Umthetho kaGauss

Isihloko mayelana nomthetho kaGauss

Mayelana Umthetho kaCoulomb, kufundwe amandla aphakathi kwamacala kagesi. Ekubuyekezweni kwensimu kagesi, kuxoxwe ngolunye uhlobo lomthetho kaCoulomb, oluvezwa yi-equation 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 kwamacala kagesi kanye nezinkundla zikagesi. Umthetho kaGauss wakhiwa ngu UCarl Friedrich Gauss (1777-1855), isazi sesayensi yezibalo kanye nesazi sezibalo saseJalimane.

Insimu kagesi ekhiqizwa yinye noma eziningana zeshaja kagesi ingabalwa kalula kusetshenziswa umthetho kaCoulomb, kodwa ukubala kuba nzima kakhulu uma okunqunywayo kuyinsimu kagesi ekhiqizwa ukusatshalaliswa kweshaja kagesi. Umthetho kaGauss unikeza indlela yemvelo yokunquma insimu kagesi ekhiqizwa ukusatshalaliswa kweshaja kagesi. Ngaphezu kwalokho, uma insimu kagesi yaziwa, umthetho kaGauss ungasetshenziswa ukunquma ukusatshalaliswa kweshaja kagesi ezikhiqiza insimu kagesi. Okulandelayo kubuyekezwa umqondo kanye nesilinganiso somthetho kaGauss.

Buyekeza ishaja kagesi elihle phakathi nebhola njengoba kuboniswe esithombeni ohlangothini. Uma irediyasi yesiyingi ingu-R, khona-ke amandla ensimu kagesi akhiqizwa yishaja kulo lonke isiyingi angu-E = k Q/R² futhi indawo engaphezulu yesiyingi ingu-A = 4 π r².

Ukuze ubone ngeso lengqondo insimu kagesi, kudwetshwe imigqa yensimu kagesi, kodwa esithombeni, kumelelwe imigqa yensimu kagesi emine kuphela. Ishaja kagesi ilungile, ngakho-ke imigqa yensimu kagesi idwetshwe kusukela enkabeni yebhola lapho kutholakala khona ishaja kagesi,

futhi umugqa ngamunye wensimu kagesi uqonde ngqo ebusweni bebhola elidlula kulo. Uma ukude kakhulu nokushaja kukagesi, insimu kagesi iba ncane kangangokuthi ibanga eliphakathi kwemigqa yensimu kagesi nalo likude kakhulu.

Ama-flux kagesi angena ebusweni be-sphere abalwa kusetshenziswa ifomula elandelayo:

F = ukugeleza kukagesi, Q = ukushaja kukagesi, k = 9 x 10⁹ N m²/C², ε_o (imvume yokuhlanza) = 8.85 x 10^-12 C²/N m², π = 3.14.

Ngokusekelwe kulesi sibalo, kuphethwa ngokuthi i-electric flux (F) edlula endaweni eyindilinga ilingana nenani lokushaja kagesi (Q) okukuyo futhi ayixhomekile ku-radius yebhola (R).

Isithombe esiseceleni sibonisa izindawo ezine ezivaliwe lapho kukhona ishaja kagesi Q. Ubuso bokuqala buyindilinga, kanti obunye ubuso bunesimo esingajwayelekile. Ishaja kagesi ilungile ukuze imigqa yensimu kagesi emelelwe yimicibisholo emine ikhishwe ekushajeni. Imigqa yensimu kagesi emine idlula ebusweni obuyindilinga, kanti ezinye izindawo ezinesimo esingajwayelekile nazo zidlula kule migqa emine.

Ekubuyekezweni kokuhamba kukagesi, kuthiwa ukuhamba kukagesi kuyimigqa yensimu kagesi engena endaweni ethile.

Imigqa yensimu kagesi edlula ezindaweni ezine iyafana ukuze ukugeleza kukagesi kuzo zonke izindawo ezine kube nobukhulu obufanayo. Ukugeleza kukagesi okudlula endaweni eyindilinga yi-Φ = Q/ε_o ukuze uketshezi lukagesi olungena kwezinye izindawo ezinezimo ezingajwayelekile lube nobukhulu obufanayo, okungukuthi Φ = Q/ε_o.

Ngokusekelwe kule ncazelo, kungaphethwa ngokuthi ukugeleza kukagesi okungena endaweni evaliwe lapho kukhona khona ishaja kagesi, akuxhomekile esimweni sobuso futhi ubukhulu bungu-Φ = 4 π k Q = Q/ε_o.

Isithombe esiseceleni sibonisa amashaja amabili kagesi angaphakathi kwendawo evaliwe. Q₁ kanye no-Q₂ zinhle kangangokuthi uma zinjalo uma idonswa, ishaja ngayinye inomugqa wensimu kagesi ophuma ngaphakathi kobuso. I-total electric flux yinani eliphelele lemigqa yensimu kagesi ephuma ebusweni obuvaliwe. Ngoba imigqa yensimu kagesi yeshaja Q₁ zilingana nokushintsha kukagesi Φ = Q₁/e_o kanye nemigqa yensimu kagesi yeshaja Q₂

zifana nokushintshashintsha kukagesi Φ = Q₂/e_o, 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 leshaja kagesi endaweni evaliwe. Lesi sitatimende siwumthetho kaGauss. Ngokwezibalo:

Φ_net = 1/ε_o (Q_inethi) ———- Isilinganiso somthetho kaGauss

I-Q net iyinani eliphelele leshaja kagesi elingaphakathi kwendawo evaliwe. Uma kukhona ishaja kagesi ngaphandle kwendawo evaliwe, ishaja ayibalwa ngoba i-flux kagesi ekhiqizayo ingu-zero. I-flux kagesi ingu-zero ngoba imigqa yensimu kagesi evela ekushajeni ingena endaweni evaliwe bese iphuma futhi.

Ubuso obuvaliwe bomthetho kaGauss buwubuso obucatshangwayo obuvezwayo ukuze kubalwe ukugeleza kukagesi okubangelwa ukushaja kukagesi.

Umthetho kaGauss ungasetshenziswa ukunquma insimu kagesi uma ukusatshalaliswa kweshaja kagesi kuyaziwa, noma ungasetshenziswa futhi ukunquma ukusatshalaliswa kweshaja kagesi uma insimu kagesi iyaziwa. Ukusetshenziswa komthetho kaGauss ukuxazulula imibuzo ehlukahlukene kuchazwe esihlokweni mayelana nokusetshenziswa komthetho kaGauss.