Mutemo waGauss

Chinyorwa pamusoro pemutemo waGauss

Kutaura Mutemo weCoulomb, simba riri pakati pemagetsi rakadzidzwa. Mukuongorora munda wemagetsi, imwe mhando yemutemo waCoulomb yakakurukurwa, iyo inoratidzwa ne equation F = q E,

apo F iri simba remagetsi, q iri simba remagetsi uye E iri simba remagetsi. Zvinogona kutaurwa kuti mutemo waCoulomb mutemo wefizikisi unotsanangura hukama huripo pakati pesimba remagetsi (q) nesimba remagetsi (E).

Mutemo waGauss mumwe mutemo wefizikisi unotsanangura hukama huripo pakati pemagetsi anochaja neminda yemagetsi. Mutemo waGauss wakagadzirwa na Carl Friedrich Gauss (1777-1855), nyanzvi yefizikisi uye nyanzvi yemasvomhu yekuGermany.

Munda wemagetsi unogadzirwa nechaja imwe chete kana dzakawanda dzemagetsi unogona kuverengerwa zviri nyore uchishandisa mutemo waCoulomb, asi kuverenga kunowedzera kuoma kana chinoonekwa chiri munda wemagetsi unogadzirwa nekugoverwa kwechaja yemagetsi. Mutemo waGauss unopa nzira yechisikigo yekuona munda wemagetsi unogadzirwa nekugoverwa kwechaja yemagetsi. Uyezve, kana munda wemagetsi uchizivikanwa, mutemo waGauss unogona kushandiswa kuona kugoverwa kwechaja dzemagetsi dzinogadzira munda wemagetsi. Zvinotevera zvinoongororwa pfungwa nekuenzanisa kwemutemo waGauss.

Ongorora chaji yemagetsi yakanaka pakati pebhora sezvakaratidzwa pamufananidzo uri padivi. Kana radius yebhora iri R, saka simba remagetsi rinogadzirwa nechaji iri mubhora iri E = k Q/R² uye nzvimbo yepamusoro yebhora iri A = 4 π r².

Kuti tifungidzire munda wemagetsi, mitsetse yemagetsi inodhirowa, asi mumufananidzo, mitsetse mina chete yemagetsi inomiririrwa. Chaji yemagetsi yakanaka, saka mitsetse yemagetsi inodhirowa kubva pakati pebhora pane chaji yemagetsi,

uye mutsetse wega wega wemunda wemagetsi wakatwasuka pamusoro pebhora rinopfuura nepakati paro. Kana kure nechaji yemagetsi, munda wemagetsi unova mudiki zvekuti daro riri pakati pemitsetse yemunda wemagetsi riri kurewo.

Mafungu emagetsi anopinda pamusoro pebhora anoverengerwa uchishandisa fomura inotevera:

F = kuyerera kwemagetsi, Q = kuchaja kwemagetsi, k = 9 x 10⁹ N m²/C², ε_o (mvumo yekubvisa mweya) = 8.85 x 10^-12 C²/N m², π = 3.14.

Zvichibva pachiyero ichi, zvakagumiswa kuti kuyerera kwemagetsi (F) kunopfuura nepadenga kwakaenzana nehuwandu hwechaji yemagetsi (Q) mairi uye hakutsamiri panharaunda yebhora (R).

Mufananidzo uri padivi unoratidza nzvimbo ina dzakavharwa dzine chaji yemagetsi Q. Nzvimbo yekutanga yakatenderera, nepo imwe nzvimbo ine chimiro chisina kurongeka. Chaji yemagetsi yakanaka zvekuti mitsara yemagetsi inomiririrwa nemiseve mina inotorwa kubva muchaji. Mitsetse mina yemagetsi inopfuura nepanzvimbo yakatenderera, uye dzimwe nzvimbo dzine chimiro chisina kurongeka dzinopfuurawo nepamitsara iyi mina.

Mukuongorora kwe electric flux, zvinonzi electric flux mitsetse yemagetsi inopinda munzvimbo chaiyo.

Mitsetse yemagetsi inopinda munzvimbo ina yakafanana zvekuti flux yemagetsi panzvimbo dzese ina ine hukuru hwakafanana. flux yemagetsi inopinda munzvimbo yakatenderera ndeye Φ = Q/ε_o zvekuti flux yemagetsi inopinda mune dzimwe nzvimbo dzine maumbirwo asina kurongeka inewo hukuru hwakafanana, hunoti Φ = Q/ε_o.

Zvichibva patsananguro iyi, zvinogona kugumiswa kuti kuyerera kwemagetsi kunopinda panzvimbo yakavharwa ine chaji yemagetsi, hakutsamiri pachimiro chepamusoro uye hukuru hwacho ndi Φ = 4 π k Q = Q/ε_o.

Mufananidzo uri padivi unoratidza machaji maviri emagetsi ari mukati menzvimbo yakavharwa.₁ uye Q₂ vane tariro zvekuti kana vari Kana chaji yega yega yadhonzwa, ine tambo yemagetsi inopinda ichibva mukati memvura. Kuyerera kwemagetsi kwakazara huwandu hwetambo dzemagetsi dzinopinda dzichibuda pamusoro pemvura yakavharwa. Nekuti tambo dzemagetsi dzemagetsi dzechaji Q₁ zvakaenzana nemagetsi Φ = Q₁/ε_o uye mitsetse yemunda wemagetsi wechaji Q₂

zvakafanana nemagetsi Φ = Q₂/ε_o, huwandu hwese hwemitsetse yemagetsi yakaenzana neQ₁/ε_o +Q₂/ε_o = 1 / ε_o (Q₁ +Q₂).

Zvichibva patsananguro iyi, zvinogona kugumiswa kuti huwandu hwemagetsi hunosvika 1/ε_o inopeta huwandu hwese hwemagetsi ari pamusoro wakavharwa. Chirevo ichi mutemo waGauss. Pamasvomhu:

Φ_mambure = 1/ε_o (Q_mambure) ———- Kuenzanisa kwemutemo waGauss

Q net ndiyo huwandu hwese hwechaji yemagetsi iri mukati menzvimbo yakavharwa. Kana paine chaji yemagetsi kunze kwenzvimbo yakavharwa, chaji haiverengerwi nekuti flux yemagetsi yainogadzira izero. flux yemagetsi izero nekuti mitsetse yemunda wemagetsi unobva pachaji inopinda mukati menzvimbo yakavharwa yozobuda zvakare.

Nzvimbo yakavharwa yemutemo waGauss ndiyo nzvimbo yekufungidzira inopihwa kuti iverenge kuyerera kwemagetsi kunokonzerwa nekuchaja kwemagetsi.

Mutemo waGauss unogona kushandiswa kuona munda wemagetsi kana kugoverwa kwechaja yemagetsi kuchizivikanwa, kana kuti unogona kushandiswawo kuona kugoverwa kwechaja yemagetsi kana munda wemagetsi uchizivikanwa. Kushandiswa kwemutemo waGauss kugadzirisa mibvunzo yakasiyana-siyana kunotsanangurwa munyaya pamusoro pekushandiswa kwemutemo waGauss.