Isihloko mayelana nokunquma insimu kagesi kusetshenziswa umthetho weGauss
Insimu kagesi ngeshaja yephuzu elilodwa
Ukuze ubale insimu kagesi ekhiqizwa yishaja eyodwa enhle, isinyathelo sokuqala ukukhetha ubuso be-Gauss obuyindilinga obune-radius r lapho isikhungo se-sphere sikhona ekushajeni okukodwa. Indawo engaphezulu yebhola ingu-4πr2.
Insimu kagesi ephuma enkabeni yendilinga ingena iqonde phezulu kwendilinga ukuze ifomula yokushintshashintsha kukagesi ibe ngu-Φ = E A. Ifomula yomthetho kaGauss ingu-Φ = Q/ε o
Insimu kagesi ebangeni lika-r ukusuka ekushajweni okukodwa yile:
E = insimu kagesi, k = i-Coulomb constant (9 x 10 9 Nm 2 /C 2 ), Q = ishaja kagesi, r = ibanga ukusuka ekushajeni kagesi.
Lena ifomula yensimu kagesi ekhiqizwa yishaja kagesi. Le fomula ingatholakala kusetshenziswa umthetho kaCoulomb.
Amasimu kagesi ngaphakathi nangaphandle kwebhola eliqinile elinogesi ofanayo oshajelwe
Ibhola eliqinile elishajwe kahle elinokulingana linomshaja ophelele ongu-Q, ivolumu V = 4/3 π R 3 kanti ubuningi bomshaja ebholeni eliqinile ngu-ρ = Q/V. Thola amandla ensimu kagesi ngaphakathi kwebhola nangaphandle kwebhola.
a) Insimu kagesi ebholeni eliqinile
Ibhola eliqinile elinerediyasi ka-R, kuyilapho ubuso beGauss obukhethiwe buyindilinga enerediyasi r, lapho u-r < R. Ivolumu yebhola eliqinile ingu-V kanti ivolumu yesphere sikaGauss ingu-V'.
Ukushaja kukagesi kumabhola eGauss yilokhu:
Insimu kagesi ephuma enkabeni yendilinga ingena iqonde phezulu kwendilinga ukuze ifomula yokushintshashintsha kukagesi ibe ngu-Φ = E A. Ifomula yomthetho kaGauss ingu-Φ = Q/ε o
Insimu kagesi ephuzwini elinebanga lika-r ukusuka enkabeni yebhola eliqinile yile:
Ngokusekelwe kufomula engenhla, insimu kagesi (E) ilingana neshaja kagesi (Q) kanye nerediyasi yobuso beGauss (r), ilingana ngokuphambene nerediyasi yebhola eliqinile ( R3 )
b) Inkundla kagesi ngaphandle kwebhola eliqinile
Ibhola eliqinile linobubanzi be-R kuyilapho ubuso be-Gauss buyindilinga obune-radius r, lapho u-r > R. Ishaja yebhola eliqinile ingu-Q; ibhola eliqinile lingaphakathi kwebhola le-gauss ukuze ishaja kagesi ebholeni le-gauss ibe ngu-Q.
Insimu kagesi iphuma enkabeni yendilinga futhi ingena ngokuqonde ngqo ebusweni obuyindilinga ukuze ifomula yokushintshashintsha kukagesi ibe ngu-Φ = E A. Ifomula yomthetho kaGauss ingu-Φ = Q/ε o
Insimu kagesi inebanga lika-r ukusuka enkabeni yebhola eliqinile:
Insimu kagesi ngaphakathi nangaphandle kwendawo yebhola engenalutho ene-homogeneous kagesi eshajelwe
Amabhola angenalutho ane-radius ka-R kanye nevolumu V = 4/3 π R 3 , ane-homogeneous positive positive powered kagesi ebusweni kanye ne-total charge Q. Thola amandla ensimu kagesi ngaphakathi nangaphandle kobuso be-sphere.
a) Insimu kagesi ebholeni elingenalutho
Ibhola liyimbobo, ngakho-ke ishaja kagesi iphezu kwebhola, kanti ngaphakathi kwebhola akukho ishaja kagesi. Uma ubuso be-gauss obukhethiwe buyindilinga futhi ibhola le-gauss lingaphakathi kwebhola eliyimbobo, akukho ishaja kagesi ngaphakathi kwebhola le-gauss. Ishaja kagesi ingu-zero, ngakho-ke insimu kagesi nayo ingu-zero. Ngakho-ke, insimu kagesi engaphakathi kwebhola eliyimbobo ingu-zero.
b) Inkundla kagesi engaphandle kwebhola elingenalutho
Ibhola liyimbobo nge-radius ka-R, kuyilapho ubuso be-Gauss obukhethiwe buyindilinga nge-radius ka-r, lapho u-r > R.
Insimu kagesi ephuma enkabeni yebhola ingena iqonde phezulu kwendilinga ukuze ifomula yokushintshashintsha kukagesi ibe ngu-Φ = EA = E 4π r 2 . Ifomula yomthetho kaGauss ingu-Φ = Q/ε o.
Insimu kagesi ephuzwini elinebanga lika-r ukusuka enkabeni yebhola elingenalutho yile:
Izinkundla zikagesi eduze kwezintambo ezincane ezishajwe ngogesi
Intambo encane inobude obungenamkhawulo, ishaja kagesi efanayo kahle enobuningi beshaja λ. Ishaja kagesi entanjeni ingu-Q = λ l. Thola amandla ensimu kagesi azungeze intambo encane.
Ubuso beGauss bukhethwa ngesimo samasilinda anobude obungu-l kanye nobubanzi obungu-r. Kunezinhlobo ezimbili zezindawo, ubuso obuyindilinga obunobubanzi obungu-r obutholakala kuzo zombili izinhlangothi zesilinda (indawo yobuso ingu-2πr2) kanye nobuso obuyindilinga obunobude obungu-l (indawo yobuso ingu-2πr l).
Ishaja kagesi ilungile, ngakho-ke insimu kagesi iphuma ngentambo iqonde phezulu kwepayipi.
ukuze i-electric flux ibe ngu-Φ = EA = E 2πr l. Esikhundleni salokho, insimu kagesi ihambisana nezinhlangothi ezimbili zepayipi eliyindilinga ukuze i-electric flux ibe yi-zero.
Insimu kagesi ebangeni lika-r ukusuka ku-wire yile:
