Umthetho kaGauss

Okuqukethwe Umthetho kaCoulomb amandla aphakathi kwamacala kagesi ahlolisisiwe. Ekubuyekezweni kwe- insimu kagesi Kuxoxwe ngolunye uhlobo lomthetho kaCoulomb, oluvezwa ngesibalo u-F = q E, lapho u-F engamandla kagesi, u-q engamandla kagesi, kanti u-E engamandla kagesi. Kungashiwo ukuthi umthetho kaCoulomb ungumthetho wefiziksi ochaza ubudlelwano phakathi kwe-electric charge (q) kanye ne-electric field (E).

Umthetho kaGauss ungomunye umthetho wefiziksi ochaza ubudlelwano phakathi kokushaja kagesi kanye nensimu kagesi. Umthetho kaGauss waklanywa nguCarl Friedrich Gauss (1777–1855), isazi sesayensi yezibalo saseJalimane kanye nesazi sezibalo. Insimu kagesi ekhiqizwa yishaji kagesi eyodwa noma ngaphezulu ingabalwa kalula kusetshenziswa umthetho kaCoulomb, kodwa ukubala kuba nzima kakhulu lapho kunqunywa insimu kagesi ekhiqizwa ukusatshalaliswa kwamacala kagesi. Umthetho kaGauss unikeza indlela elula yokunquma insimu kagesi ekhiqizwa ukusatshalaliswa kwamacala kagesi. Ngaphezu kwalokho, uma insimu kagesi yaziwa, umthetho kaGauss ungasetshenziswa ukunquma ukusatshalaliswa kwamacala kagesi akhiqiza insimu kagesi. Okulandelayo kuxoxa ngemiqondo namafomula. Umthetho kaGauss.

Cabanga ngokushaja kagesi okuhle phakathi nebhola njengoba kuboniswe esithombeni ohlangothini. Uma irediyasi yebhola ingu-R khona-ke amandla ensimu kagesi akhiqizwa ukushaja ebusweni bebhola ngu-E = k Q / R² futhi indawo engaphezulu yesiyingi ingu-A = 4 π R²Ukuze ubone ngeso lengqondo insimu kagesi, kudwetshwa imigqa yensimu kagesi, kodwa isithombe sibonisa ezine kuphela. Njengoba ishaja kagesi ilungile, imigqa yensimu kagesi idwetshwa ivela enkabeni yendilinga lapho kutholakala khona ishaja kagesi, futhi umugqa ngamunye wensimu kagesi uqonde ngqo ebusweni bendilinga edlula kuyo. Uma uqhelelene neshaja kagesi, insimu kagesi iba ncane, ngakho ibanga phakathi kwemigqa yensimu kagesi nalo liyakhula.

Uketshezi lukagesi olungena ebusweni be-sphere lubalwa kusetshenziswa ifomula elandelayo:

Imininingwane: Φ = ukugeleza kukagesi, Q = ukushaja kukagesi, k = 9 x 10⁹ N m²/C², ε_o (ukuvumela isikhala esikhululekile) = 8,85 x 10^-12 C²/N m², π = 3,14. Ngokusekelwe kulesi sibalo kuphethwa ngokuthi ukugeleza kukagesi (Φ) edlula endaweni eyindilinga, ilingana nenani lokushaja kagesi (Q) okukuyo futhi ayixhomekile erediyasini yendilinga (R).

Isithombe ngakwesokudla sibonisa izindawo ezine ezivaliwe eziqukethe ishaja kagesi Q. Ubuso bokuqala buyindilinga kanti ezinye izindawo zinezimo ezingajwayelekile. Ishaja kagesi ilungile ukuze imigqa yensimu kagesi emelelwe yimicibisholo emine idwetshwe kusukela ekushajeni. Imigqa emine yensimu kagesi idlula ebusweni obuyindilinga kanye nobuso obunesimo esingajwayelekile. Ekubuyekezweni okuphathelene ukugeleza kukagesi kuthiwa Ugesi ogelezayo yimigqa yensimu kagesi engena endaweni ethile.Imigqa yensimu kagesi edlula kuzo zonke izindawo ezine iyafana ukuze ukugeleza kukagesi kuzo zonke izindawo ezine kube nenani elifanayo. Ukugeleza kukagesi okudlula endaweni eyindilinga kufana no-Φ = Q/ε_o , ukuze uketshezi lukagesi olungena kwezinye izindawo ezinezimo ezingajwayelekile lube nenani elifanayo, okungukuthi Φ = Q/ε_oNgokusekelwe kule ncazelo, kungaphethwa ngokuthi ukugeleza kukagesi okungena endaweni evaliwe equkethe ishaja kagesi akuxhomekile ekubunjweni kwendawo futhi ubukhulu bayo bungu-Φ = 4 π k Q = Q/ε_o.

Isithombe ngakwesokudla sibonisa amashaja kagesi amabili ngaphakathi kwendawo evaliwe. Ishaja Q₁ kanye no-Q₂ okuhle kangangokuthi uma kuboniswe, ishaja ngayinye inomugqa wensimu kagesi ophuma ngaphakathi kobuso. Ingqikithi yokushintsha kukagesi iyinani eliphelele lemigqa yensimu kagesi ephuma ebusweni obuvaliwe. Ngoba imigqa yensimu kagesi yokushaja Q₁ okulingana nokushintsha kukagesi kwe-Φ = Q₁/e_o kanye nemigqa kagesi yokushaja Q₂ okulingana nokushintsha kukagesi kwe-Φ = Q₂/e_o khona-ke inani eliphelele lemigqa kagesi lilingana no-Q₁/e_o +Q₂/e_o = 1/ε_o (Q₁ +Q₂).

Ngokusekelwe kule ncazelo, kungaphethwa ngokuthi i-flux kagesi iyonke ingu-1/ε_o kuphinda kabili inani lokushaja kukagesi endaweni evaliwe. Lesi sitatimende siwumthetho kaGauss. Ngokwezibalo:

Φ_Inani = 1/ε_o (Q_Inani) ———- Isilinganiso somthetho kaGauss

Ingqikithi ye-Q iyinani eliphelele leshaja kagesi ngaphakathi kwendawo evaliwe. Uma kukhona ishaja kagesi ngaphandle kwendawo evaliwe, khona-ke ishaja ayicatshangelwa ngoba i-flux kagesi ekhiqizayo ingu-zero. I-flux kagesi ingu-zero ngoba imigqa yensimu kagesi evela ekushajeni ingena endaweni evaliwe bese iphuma futhi ukuze i-flux ephumelayo ibe ngu-zero. Indawo evaliwe emthethweni kaGauss iyindawo ecatshangwayo eyethulwa ukubala i-flux kagesi ekhiqizwa yizindleko zikagesi. Ngamanye amazwi, izindleko zikagesi akudingeki zibe ngaphakathi kwendawo evaliwe yangempela. Umthetho kaGauss ungasetshenziswa ukunquma insimu kagesi uma ukusatshalaliswa kwamacala kagesi kwaziwa noma kungasetshenziswa futhi ukunquma ukusatshalaliswa kwamacala kagesi uma insimu kagesi yaziwa. Ukusetshenziswa komthetho kaGauss ukuxazulula izinkinga ezahlukahlukene kuchazwe esihlokweni esinesihloko esithi thola insimu kagesi usebenzisa umthetho kaGauss.