Maqaal ku saabsan Go'aaminta goobta korantada iyadoo la adeegsanayo sharciga Gauss
Goobta korontada iyadoo la adeegsanayo hal dhibic oo dallac ah
Si loo xisaabiyo goobta korantada ee ay soo saarto hal dallac togan, tallaabada ugu horreysa waa in la doorto dusha sare ee Gauss-ka wareegsan oo leh radius r halkaas oo bartamaha kubbadda ay ku taal dallac keliya. Bedka dusha sare ee kubbadda waa 4πr2.
Goobta korontada ee ka soo baxda bartamaha wareegga waxay si toosan ugu gudubtaa dusha sare ee wareegga si qaacidada qulqulka korontada ay u noqoto Φ = E A. Qaaciddada sharciga Gauss waa Φ = Q/ε o
Goobta korontada ee masaafada r u jirta hal dallac waa:
E = goob koronto, k = Joogto Coulomb ah (9 x 10 9 Nm 2 /C 2 ), Q = dallac koronto, r = masaafada u jirta dallacaadda korontada.
Kani waa qaacidada goobta korontada ee ay soo saarto dallacaadda korontada. Qaacidadan waxaa laga soo saari karaa iyadoo la adeegsanayo sharciga Coulomb.
Garoomada korontada gudaha iyo dibadda kubadda adag oo leh koronto isku mid ah oo lagu dallacay
Kubbad adag oo isku mid ah oo si togan loo dallacay waxay leedahay wadarta guud ee dallacaadda Q, mugga V = 4/3 π R 3 cufnaanta dallacaadda ee kubbadda adagna waa ρ = Q/V. Go'aami xoogga goobta korantada ee gudaha kubadda iyo dibadda kubadda.
a) Goobta korantada ee ku jirta kubbadda adag
Kubadda adag ee leh gacanka R, halka dusha sare ee Gauss ee la doortay ay tahay mid wareegsan oo leh gacanka r, halkaas oo r < R. Mugga kubbadda adag uu yahay V mugga kubbadda Gauss-na uu yahay V'.
Kubbadaha Gauss-ka waxaa ku dallaca koronto:
Goobta korontada ee ka soo baxda bartamaha wareegga waxay si toosan ugu gudubtaa dusha sare ee wareegga si qaacidada qulqulka korontada ay u noqoto Φ = E A. Qaaciddada sharciga Gauss waa Φ = Q/ε o
Goobta korantada ee barta ay ku taal masaafada r ee u dhaxaysa bartamaha kubadda adag waa:
Iyada oo ku saleysan qaacidada kore, goobta korantada (E) waxay u dhigantaa dallacaadda korantada (Q) iyo radius-ka dusha sare ee Gauss (r), si liddi ku ah u dhiganta radius-ka kubbadda adag ( R3 )
b) Garoon koronto oo ka baxsan kubadda adag
Kubbad adag waxay leedahay gacanka R halka dusha sare ee Gauss ay tahay mid wareegsan oo leh gacanka r, halkaas oo r > R. Dareeraha kubbadda adag waa Q; kubbadda adag waxay ku jirtaa gudaha kubbadda gauss si dallacaadda korantada ee kubbadda gauss ay u noqoto Q.
Goobta korontadu waxay ka baxdaa bartamaha wareegga waxayna si toosan ugu gudubtaa dusha sare ee wareegga si qaacidada qulqulka korontadu ay u noqoto Φ = E A. Qaaciddada sharciga Gauss waa Φ = Q/ε o
Goobta korontada waxay leedahay masaafada r ee u dhaxaysa bartamaha kubadda adag waa:
Goobta korontada ee gudaha iyo dibaddaba dusha sare ee kubadda godan oo leh koronto isku mid ah oo lagu dallacay
Kubbado godan oo leh gacanka R iyo mugga V = 4/3 π R 3 , oo leh koronto isku mid ah oo si togan loogu dallacay dusha sare oo leh kharash dhan Q. Go'aami xoogga goobta korantada gudaha iyo dibadda dusha sare ee wareegga.
a) Goobta korantada ee ku jirta kubbadda godka ah
Kubbadu waa godan tahay, sidaas darteed dallacaadda korontadu waxay saaran tahay dusha sare ee kubadda, halka gudaha kubadda aysan jirin dallacaad koronto. Haddii dusha sare ee gauss-ka la doortay ay tahay mid wareegsan oo kubbadda gauss-ku ay ku jirto kubbadda godan, ma jiro dallacaad koronto oo gudaha kubadda gauss-ka ku jirta. Dallaca korontadu waa eber, sidaa darteed garoonka korontadu sidoo kale waa eber. Markaa, garoonka korontadu ku jirto kubadda godan waa eber.
b) Garoon koronto oo ka baxsan kubadda godka ah
Kubbadu waa godan tahay iyadoo leh gacanka R, halka dusha sare ee Gauss ee la doortay ay tahay mid wareegsan oo leh gacanka r, halkaas oo r > R.
Goobta korantada ee ka soo baxda bartamaha kubadda ayaa si toosan ugu gudubta dusha sare ee wareegga si qaacidada qulqulka korontada ay u noqoto Φ = EA = E 4π r 2. Qaaciddada sharciga Gauss waa Φ = Q/ε o.
Goobta korantada ee barta ay ku taal masaafada r ee u dhaxaysa bartamaha kubadda godka ah waa:
Goobaha korontada ee u dhow fiilooyinka khafiifka ah ee korontada lagu dallaco
Fiilo khafiif ah waxay leedahay dherer aan dhammaad lahayn, oo ah dallac koronto oo isku mid ah oo leh cufnaanta dallacaadda λ. Dallaca korontada ee fiilada ku taal waa Q = λ l. Go'aami xoogga goobta korantada ee ku wareegsan fiilada khafiifka ah.
Dusha sare ee Gauss waxaa lagu xushaa qaabka dhululubada leh dhererka l iyo radius r. Waxaa jira laba nooc oo dusha sare ah, dusha wareegsan oo leh radius r oo ku yaal labada daraf ee dhululubada ah (bedka dusha sare waa 2πr)2) iyo dusha dhululubo leh dherer l ah (beegga dusha sare waa 2πr l).
Dakhli korontadu waa mid togan, sidaas darteedna goobta korontadu waxay ka baxdaa siligga oo ku toosan dusha sare ee tuubada.
si qulqulka korontadu uu u noqdo Φ = EA = E 2πr l. Taa beddelkeeda, goobta korontadu waxay la siman tahay labada daraf ee tuubada wareegsan si qulqulka korontadu uu eber u noqdo.
Goobta korontada ee masaafada r u jirta fiilada waa:
