Cov hluav taws xob ntws

Kev txhais ntawm lub zog hluav taws xob

Hais txog lub zog hluav taws xob, nws tau raug tham txog qhov kev txhais thiab kev sib npaug ntawm fais fab teb uas siv tau los xam lub zog hluav taws xob uas tsim los ntawm lub zog hluav taws xob, ntau lub zog hluav taws xob lossis los ntawm kev faib hluav taws xob. Kev suav ntawm lub zog hluav taws xob uas tsim los ntawm lub zog hluav taws xob lossis ob lub zog hluav taws xob tau yooj yim daws tau siv cov mis ntawm lub zog hluav taws xob. Yog tias qhov uas suav yog lub zog hluav taws xob uas tsim los ntawm kev faib hluav taws xob, kev suav yuav nyuaj dua yog tias siv cov mis rau lub zog hluav taws xob, tab sis nws yooj yim dua rau siv. Txoj cai GaussUa ntej kawm txog Gauss txoj cai tob tob, xub nkag siab tias hluav taws xob flux vim yog lub tswv yim ntawm hluav taws xob flux siv hauv Gauss txoj cai.

Lo lus flux yog los ntawm lo lus Latin, fluere, uas txhais tau tias ntws. Cov hluav taws xob flux tuaj yeem txhais tau tias yog cov hluav taws xob ntws. Lo lus ntws ntawm no tsis qhia txog cov hluav taws xob ntws zoo li dej ntws, tab sis piav qhia txog qhov muaj hluav taws xob uas coj mus rau ib qho kev taw qhia tshwj xeeb. Hais txog cov kab hluav taws xob, nws tau piav qhia tias cov hluav taws xob tau pom lossis kos siv cov kab hluav taws xob, thiab yog li ntawd cov hluav taws xob flux kuj tau piav qhia tias yog cov kab hluav taws xob. Yog li cov hluav taws xob flux yog cov kab hluav taws xob uas hla ib cheeb tsam tshwj xeeb, raws li piv txwv hauv daim duab hauv qab no.

Cov qauv ntawm lub zog hluav taws xob

Hauv lej, cov hluav taws xob flux yog cov khoom ntawm lub teb hluav taws xob (E), thaj chaw ntawm qhov chaw (A) thiab cosine ntawm lub kaum sab xis ntawm txoj kab teb hluav taws xob thiab txoj kab ib txwm perpendicular rau qhov chaw.

F = EA cos θ……………. (Kev sib npaug 1)

Yog tias cov kab hluav taws xob yog perpendicular rau thaj chaw uas lawv hla raws li hauv daim duab, ces lub kaum sab xis ntawm cov kab hluav taws xob thiab cov kab ib txwm yog 0^o, qhov twg cos 0^o = 1. Yog li, tus qauv rau cov hluav taws xob flux hloov mus rau:

F = EA cos 0^o = EA (1)

F = EA ………………. (Zaj lej 2)

Raws li cov qauv, cov hluav taws xob flux saum toj no xaus ntau yam. Ua ntej, cov hluav taws xob flux yog qhov siab tshaj plaws thaum txoj kab hluav taws xob yog perpendicular rau thaj chaw vim tias ntawm qhov xwm txheej no lub kaum sab xis ntawm txoj kab hluav taws xob thiab txoj kab ib txwm yog 0o, qhov twg cosine 0o yog 1. Qhov thib ob, cov hluav taws xob flux yog qhov tsawg kawg nkaus thaum txoj kab hluav taws xob sib luag rau thaj chaw vim tias ntawm qhov xwm txheej no lub kaum sab xis ntawm txoj kab hluav taws xob thiab txoj kab ib txwm yog 90^o, qhov twg cosine yog 90^o yog 0. Qhov thib peb, qhov hluav taws xob flux nyob ntawm lub teb hluav taws xob (E) thiab thaj chaw ntawm qhov chaw (A). Ntxiv rau thaj chaw ntawm qhov chaw zoo li lub xwmfab zoo li hauv qhov piv txwv saum toj no, thaj chaw ntawm qhov chaw kuj tuaj yeem yog lub voos xwmfab thiab lwm yam.

Fais fab flux ntawm qhov chaw kaw

Cov nqi hluav taws xob uas tau piav qhia ua ntej siv ib qho piv txwv ntawm qhov chaw qhib (cheeb tsam plaub fab lossis plaub fab). Cov hluav taws xob ntws li cas ntawm cov chaw kaw xws li lub voos xwmfab, cov ntoo khaub lig, lossis cov pob? Xav tias muaj cov kab hluav taws xob uas hla dhau lub ntoo khaub lig, raws li qhia hauv qab no.

Cov kab hluav taws xob uas muaj xim xiav sib phim nrog cov nplaim sab saud thiab sab qis ntawm lub teeb kom lawv tsim lub kaum sab xis ntawm 90^o nrog rau txoj kab ib txwm ntawm cov nplaim sab saud thiab qis. Yog li, cov hluav taws xob flux ntawm cov nplaim sab saud thiab qis ntawm lub beam yog F = EA cos 90^o = EA (0) = 0.

