Goobta korontada oo ay ugu wacan tahay hal dallac
Si loo xisaabiyo garoonka korontada Marka la sameeyo hal dallac togan, tallaabada ugu horreysa waa in la doorto dusha sare ee Gaussian ee wareegsan ee radius r halkaas oo bartamaha kubbadda ay ku taal hal dallac. Bedka dusha sare ee kubbadda waa 4..r2.
Garoon koronto oo ka soo baxaya bartamaha kubbadda ayaa si toosan ugu dhex gala dusha sare ee kubbadda si qaacidada qulqulka korantada ay u noqoto Φ = E A. Qaaciddada sharciga Gauss waa Φ = Q / ε o
Goobta korantada ee meel fog ka jirta hal dallac waa:
Sharaxaad: E = goob koronto, k = Joogtada Coulomb (9 x 109 Nm2/C2), Q = dallacaadda korantada, r = masaafada u jirta dallacaadda korontada
Kani waa qaacidada loogu talagalay goobta korantada ee ay soo saarto dallacaadda korontada . Qaacidadan waxaa laga soo saari karaa iyadoo la adeegsanayo sharciga Coulomb.
Goobaha korontada ee gudaha iyo dibaddaba leh goob adag oo koronto ku shaqeeya oo isku mid ah
Goobo adag oo leh dallac koronto oo isku mid ah ama isku mid ah waxay leedahay dallac dhan Q, mugga V = 4/3 π R 3 cufnaanta dallacaadda ee kubbadda adag waa ρ = Q/V. Go'aami xoogga goobta korantada ee gudaha kubbadda iyo dibadda kubbadda.
a) Garoon koronto oo ku dhex jira kubad adag
Wareegga adag wuxuu leeyahay radius R, halka dusha sare ee Gaussian ee la doortay ay tahay radius r, halkaas oo r < R. Mugga wareegga adag uu yahay V mugga wareegga Gaussian-na uu yahay V'.
Dareeraha korontada ee ku jira qaybta Gauss waa:
Goobta korontada ee ka soo baxda bartamaha kubadda ayaa si toosan ugu soo gasha dusha sare ee kubadda si qaacidada socodka korontada ay u noqoto Φ = E A. Qaacidada sharciga Gauss waa Φ = Q / εo
Goobta korantada ee meel fog r ka jirta bartamaha wareegga adag waa:
Iyada oo ku saleysan qaacidada kore, goobta korantada (E) waxay u dhigantaa dallacaadda korantada (Q) iyo radius-ka dusha sare ee Gaussian (r), si liddi ku ah u dhiganta saddexjibbaarka radius-ka wareega adag (R3 ).
b) Goob koronto oo ka baxsan goob adag
Goobo adag waxay leedahay radius R halka dusha sare ee Gaussian ee wareegsan ay leedahay radius r, halkaas oo r > R. Xajmiga wareegga adag uu yahay Q; goobada adag waxay ku jirtaa gudaha goobada Gaussian sidaa darteed korontada ku jirta gudaha goobada Gaussian waa Q.
Goobta korontadu waxay ka soo baxdaa bartamaha kubadda waxayna si toosan ugu gashaa dusha sare ee kubadda si qaacidada qulqulka korontadu ay u noqoto Φ = E A. Qaaciddada sharciga Gauss waa Φ = Q / ε o
Goobta korontada ee masaafada r ka jirta bartamaha wareegga adag waa:
Goobta korantada ee gudaha iyo dibadda qolofka goob godan oo koronto ku shaqeeya oo isku mid ah
Goob godan oo leh gacan R iyo mug V = 4/3 π R 3 , waxay leedahay dallac koronto oo isku mid ah oo qolofkeeda ku yaal oo leh dallac dhan Q. Go'aami xoogga goobta korantada gudaha iyo dibadda qolofka kubbadda.
a) Goob koronto oo ku dhex taal goob godan
Sidaa darteed, goobada godan waxaa lagu gartaa koronto ku dul taal dusha sare ee goobta, halka aysan jirin koronto ku dhex jirta gudaha goobta. Haddii dusha sare ee Gaussian ee la doortay ay tahay mid wareegsan oo goobta Gaussian ay ku jirto goob godan, markaa ma jiro koronto ku dhex jirta goobta Gaussian. Korontadu waa eber, sidaas darteed goobta korontadu sidoo kale waa eber. Sidaa darteed, goobta korontada ee ku jirta goobta godan waa eber.
b) Goob koronto oo ka baxsan goobta godan
Goobta godan waxay leedahay radius R, halka dusha sare ee Gaussian ee la doortay ay tahay ball oo leh radius r, halkaas oo r > R.
Goobta korontada ee ka soo baxda bartamaha kubadda ayaa si toosan ugu dhex gasha dusha sare ee kubadda si qaacidada socodka korontada ay u noqoto Φ = EA = E 4π r 2. Qaaciddada sharciga Gauss waa Φ = Q / ε o.
Goobta korontada ee meel fog ka jirta bartamaha godka godan waa:
Goob koronto oo u dhow silig khafiif ah oo koronto lagu dallacay
Silig khafiif ah oo dhererkiisu aanu dhammaanayn wuxuu sitaa dallac koronto oo isku mid ah oo leh cufnaanta dallacaadda oo ah λ . Daboolka korontada ee fiilada ku yaal waa Q = λl. Go'aami xoogga goobta korantada ee ku wareegsan siligga khafiifka ah.
Dusha sare ee Gaussian waxaa loo doortay inay noqoto dhululubo leh dherer l iyo radius r. Waxaa jira laba nooc oo dusha sare ah, kuwaas oo kala ah dusha wareegsan oo leh radius r oo ku yaal labada daraf ee dhululubada (bedka dusha sare waa .r2) iyo dusha dhululubo leh oo dhererkeedu yahay l (beeggeeda dusha sare waa 2πr l).
Dakhli korontadu waa togan tahay, sidaas darteed goobta korontadu waxay ka soo baxdaa siligga oo ku toosan dusha sare ee tuubada si qulqulka korontadu uu u yeesho qiime ah Φ = EA = E 2πr l . Dhanka kale, goobta korontadu waxay la siman tahay labada daraf ee tuubada qaab wareegsan si qulqulka korontadu uu u yeesho qiime eber ah.
Goobta korontada ee meel fog ka jirta fiilada waa:
