Kuziva munda wemagetsi uchishandisa mutemo weGauss

Chinyorwa pamusoro peKuona munda wemagetsi uchishandisa mutemo weGauss

Munda wemagetsi nekubhadharisa poindi imwe chete

Kuti uverenge munda wemagetsi unogadzirwa nechaji imwe chete, danho rekutanga nderekusarudza nzvimbo yeGauss yakatenderera ine radius r apo pakati pebhora iri pachaji imwe chete. Nzvimbo yepamusoro yebhora i4πr².

Munda wemagetsi unobuda pakati pedenderedzwa unopinda wakatwasuka pamusoro pedenderedzwa zvekuti fomura yemagetsi inoyerera Φ = E A. Fomura yemutemo waGauss ndeye Φ = Q/ε_o

Munda wemagetsi uri kure ne r kubva pakuchaja kamwe chete ndewekuti:

E = munda wemagetsi, k = Coulomb constant (9 x 10)⁹ Nm²/C²), Q = kuchaja yemagetsi, r = chinhambwe kubva kuchaja yemagetsi.

Iyi ndiyo fomura yesimba remagetsi rinogadzirwa nechaji yemagetsi. Fomura iyi inogona kuwanikwa uchishandisa mutemo waCoulomb.

Minda yemagetsi mukati nekunze kwebhora rakasimba rine magetsi akafanana

Bhora rakasimba rakanyatso charged rine huwandu hweQ, vhoriyamu V = 4/3 π R³ uye huwandu hwechaji mubhora rakasimba ndi ρ = ​​Q/V. Tsvaga simba remagetsi mukati mebhora nekunze kwebhora.

a) Munda wemagetsi uri mubhora rakasimba

Bhora rakasimba rine radius yeR, nepo Gauss surface yakasarudzwa yakaita denderedzwa ine radius r, apo r < R. Vhoriyamu yebhora rakasimba ndiV uye vhoriyamu yeGauss sphere ndiV'.

Chaja yemagetsi mumabhora eGauss ndeiyi:

Munda wemagetsi unobuda pakati pedenderedzwa unopinda wakatwasuka pamusoro pedenderedzwa zvekuti fomura yemagetsi inoyerera Φ = E A. Fomura yemutemo waGauss ndeye Φ = Q/ε_o

Munda wemagetsi uri panzvimbo ine daro re r kubva pakati pebhora rakasimba ndewekuti:

Zvichibva pafomura iri pamusoro, munda wemagetsi (E) unoenderana nechaji yemagetsi (Q) uye radius yeGauss surface (r), zvichipesana ne radius yebhora rakasimba (R).³)

b) Munda wemagetsi kunze kwebhora rakasimba

Bhora rakasimba rine radius yeR nepo Gauss surface yakaita denderedzwa ine radius r, uko r > R. Charge yebhora rakasimba ndeye Q; bhora rakasimba riri mukati megauss ball kuitira kuti electric charge iri mugauss ball ive Q.

Munda wemagetsi unobuda pakati pebhora wopinda wakananga pamusoro pebhora zvekuti fomura yemagetsi inoyerera Φ = E A. Fomura yemutemo waGauss ndeye Φ = Q/ε_o

Munda wemagetsi une daro re r kubva pakati pebhora rakasimba ndeiri:

Munda wemagetsi mukati nekunze kwebhora risina chinhu une simba rakafanana remagetsi

Mabhora asina chinhu ane radius yeR uye vhoriyamu V = 4/3 π R³, ine simba rakafanana remagetsi pamusoro uye inochajwa zvizere Q. Sarudza simba remagetsi mukati nekunze kwenzvimbo yacho.

a) Munda wemagetsi uri mu ari bhora rine mhango

Bhora harina chinhu, saka chaji yemagetsi iri pamusoro pebhora, nepo mukati mebhora pasina chaji yemagetsi. Kana nzvimbo yakasarudzwa yegauss iri denderedzwa uye bhora regauss riri mukati mebhora risina chinhu, hapana chaji yemagetsi iri mukati mebhora regauss. Chaji yemagetsi izero, saka nzvimbo yemagetsi izerowo. Saka, nzvimbo yemagetsi iri mukati mebhora risina chinhu izero.

b) Munda wemagetsi uri kunze kwebhora risina chinhu

Bhora harina chinhu neradius yaR, nepo Gauss surface yakasarudzwa yakaita denderedzwa neradius yaR, uko r > R.

Munda wemagetsi unobuda pakati pebhora unopinda wakatwasuka pamusoro pebhora zvekuti fomura yemagetsi inoyerera Φ = EA = E 4π r²Fomura yemutemo waGauss ndeye Φ = Q/ε_o.

Munda wemagetsi uri panzvimbo ine daro re r kubva pakati pebhora risina chinhu ndewekuti:

Minda yemagetsi iri pedyo newaya dzakatetepa dzine magetsi

Waya yakatetepa ine urefu husingaperi, chaji yemagetsi yakafanana zvakanaka ine huwandu hwekuchaja λ. Chaji yemagetsi iri pawaya ndeye Q = λ l. Tsvaga simba remagetsi rakatenderedza waya yakatetepa.

Nzvimbo yeGauss inosarudzwa ine chimiro chemasirinda ane hurefu l uye radius r. Kune mhando mbiri dzenzvimbo, nzvimbo yakatenderera ine radius r iri kumativi ese e cylindrical (nzvimbo yenzvimbo i2πr).²) uye pamusoro pe cylindrical ine urefu hwe l (nzvimbo yepamusoro i 2πr l).

Chaji yemagetsi yakanaka, saka simba remagetsi rinobuda pawaya rakanamira pamusoro pechubhu.

saka kuyerera kwemagetsi kuri Φ = EA = E 2πr l. Pane kudaro, munda wemagetsi wakaenzana nemagumo maviri echubhu yakatenderera kuitira kuti kuyerera kwemagetsi kuve zero.

Munda wemagetsi uri kure ne r kubva pawaya ndewekuti: