Inkundla kagesi ngenxa yokushaja okukodwa
Ukubala insimu kagesi okukhiqizwa yishaja eyodwa enhle, isinyathelo sokuqala ukukhetha ubuso be-Gaussian obuyindilinga be-radius r lapho isikhungo se-sphere sikhona kushaja eyodwa. Indawo yobuso be-sphere ingu-4.r2.
Insimu kagesi ephuma phakathi kwebhola ingena ngokuqonde ngqo ebusweni bebhola ukuze ifomula yokushintshashintsha kukagesi ibe ngu -Φ = E A. Ifomula yomthetho kaGauss ingu-Φ = Q / ε o
Insimu kagesi endaweni ethile ekude ne-r ukusuka ekushajweni okukodwa yile:
Incazelo: E = insimu kagesi, k = okungaguquki kukaCoulomb (9 x 109 I-Nm2/C2), Q = ishaja kagesi, r = ibanga ukusuka ekushajeni kagesi
Lena ifomula yensimu kagesi ekhiqizwa yishaja kagesi . Le fomula ingatholakala kusetshenziswa umthetho kaCoulomb.
Izinkundla zikagesi ngaphakathi nangaphandle i-sphere eqinile eshajelwe ngogesi efanayo
I-sphere eqinile ene-chaji kagesi efanayo noma efanayo ine-chaji ephelele Q, ivolumu V = 4/3 π R 3 kanti ubuningi be-chaji ku-sphere eqinile ngu-ρ = Q/V. Thola amandla ensimu kagesi ngaphakathi kwe-sphere nangaphandle kwe-sphere.
a) Inkundla kagesi ngaphakathi kwebhola eliqinile
I-solid sphere ine-radius R, kuyilapho ubuso be-Gaussian obukhethiwe buyi-sphere ye-radius r, lapho u-r < R. Umthamo we-solid sphere ingu-V kanti umthamo we-Gaussian sphere ingu-V'.
Ishaja kagesi ngaphakathi kwe-Gauss sphere yile:
Insimu kagesi ephuma phakathi nebhola ingena ngokuqondile ebusweni bebhola ukuze ifomula yokushintshashintsha kukagesi ibe Φ = Ifomula yomthetho ka-E A. Gauss ithi Φ = Q / εo
Insimu kagesi esendaweni ekude kakhulu nebanga eliphakathi nendawo ye-solid sphere yile:
Ngokusekelwe kufomula engenhla, insimu kagesi (E) ilingana neshaja kagesi (Q) kanye nerediyasi yobuso beGaussian (r), ilingana ngokuphambene nekhiyubhu yerediyasi yesphere esiqinile (R3 ).
b) Insimu kagesi engaphandle kwendilinga eqinile
I-solid sphere ine-radius R kuyilapho ubuso be-Gaussian obuyindilinga bune-radius r, lapho u-r > R. Ishaja ye-solid sphere ingu-Q; i-solid sphere ingaphakathi kwe-Gaussian sphere ngakho-ke ishaja kagesi ngaphakathi kwe-Gaussian sphere ingu-Q.
Insimu kagesi iphuma enkabeni yebhola bese ingena ngokuqonde ngqo ebusweni bebhola ukuze ifomula yokushintshashintsha kukagesi ibe ngu- Φ = E A. Ifomula yomthetho kaGauss ingu-Φ = Q / ε o
Insimu kagesi ekude r ukusuka enkabeni ye-solid sphere yile:
Insimu kagesi ngaphakathi nangaphandle kwegobolondo lendilinga engenalutho eshajelwe ngogesi efanayo
Imbulunga engenalutho ene-radius R kanye nevolumu V = 4/3 π R 3 , ineshaja kagesi evumayo efanayo egobolondweni layo eneshaja ephelele engu-Q . Thola amandla ensimu kagesi ngaphakathi nangaphandle kwegobolondweni lembulunga.
a) Insimu kagesi ngaphakathi kwendilinga engenalutho
Ngakho-ke imbulunga engenalutho ichazwa yishaja kagesi ebusweni bembulunga, kuyilapho kungekho shaja kagesi ngaphakathi kwembulunga. Uma ubuso beGaussian obukhethiwe buyindilinga futhi imbulunga yeGaussian ingaphakathi kwembulunga engenalutho, khona-ke akukho shaja kagesi ngaphakathi kwembulunga yeGaussian. Ishaja kagesi ingu-zero, ngakho-ke insimu kagesi nayo ingu-zero. Ngakho-ke, insimu kagesi ngaphakathi kwembulunga engenalutho ingu-zero.
b) Insimu kagesi engaphandle kwendilinga engenalutho
I-hollow sphere ine-radius R, kuyilapho ubuso be-Gaussian obukhethiwe buyi-sphere ene-radius r, lapho i-r > R.
Insimu kagesi ephuma enkabeni yebhola ingena ngokuqonde ngqo ebusweni bebhola ukuze ifomula yokushintshashintsha kukagesi ibe ngu -Φ = EA = E 4π r 2. Ifomula yomthetho kaGauss ingu-Φ = Q / ε o.
Insimu kagesi endaweni ethile ebangeni elingu-r ukusuka enkabeni ye-hollow sphere yile:
Inkundla kagesi eduze kwentambo encane eshajelwe ngogesi
Intambo encane enobude obungenamkhawulo ithwala ishaja kagesi elinganayo enobuningi beshaja obungu -λ . Ishaja kagesi entanjeni ingu-Q = λl. Thola amandla ensimu kagesi azungeze intambo encane.
Ubuso beGaussian bukhethwa ukuthi bube yi-cylindrical enobude obungu-l kanye ne-radius r. Kunezinhlobo ezimbili zobuso, okungukuthi ubuso obuyindilinga obunobubanzi obungu-r obutholakala kuzo zombili izinhlangothi zesilinda (indawo yobuso i- .r2) kanye nobuso obuyindilinga obunobude obungu-l (indawo yalo yobuso ingu-2πr l).
Ishaja kagesi ilungile, ngakho-ke insimu kagesi iphuma ocingweni oluqondile ebusweni bepayipi ukuze i-flux kagesi ibe nenani elingu- Φ = EA = E 2πr l . Ngakolunye uhlangothi, insimu kagesi ihambisana nezinhlangothi zombili zepayipi ngesimo esiyindilinga ukuze i-flux kagesi ibe nenani elingu-zero.
Insimu kagesi endaweni ethile ekude nentambo yile:
