Ita theorem yeGauss uye iyo inonyanya kukosha

Gauss's theorem ndiyo imwe yemitemo inokosha ye electrodynamics, yakarongeka mumasangano ekuenzanisa kweimwe nyanzvi yezvemasayendisiti, Maxwell. Inoratidzira kubatana pakati pemafuta emagetsi emagetsi ose emagetsi uye electrodynamic achipfuura nepasi pevharo yakavharwa. Zita raKarl Gauss rinonzwika munyika yesayenzi kwete zvishoma kudanidzira kupfuura, somuenzaniso, Archimedes, Newton kana Lomonosov. Mufizikiki, nyeredzi uye masvomhu, hazvirevi kuti zvikawanda zvakadai zvinowanikwa, pakubudirira kweruzivo rwechiGermany anonyanya kushandisika asina kubatsira zvakananga.

Inotori yeGauss yakaita basa rinokosha mukudzidza uye kunzwisisa kwechimiro che electromagnetism. Kazhinji, rava rudzi rwechimiro uye, pane imwe nzvimbo, kududzirwa kwemitemo yakakurumbira yaCoulomb. Izvi ndezvakaitika, zvisingawanzoitiki musayenzi, kana chiitiko ichocho chinogona kurondedzerwa uye kuumbwa nenzira dzakasiyana. Asi dzidziso yeGauss haina kungowana kukosha kwekubatsira nekushanda kwekushandisa, yakabatsira kutarisa mitemo inozivikanwa yezvisikwa nenzira yakasiyana.

Mune dzimwe nzira, zvakabatsira pakubudirira kukuru mune sayenzi, kuisa nheyo yezivo yemazuva ano mumunda we electromagnetism. Saka chii chinonzi Gauss theorem uye ndeipi inoshanda yaro? Kana tikatora mapeji maviri ekutengesa, chidimbu chakaunzwa kwavari chichakwezva kana kupindurwa nesimba rinenge rakaenzana ne algebraic sum yekukura kwezvinhu zvose zvehutano. Panguva imwecheteyo, kuwedzera kwemazana ekugadzirisa munda wakaumbwa semugumisiro wekubatana uku kuchave kuwandisa kwezvikamu zvayo. Ihu hukama hwave huchinyatsozivikanwa sehutano hwepamusoro, izvo zvinoita kuti zvikwanise kunyatsorondedzera chero sarudzo yakagadzirwa ne-multi-vector mashandiro, pasinei nenhamba yavo yose.

Zvisinei, kana pane zvakawanda zvakadaro, masayendisiti pakutanga aive nematambudziko muhuwandu, izvo zvisingagoni kugadziriswa uchishandisa mutemo weCoulomb. Kuti uzvikunde, iyo inonzi Gauss theorem ye magnetic field yakabatsirwa, iyo, zvisinei, iyo yakakosha kune chero masimba emagariro ezvimhosva ane kupera kwekukanda kuenzana ne r ^-2 . Chinokosha chayo chinonyangadza kusvika pakuti kunyanya kwezvikwereti zvakapoteredzwa nevhavha yepamusoro kuchava nehuwandu hwekukura kwakakwana kwakaenzana nehuwandu hwehuwandu hwemagetsi emagetsi ega imwe neimwe yendege inopiwa. Muchiitiko ichi, mitemo yekubatana pakati pezvikamu muhuwandu haigamuchirwi, iyo inonyatsoita kuti kuverenga kuve nyore. Nokudaro, iyi myorem inoita kuti zvikwanise kuverenga munda kunyange nenhamba isingaperi yevatakuri vemotokari.

Ichokwadi, chaizvoizvo izvi zvinokwanisika chete mune zvimwe zviitiko zvehutano hwavo hwakasiyana, apo pane nzvimbo yakakodzera iyo simba uye simba rekuyerera zvinogona kuverengwa nyore nyore. Semuenzaniso, mutero wekuedzwa unoiswa mukati memutumbi unofambisa muviri haugoni kuwana simba shoma, sezvo simba remunda riri zero. Iko kukwanisa kwevatungamiri kukura kunze kwemasimba akasiyana-siyana emagetsi kunotsanangurwa chete nekuvapo kwevanotakura vatakuri mavari. Muzvinhu zvesimbi, basa iri rinoshandiswa nema electrons. Zvinhu zvakadaro zvakanyanya kushandiswa muunyanzvi kuti dzigadzire nzvimbo dzakasiyana-siyana umo magetsi emagetsi asingaiti. Izvi zvinoshamisa zvinotsanangura zvakananga neGauss theorem ye dielectrics, iyo ine simba pane zvigadzirwa zvepakutanga zvikamu zvinoderedza kuisa pachena kwezvavanenge vaita.

Kuti zvive nemigumisiro yakadaro, zvakakwana kukomberedza imwe nzvimbo yenharo neganda rekuongorora. Saka, inofungidzirwa yakagadziriswa yakakosha uye vanhu vanodzivirirwa kubva pamagetsi emagetsi.