Gauss theorem thiab cov cai hais txog superposition

Gauss theorem yog ib tug ntawm cov yuav tsum muaj kev cai lij choj ntawm electrodynamics, yog structurally muaj nyob rau hauv lub system ntawm sib npaug yog tseem yog ib qho ntawm cov poj tus paub txog - Maxwell. Nws qhia txoj kev sib raug ntawm cov tsev nro ob electrostatic thiab electrodynamic teb txuas rau thoob plaws qhov chaw ntawm lub kaw hom. Lub npe Karl Gauss suab nyob rau hauv lub scientific ntiaj teb no tsis muaj tsawg nrov nrov tshaj, piv txwv li, Archimedes, Newton thiab Lomonosov. Nyob rau hauv physics, astronomy thiab lej yuav pom tsis dhau ntau qhov chaw, txoj kev loj hlob ntawm cov uas yog lub feem ntau ncaj qha txoj kev tsis pab qhov ci ntsa iab German tus paub txog.

Gauss theorem tau ua si ib tug tseem ceeb luag hauj lwm nyob rau hauv txoj kev kawm thiab kev nkag siab txog qhov ntawm electromagnetism. By thiab loj nws tau ua ib tug zoo ntawm generalization thiab rau ib co raws li tus txhais lus los ntawm tus naas ej Coulomb txoj kev cai. Qhov no yog cov ntaub ntawv, tsis yog li ntawd tsawg nyob rau hauv science hais tias cov tib phenomenon yuav tau piav thiab formulated nyob rau hauv ntau txoj kev. Tab sis Gauss theorem tsis tsuas tau cov tswv yim tseem ceeb thiab ua daim ntawv thov, nws pab mus saib nyob rau lub zoo-paub cov kev cai ntawm qhov nyob rau hauv ib tug me ntsis txawv foundations.

Nyob rau hauv ib co txoj kev uas nws tau pab rau ib tug neeg pej xeem nrog txhob nyob rau hauv science, tso lub hauv paus ntawm niaj hnub paub nyob rau hauv lub teb ntawm electromagnetism. Yog li ntawd yog dab tsi yog ib tug Gauss theorem thiab dab tsi yog nws ua daim ntawv thov? Yog hais tias koj noj ib ob peb ntawm zoo li qub point nqi, ces los so lawv particle yuav attracted los yog repelled nrog ib tug dag zog yuam uas yog sib npaug zos rau cov algebraic sum ntawm qhov tseem ceeb ntawm tag nrho cov ntsiab ntawm lub cev. Yog li tag nrho cov chav nro teb tsim raws li ib tug ntawm xws li kev sis raug zoo yog lub sum ntawm nws cov neeg lub Cheebtsam. Qhov no kev sib raug zoo los ua lug paub li tus superposition hauv paus ntsiab lus, uas kom meej piav qhia txog tej system tsim los ntawm lwm haiv neeg nqi, tsis hais ntawm tag nrho cov.

Txawm li cas los, thaum zoo li no hais ntau ntau li, tus zaum thawj nyob rau hauv cov lus teb muaj ib co teeb meem uas tsis tau daws siv Coulomb tus Law. Nws tau pab los mus kov yeej lawv Gauss theorem rau lub magnetic teb, uas, li cas los xij, yog siv tau rau tej nqi fais tshuab muaj ib tug zuj zus lawm voltage proportional rau r ^-2. Nws essence yog hais tias ib tug arbitrary tus naj npawb ntawm cov nqi, yog surrounded los ntawm ib tug qhov chaw kaw, yuav muaj ib tug tag nrho flux ntawm kev siv sib npaug zos rau tag nrho cov nqi ntawm cov hluav taws xob peev xwm ntawm txhua taw tes ntawm lub dav hlau. Nyob rau tib lub sij hawm lub hauv paus ntsiab lus ntawm kev sis raug zoo ntawm lub ntsiab tsis coj mus rau hauv tus account, uas zoo heev simplifies cov lus teb. Yog li, qhov no theorem ua kom peb los mus laij lub teb txawm nrog ib tug infinite tus naj npawb ntawm muaj ntawm hluav taws xob xwb.

Txawm li cas los, nyob rau hauv kev muaj tiag qhov no yog tsuas tau nyob rau hauv tej rooj plaub, lawv symmetrical arrangement, thaum muaj ib tug yooj yim nto los ntawm kev uas lub hwj chim yog yooj yim payment thiab cov khiav muaj zog. Piv txwv li, ib txoj kev kuaj xwb pov tseg nyob rau hauv lub conductive lub cev ntawm kheej kheej zoo lawm, yuav tsis muaj lub slightest quab yuam kev ua raws li qhia teb nyob rau ntawd yog pes tsawg. Muaj peev xwm mus extrude nyob ntawm tej los ntawm ib tug ntau yam ntawm hluav taws xob field vim thiaj tau tuaj mus rau lub xub ntiag ntawm cov them nyiaj nqa. Nyob rau hauv cov hlau, lub electrons ua no muaj nuj nqi. Tej nta tam sim no dav siv nyob rau hauv lub kos duab rau kom muaj ntau spatial cheeb tsam nyob rau hauv uas muaj yog tsis muaj hluav taws xob field. Cov phenomena yog zoo piav Gauss theorem rau dielectrics uas nws hwj lub system ntawm elementary particle yog txo mus rau lub polarization ntawm lawv cov nqi.

Yuav kom tsim zoo li no los, nws yog txaus rau puag khawm ib tug tej yam cheeb tsam ntawm lub nro ntawm cov hlau shielding daim phiaj. Yog li ntawd tiv thaiv los ntawm cov teebmeem ntawm hluav taws xob teb yog rhiab precision seev thiab tib neeg.