Cov kab hluav taws xob uas tau muab xim daj sib phim nrog sab xis thiab sab laug ntawm lub teeb kom lawv tsim lub kaum sab xis ntawm 90^o nrog rau txoj kab ib txwm ntawm sab laug thiab sab xis. Yog li, lub zog hluav taws xob ntawm sab xis thiab sab laug ntawm lub teeb yog F = EA cos 90^o = EA (0) = 0.

Cov kab hluav taws xob tau muab ib daim duab liab perpendicular rau sab pem hauv ntej thiab sab nraub qaum ntawm lub beam kom lawv tsim ib qho 0^o lub kaum sab xis nrog txoj kab ib txwm ntawm sab pem hauv ntej thiab sab nraub qaum. Yog li, lub zog hluav taws xob yog F = EA cos 0^o = EA (1) = E A.

Hauv daim duab saum toj no, cov kab liab pom ntawm lub zog hluav taws xob txav mus rau hauv lub teeb thiab tom qab ntawd txav tawm ntawm lub teeb. Thaum cov kab hluav taws xob txav mus rau hauv lub teeb zoo li muaj lub zog tsis zoo hauv lub teeb, lub zog hluav taws xob flux yog tsis zoo. Ntawm qhov tod tes, thaum cov kab hluav taws xob txav tawm ntawm lub teeb zoo li muaj lub zog zoo hauv lub teeb, lub zog hluav taws xob flux yog zoo. Zoo, yog tias tus lej ntawm cov kab hluav taws xob uas nkag mus rau hauv lub teeb sib npaug rau tus lej ntawm cov kab hluav taws xob tawm ntawm lub teeb, lub zog hluav taws xob flux tshwm sim yog xoom. Quantitatively, lub zog hluav taws xob flux dhau los ntawm lub teeb raug suav ua raws li hauv qab no: lub zog hluav taws xob nkag = F₁ = – EA cos 0^o = – EA (1) = -EA thiab cov hluav taws xob tawm = F₂ = + EA cos 0^o = + EA (1) = + E A. Tag nrho cov hluav taws xob flux yog F = - F₁ +F₂ = -EA + EA = 0.

Raws li cov kev xam saum toj no, nws tau xaus lus tias tag nrho cov hluav taws xob flux hla lub beam raws li hauv daim duab saum toj no yog xoom. Nws tuaj yeem hais tias tag nrho cov hluav taws xob flux yog xoom vim tias tsis muaj hluav taws xob them hauv lub beam. Yog li ntawd, yog tias tsis muaj hluav taws xob them hauv qhov chaw kaw xws li beams, cubes, spheres, thiab lwm yam, tag nrho cov hluav taws xob flux yog xoom. Yuav ua li cas yog tias muaj hluav taws xob them rau ntawm qhov chaw kaw?

Xav tias muaj ib qho hluav taws xob nyob hauv nruab nrab ntawm lub pob, raws li pom hauv daim duab ntawm sab. Plaub kab ntawm lub teb hluav taws xob tau piav qhia tias sawv cev rau cov kab ntawm lwm lub teb hluav taws xob uas txav tawm ntawm nruab nrab ntawm lub pob uas tig mus rau saum npoo ntawm lub pob. Txhua kab yog tig mus rau saum npoo ntawm lub pob, uas nws tsim lub kaum sab xis ntawm 0.^o nrog ib txoj kab ib txwm uas perpendicular rau qhov chaw ntawm lub pob.

Fais fab flux ntawm lub pob: Φ = E A.

Cov mis ntawm lub zog hluav taws xob yog E = kq / r², thiab qhov sib npaug ntawm thaj chaw ntawm lub pob zeb yog A = 4 pr² yog li ntawd cov mis ntawm hluav taws xob flux hloov mus rau:

Yog tias qhov them nyiaj ntawm qhov chaw nruab nrab ntawm lub pob yog + 2Q, ces qhov hluav taws xob ntawm lub pob yog

Raws li cov qauv hluav taws xob flux, nws xaus lus tias yog tias muaj hluav taws xob them rau hauv qhov chaw kaw spherical,

tus nqi ntawm cov hluav taws xob flux ntawm lub pob tsis nyob ntawm lub cheeb lossis lub vojvoog ntawm lub pob. Qhov loj ntawm cov hluav taws xob flux yog 4πk npaug ntawm tag nrho cov nqi hluav taws xob hauv lub pob, lossis 1 / ε_o npaug ntawm tag nrho cov hluav taws xob hauv lub pob.

Chav ntawm cov hluav taws xob flux

Tus qauv yooj yim ntawm cov hluav taws xob flux yog F = EA, qhov twg E yog lub zog hluav taws xob thiab A yog thaj chaw saum npoo. Chav tsev hluav taws xob yog Newton ib Coulomb (N/C), thiab chav tsev ntawm thaj chaw saum npoo yog square meter (m²) yog li ntawd lub chav ntawm cov hluav taws xob flux yog Newton square meter ib Coulomb (Nm)²/C).