Tsab xov xwm hais txog Kev Txheeb Xyuas Lub Zog Hluav Taws Xob Siv Txoj Cai Gauss
Lub zog hluav taws xob los ntawm ib qho chaw them nqi
Yuav kom xam tau lub teb hluav taws xob uas tsim los ntawm ib qho nqi zoo, thawj kauj ruam yog xaiv qhov chaw ntawm lub pob kheej kheej Gauss nrog lub vojvoog r qhov twg qhov chaw nruab nrab ntawm lub pob kheej kheej yog nyob rau ntawm ib qho nqi. Lub cheeb tsam ntawm lub pob yog 4πr2.
Lub teb hluav taws xob uas tawm hauv nruab nrab ntawm lub pob zeb nkag mus rau hauv qhov chaw perpendicular rau qhov chaw ntawm lub pob zeb kom cov mis ntawm cov hluav taws xob flux yog Φ = E A. Cov mis ntawm Gauss txoj cai yog Φ = Q/ε o
Lub teb hluav taws xob ntawm qhov deb ntawm r ntawm ib qho nqi yog:
E = lub teb hluav taws xob, k = Coulomb tas li (9 x 10 9 Nm 2 /C 2 ), Q = nqi hluav taws xob, r = qhov deb ntawm tus nqi hluav taws xob.
Qhov no yog tus qauv ntawm lub zog hluav taws xob uas tsim los ntawm lub zog hluav taws xob. Tus qauv no tuaj yeem muab tau los ntawm kev siv Coulomb txoj cai.
Cov teb hluav taws xob sab hauv thiab sab nraum lub pob khoom khov kho nrog cov hluav taws xob sib npaug
Ib lub pob khoom khov uas muaj cov nqi hluav taws xob zoo sib xws muaj tag nrho cov nqi hluav taws xob ntawm Q, ntim V = 4/3 π R 3 thiab qhov ceev ntawm cov nqi hluav taws xob hauv lub pob khoom khov yog ρ = Q/V. Txheeb xyuas lub zog hluav taws xob hauv lub pob thiab sab nraum lub pob.
a) Lub zog hluav taws xob hauv lub pob khov kho
Lub pob khoom khov kho nrog lub vojvoog ntawm R, thaum qhov chaw Gauss xaiv yog lub vojvoog kheej kheej nrog lub vojvoog r, qhov twg r < R. Lub ntim ntawm lub pob khoom khov kho yog V thiab lub ntim ntawm Gauss lub voos kheej kheej yog V'.
Lub zog hluav taws xob hauv Gauss pob yog:
Lub teb hluav taws xob uas tawm hauv nruab nrab ntawm lub pob zeb nkag mus rau hauv qhov chaw perpendicular rau qhov chaw ntawm lub pob zeb kom cov mis ntawm cov hluav taws xob flux yog Φ = E A. Cov mis rau Gauss txoj cai yog Φ = Q/ε o
Lub teb hluav taws xob ntawm qhov chaw nrog qhov deb ntawm r los ntawm qhov chaw ntawm lub pob khoom khov kho yog:
Raws li cov mis saum toj no, lub teb hluav taws xob (E) yog proportional rau lub zog hluav taws xob (Q) thiab lub vojvoog ntawm Gauss nto (r), inversely proportional rau lub vojvoog ntawm lub pob khoom khov ( R3 )
b) Lub zog hluav taws xob sab nraum lub pob khov kho
Ib lub pob khov kho muaj lub vojvoog ntawm R thaum lub ntsej muag Gauss yog kheej kheej nrog lub vojvoog r, qhov twg r > R. Lub pob khov kho them yog Q; lub pob khov kho nyob hauv lub pob gauss kom lub zog hluav taws xob hauv lub pob gauss yog Q.
Lub teb hluav taws xob tawm hauv nruab nrab ntawm lub pob thiab nkag mus rau hauv qhov chaw ntawm lub pob kom cov mis ntawm cov hluav taws xob flux yog Φ = E A. Cov mis ntawm Gauss txoj cai yog Φ = Q / ε o
Lub zog hluav taws xob muaj qhov deb ntawm r los ntawm qhov chaw ntawm lub pob khov kho yog:
Lub teb hluav taws xob sab hauv thiab sab nraum lub pob hollow nrog cov homogeneous electrically them
Cov pob khoob uas muaj lub vojvoog ntawm R thiab ntim V = 4/3 π R3 , nrog rau cov hluav taws xob zoo sib xws ntawm qhov chaw nrog tag nrho cov nqi Q. Txheeb xyuas lub zog hluav taws xob sab hauv thiab sab nraud ntawm qhov chaw ntawm lub pob.
a) Lub zog hluav taws xob hauv lub pob hollow
Lub pob yog khoob, yog li ntawd lub zog hluav taws xob nyob rau ntawm qhov chaw ntawm lub pob, thaum sab hauv ntawm lub pob tsis muaj zog hluav taws xob. Yog tias qhov chaw gauss xaiv yog lub pob kheej kheej thiab lub pob gauss nyob hauv lub pob khoob, tsis muaj zog hluav taws xob hauv lub pob gauss. Zog hluav taws xob yog xoom, yog li lub teb hluav taws xob kuj yog xoom. Yog li, lub teb hluav taws xob hauv lub pob khoob yog xoom.
b) Lub teb hluav taws xob sab nraum lub pob khoob
Lub pob yog hollow nrog lub vojvoog ntawm R, thaum qhov chaw Gauss xaiv yog spherical nrog lub vojvoog ntawm r, qhov twg r > R.
Lub teb hluav taws xob uas tawm hauv nruab nrab ntawm lub pob nkag mus rau hauv qhov chaw perpendicular rau qhov chaw ntawm lub pob kom cov mis ntawm hluav taws xob flux yog Φ = EA = E 4π r 2. Cov mis ntawm Gauss txoj cai yog Φ = Q/ε o.
Lub teb hluav taws xob ntawm qhov chaw nrog qhov deb ntawm r los ntawm qhov chaw ntawm lub pob hollow yog:
Cov teb hluav taws xob nyob ze ntawm cov xov hlau nyias nyias uas them hluav taws xob
Ib txoj xov hlau nyias muaj qhov ntev tsis kawg, muaj hluav taws xob sib npaug zoo nrog qhov ceev ntawm hluav taws xob λ. Lub zog hluav taws xob ntawm txoj xov hlau yog Q = λ l. Txheeb xyuas lub zog hluav taws xob nyob ib puag ncig txoj xov hlau nyias.
Gauss nto yog xaiv nrog daim ntawv ntawm cov thooj voos kheej kheej nrog ntev l thiab radius r. Muaj ob hom ntawm cov nto, ib qho puag ncig nto nrog radius r nyob ntawm ob qho kawg cylindrical (qhov chaw nto yog 2πr2) thiab ib qho chaw cylindrical nrog qhov ntev ntawm l (qhov chaw ntawm qhov chaw yog 2πr l).
Lub nqi hluav taws xob yog qhov zoo, thiab yog li ntawd lub teb hluav taws xob tawm ntawm cov hlau perpendicular rau qhov chaw ntawm lub raj.
yog li ntawd cov hluav taws xob flux yog Φ = EA = E 2πr l. Hloov chaw, lub teb hluav taws xob yog sib luag rau ob qho kawg ntawm lub raj voj voog kom cov hluav taws xob flux yog xoom.
Lub teb hluav taws xob ntawm qhov deb ntawm r ntawm cov hlau yog:
