ʻAtikala e pili ana i ka hoʻoholo ʻana i ke kahua uila me ka hoʻohana ʻana i ke kānāwai Gauss
Kahua uila ma o kahi hoʻopiʻi kiko hoʻokahi
No ka helu ʻana i ke kahua uila i hana ʻia e kahi uku maikaʻi hoʻokahi, ʻo ka hana mua, ʻo ke koho ʻana i ka ʻili poepoe Gauss me ka radius r kahi o ke kikowaena o ka poepoe ma ka uku hoʻokahi. ʻO ka ʻili o ka pōpō he 4πr2.
ʻO ke kahua uila e puka mai ana mai ke kikowaena o ka poepoe e komo pololei ana i ka ʻili o ka poepoe i hiki ai ke ʻano o ke kahe uila he Φ = E A. ʻO ke ʻano o ke kānāwai o Gauss ʻo Φ = Q/ε o
ʻO ke kahua uila ma kahi mamao o r mai ka hoʻopiʻi hoʻokahi:
E = kahua uila, k = kūpaʻa Coulomb (9 x 10 9 Nm 2 /C 2 ), Q = hoʻouku uila, r = mamao mai ka hoʻouku uila.
ʻO kēia ke ʻano o ke kahua uila i hana ʻia e kahi uku uila. Hiki ke loaʻa kēia ʻano me ka hoʻohana ʻana i ke kānāwai o Coulomb.
Nā kahua uila i loko a ma waho o ka pōpō paʻa me ka uila like i hoʻopiʻi ʻia
ʻO ka huina o ka uku o kahi pōpō paʻa homogeneous me ka hoʻopiʻi maikaʻi ʻia he Q, ka nui V = 4/3 π R 3 a ʻo ka nui o ka uku i loko o ka pōpō paʻa he ρ = Q/V. E hoʻoholo i ka ikaika o ke kahua uila i loko o ka pōpō a ma waho o ka pōpō.
a) Ke kahua uila i loko o ka pōpō paʻa
ʻO ka pōpō paʻa me ka radius o R, ʻoiai ʻo ka ʻili Gauss i koho ʻia he poepoe me ka radius r, kahi r < R. ʻO ka nui o ka pōpō paʻa ʻo V a ʻo ka nui o ka poepoe Gauss ʻo V'.
ʻO ke kumukūʻai uila i loko o nā pōpō Gauss:
ʻO ke kahua uila e puka mai ana mai ke kikowaena o ka poepoe e komo pololei ana i ka ʻili o ka poepoe i hiki ai ke ʻano o ke kahe uila he Φ = E A. ʻO ke ʻano no ke kānāwai o Gauss ʻo Φ = Q/ε o
ʻO ke kahua uila ma ke kiko me ka mamao o r mai ke kikowaena o ka pōpō paʻa:
Ma muli o ke ʻano ma luna, ua like ke kahua uila (E) me ka uku uila (Q) a me ke anawaena o ka ʻili Gauss (r), kūlike ʻole me ke anawaena o ka pōpō paʻa (R 3 )
b) Ke kahua uila ma waho o ka pōpō paʻa
He radius R ko ka pōpō paʻa ʻoiai he poepoe ka ʻili Gauss me ka radius r, kahi r > R. ʻO ka uku pōpō paʻa ʻo Q; aia ka pōpō paʻa i loko o ka pōpō gauss i hiki ai i ka uku uila i loko o ka pōpō gauss ʻo Q.
Puka ke kahua uila i ke kikowaena o ka poepoe a komo pololei i ka ʻili poepoe i hiki ai ke ʻano o ke kahe uila he Φ = E A. ʻO ke ʻano o ke kānāwai o Gauss he Φ = Q/ε o
ʻO ka mamao o ke kahua uila he r mai ke kikowaena o ka pōpō paʻa:
ʻO ke kahua uila i loko a ma waho o ka ʻili poepoe hakahaka me ka homogeneous electrically charged
Nā pōpō hakahaka me ka radius o R a me ka leo V = 4/3 π R 3 , me ka hoʻopiʻi uila maikaʻi like ma luna o ka ʻili me ka uku holoʻokoʻa Q. E hoʻoholo i ka ikaika o ke kahua uila i loko a ma waho o ka ʻili o ka poepoe.
a) Ke kahua uila i loko o ka pōpō hakahaka
He hakahaka ka pōpō, no laila aia ka uku uila ma luna o ka pōpō, ʻoiai ma loko o ka pōpō ʻaʻohe uku uila. Inā he poepoe ka ʻili gauss i koho ʻia a aia ka pōpō gauss i loko o ka pōpō hakahaka, ʻaʻohe uku uila i loko o ka pōpō gauss. ʻAʻohe uku uila, no laila ʻaʻohe nō hoʻi ke kahua uila. No laila, ʻaʻohe ke kahua uila i loko o ka pōpō hakahaka.
b) Kahua uila ma waho o ka pōpō hakahaka
He hakahaka ka pōpō me ke radius o R, ʻoiai he poepoe ka ʻili Gauss i koho ʻia me ke radius o r, kahi r > R.
ʻO ke kahua uila e puka mai ana mai ke kikowaena o ka pōpō e komo pololei ana i ka ʻili o ka poepoe i hiki ai ke ʻano o ke kahe uila he Φ = EA = E 4π r 2. ʻO ke ʻano o ke kānāwai o Gauss ʻo Φ = Q/ε o.
ʻO ke kahua uila ma ke kiko me ka mamao o r mai ke kikowaena o ka pōpō hakahaka:
Nā kahua uila kokoke i nā uea lahilahi i hoʻopiʻi ʻia e ka uila
He palena ʻole ka lōʻihi o kahi uea lahilahi, he hoʻouku uila like maikaʻi me ka nui o ka hoʻouku ʻana he λ. ʻO ka hoʻouku uila ma luna o ke uea ʻo Q = λ l. E hoʻoholo i ka ikaika o ke kahua uila a puni ke uea lahilahi.
Ua koho ʻia ka ʻili Gauss me ke ʻano o nā cylinders me ka lōʻihi l a me ka radius r. ʻElua ʻano o nā ʻili, kahi ʻili poepoe me ka radius r aia ma nā wēlau cylindrical ʻelua (ʻo ka ʻili he 2πr2) a me kahi ʻili poepoe me ka lōʻihi o l (ʻo ka ʻili he 2πr l).
He maikaʻi ka hoʻouku uila, a no laila ke puka aku nei ke kahua uila mai ka uea e kū pono ana i ka ʻili o ka paipu.
i ʻo ke kahe uila he Φ = EA = E 2πr l. Akā, ua like ke kahua uila me nā wēlau ʻelua o ka paipu poepoe i ʻole ai ke kahe uila he ʻole.
ʻO ke kahua uila ma kahi mamao o r mai ke kaula:
