Kahua uila ma muli o hoʻokahi uku
E helu kahua uila i hana ʻia e kahi uku maikaʻi hoʻokahi, ʻo ka hana mua ke koho i kahi ʻili Gaussian poepoe o ka radius r kahi o ke kikowaena o ka poepoe ma ka uku hoʻokahi. ʻO ka ʻili o ka poepoe he 4r2.
ʻO ke kahua uila e puka mai ana mai ke kikowaena o ka pōpō e komo pololei ana i ka ʻili o ka pōpō i hiki ai i ke ʻano hana kahe uila is Φ = E A. Haʻilula Ke kānāwai o Gauss ʻo Φ = Q / εo
ʻO ke kahua uila ma kahi kiko ma kahi mamao r mai kahi hoʻopiʻi hoʻokahi:
Wehewehena: E = kahua uila, k = ke kūpaʻa o Coulomb (9 m 109 Nm2/C2), Q = ka hoʻouku uila, r = ka mamao mai ka hoʻouku uila
ʻO kēia ke ʻano hana no ke kahua uila i hana ʻia e kahi hoʻouka uilaHiki ke loaʻa kēia haʻilula me ka hoʻohana ʻana i Ke kānāwai o Coulomb.
Nā kahua uila i loko a ma waho o kahi poepoe paʻa i hoʻopiʻi ʻia me ka uila like
ʻO kahi poepoe paʻa me kahi uku uila like a like paha he uku holoʻokoʻa Q, ka nui V = 4/3 pi R3 a ʻo ka nui o ka hoʻouku ʻana i loko o kahi poepoe paʻa ʻo ρ = Q/V. E hoʻoholo i ka ikaika uila ke kahua uila i loko o ka pōpō a ma waho o ka pōpō.
a) Kahua uila i loko o kahi pōpō paʻa
He radius R ko ka poepoe paʻa, ʻoiai ʻo ka ʻili Gaussian i koho ʻia he poepoe o ka radius r, kahi r < R. ʻO ka nui o ka poepoe paʻa ʻo V a ʻo ka nui o ka poepoe Gaussian ʻo V'.
ʻO ke kumukūʻai uila i loko o ka poepoe Gauss penei:
ʻO ke kahua uila e puka mai ana mai ke kikowaena o ka pōpō e komo pololei ana i ka ʻili o ka pōpō i hiki ai ke ʻano no ka flux uila Φ = E A. ʻO ke kumu kānāwai o Gauss ʻo Φ = Q / εo
ʻO ke kahua uila ma kahi kiko ma kahi mamao r mai ke kikowaena o ka poepoe 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 Gaussian (r), kūlike ʻole me ka cube o ke anawaena o ka poepoe paʻa (R).3).
b) Kahua uila ma waho o kahi poepoe paʻa
He radius R ko ka poepoe paʻa ʻoiai he radius r ko ka ʻili Gaussian poepoe, kahi r > R. ʻO ka uku o ka poepoe paʻa ʻo Q; aia ka poepoe paʻa i loko o ka poepoe Gaussian no laila ʻo ka uku uila i loko o ka poepoe Gaussian ʻo Q.
Puka mai ke kahua uila mai ke kikowaena o ka pōpō a komo pololei i ka ʻili o ka pōpō no laila ʻo ke ʻano hana no ka flux uila Φ = E A. ʻO ke kumu kānāwai o Gauss ʻo Φ = Q / εo
ʻO ke kahua uila ma kahi mamao r mai ke kikowaena o ka poepoe paʻa:
ʻO ke kahua uila i loko a ma waho o ka pūpū o kahi poepoe hakahaka i hoʻopiʻi ʻia me ka uila like
He poepoe hakahaka me ke kaapuni R a me ka nui V = 4/3 pi R3, he uku uila maikaʻi like ma kona ʻili me ka uku holoʻokoʻa QE hoʻoholo ka ikaika o ke kahua uila i loko a ma waho o ka pūpū poepoe.
a) Kahua uila i loko o kahi poepoe hakahaka
No laila, ua hōʻailona ʻia kahi poepoe hakahaka e kahi uku uila ma luna o ka ʻili o ka poepoe, ʻoiai ʻaʻohe uku uila i loko o ka poepoe. Inā he poepoe ka ʻili Gaussian i koho ʻia a aia ka poepoe Gaussian i loko o kahi poepoe hakahaka, a laila ʻaʻohe uku uila i loko o ka poepoe Gaussian. ʻAʻohe uku uila, no laila ʻaʻohe nō hoʻi ke kahua uila. No laila, ʻaʻohe ke kahua uila i loko o ka poepoe hakahaka.
b) Kahua uila ma waho o ka poepoe hakahaka
He radius R ko ka poepoe hakahaka, ʻoiai ʻo ka ʻili Gaussian i koho ʻia he poepoe me ka radius 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 pōpō i hiki ai ke ʻano no ka flux uila Φ = EA = E 4π r2ʻO ke ʻano hana no ke kānāwai o Gauss ʻo Φ = Q / εo .
ʻO ke kahua uila ma kahi kiko ma kahi mamao r mai ke kikowaena o ka poepoe hakahaka penei:
Kahua uila kokoke i kahi uea lahilahi i hoʻopiha ʻia i ka uila
He uea lahilahi o ka lōʻihi palena ʻole e halihali ana i kahi uku uila maikaʻi like me ka nui o ka uku o λʻO ka uku uila ma luna o ke kaula he Q = λl. E hoʻoholo i ka ikaika uila. kahua uila a puni ka uea lahilahi.
Ua koho ʻia ka ʻili Gaussian he cylindrical me ka lōʻihi l a me ka radius r. ʻElua ʻano o ka ʻili, ʻo ia hoʻi kahi ʻili poepoe me ka radius r aia ma nā wēlau ʻelua o ka cylinder (ʻo ka ʻili ka nui r2) a me kahi ʻili poepoe me ka lōʻihi l (ʻo kona ʻili he 2πr l).
He maikaʻi ka hoʻouku uila, no laila ke puka mai nei ke kahua uila mai ka uea e kū pono ana i ka ʻili o ka paipu i loaʻa ai ka waiwai o ke kahe uila Φ = EA = E 2πr lMa ka ʻaoʻao ʻē aʻe, ua like ke kahua uila me nā wēlau ʻelua o ka paipu poepoe i ʻole ai ka flux uila.
ʻO ke kahua uila ma kahi kiko ma kahi mamao r mai ke kaula:
