 \times 10^{-2} \, \kikokikona{m} \)
No laila:
\[ C = 8.85 \times 10^{-12} \, \text{F/m} \times \frac{0.5 \, \text{m}^2}{0.5 \times 10^{-2} \, \text{m}} \]
\[ C = 8.85 \times 10^{-12} \times 10 \, \text{F} \]
\[ C = 88.5 \times 10^{-12} \, \text{F} \]
\[ C = 88.5 \, \text{pF} \]
2. Kahua Uila \( E \) :
No ka helu ʻana i ke kahua uila, pono mua mākou e ʻike i ka ʻokoʻa hiki \( V \). Hiki ke helu ʻia ka ʻokoʻa hiki \( V \) penei:
\[ V = \frac{Q}{C} \]
Ua ʻike ʻia:
– \( Q = 2 \, \mu \text{C} = 2 \times 10^{-6} \text{C} \)
– \( C = 88.5 \times 10^{-12} \text{F} \)
No laila:
\[ V = \frac{2 \times 10^{-6} \, \text{C}}{88.5 \times 10^{-12} \, \text{F}} \]
\[ V = 22.6 \times 10^3 \, \text{V} \]
\[ V = 22.6 \, \text{kV} \]
ʻO ka mea aʻe, me ka hoʻohana ʻana i ke ʻano hana \( E = \frac{V}{d} \), ʻo ke kahua uila:
\[ E = \frac{22.6 \, \text{kV}}{0.5 \times 10^{-2} \, \text{m}} \]
\[ E = 22.6 \times 10^3 \, \frac{\text{V}}{0.5 \times 10^{-2} \, \text{m}} \]
\[ E = 4.52 \times 10^6 \, \text{V/m} \]
No laila, ʻo ka capacitance o ka capacitor he \( 88.5 \, \text{pF} \) a ʻo ke kahua uila ma waena o nā papa he \( 4.52 \times 10^6 \, \text{V/m} \).
Ka hopena
He mea koʻikoʻi ka hoʻomaopopo ʻana i ke kahua uila i nā papa like ʻole ʻaʻole wale no nā hoʻokolohua hoʻonaʻauao akā no nā noi hana maoli hoʻi ma nā ʻano like ʻole o ka ʻenekinia a me ka physics. Me nā pilikia hoʻohālike a me nā kūkākūkā ma luna, ke manaʻolana ʻia e loaʻa i ka poʻe heluhelu kahi ʻike maikaʻi aʻe o ke kumumanaʻo a me kāna noi, e hiki ai iā lākou ke hoʻokokoke aku me ka hilinaʻi nui i nā kūlana o ka honua maoli a me nā hoʻokolohua.
