Filin lantarki saboda caji ɗaya kawai
Don yin lissafi filin lantarki An samar da shi ta hanyar caji mai kyau guda ɗaya, mataki na farko shine zaɓar saman Gaussian mai siffar radius r inda tsakiyar ƙwallon yake a kan caji ɗaya. Yankin saman ƙwallon shine 4..r2.
Filin lantarki da ke fitowa daga tsakiyar ƙwallon yana ratsawa kai tsaye zuwa saman ƙwallon don haka tsarin kwararar wutar lantarki shine Φ = E A. Tsarin dokar Gauss shine Φ = Q / ε o
Filin lantarki a wani wuri a nesa da caji ɗaya shine:
Bayani: E = filin lantarki, k = Madaidaitan Coulomb (9 x 109 Nm2/C2), Q = cajin lantarki, r = nisan daga cajin lantarki
Wannan ita ce dabarar filin lantarki da aka samar ta hanyar cajin lantarki . Ana iya samo wannan dabarar ta amfani da dokar Coulomb.
Filayen lantarki a ciki da wajen wani yanki mai kama da juna mai caji da wutar lantarki
Sphere mai ƙarfi wanda ke da caji mai kama da juna ko iri ɗaya yana da jimlar caji Q, girma V = 4/3 π R 3 kuma yawan caji a cikin sifar mai ƙarfi shine ρ = Q/V. Kayyade ƙarfin filin lantarki a cikin sifar da wajen sifar.
a) Filin lantarki a cikin ƙwallon da aka yi da ƙarfe
Sphere mai ƙarfi yana da radius R, yayin da saman Gaussian da aka zaɓa shine spiral na radius r, inda r < R. Girman spiral mai ƙarfi shine V kuma girman spiral na Gaussian shine V'.
Cajin wutar lantarki da ke cikin yankin Gauss shine:
Filin lantarki da ke fitowa daga tsakiyar ƙwallon yana ratsawa a tsaye zuwa saman ƙwallon don haka dabarar kwararar lantarki ta kasance Φ = E A. Gauss's formula formula is Φ = Q / εo
Filin lantarki a wani wuri a nesa daga tsakiyar r shine:
Dangane da dabarar da ke sama, filin lantarki (E) yana daidai da cajin lantarki (Q) da radius na saman Gaussian (r), wanda ya yi daidai da kubiyar radius na ƙwallo mai ƙarfi (R3 ).
b) Filin lantarki a wajen wani yanki mai ƙarfi
Sphere mai ƙarfi yana da radius R yayin da saman Gaussian mai zagaye yana da radius r, inda r > R. Cajin sphere mai ƙarfi shine Q; sphere mai ƙarfi yana cikin Sphere na Gaussian don haka cajin wutar lantarki da ke cikin Sphere na Gaussian shine Q.
Filin lantarki yana fitowa daga tsakiyar ƙwallon kuma yana ratsawa a tsaye zuwa saman ƙwallon don haka tsarin kwararar lantarki shine Φ = E A. Tsarin dokar Gauss shine Φ = Q / ε o
Filin lantarki a nesa daga tsakiyar ƙwallo mai ƙarfi shine:
Filin lantarki a ciki da wajen harsashin wani rami mai kama da na lantarki mai caji
Wani ƙwallo mai rami mai radius R da girma V = 4/3 π R 3 , yana da cajin lantarki mai kama da na gaske a kan harsashinsa tare da jimlar caji na Q. Kayyade ƙarfin filin lantarki a ciki da wajen harsashin ƙwallo.
a) Filin lantarki a cikin ramin da babu komai
Saboda haka, wani yanki mai rami yana da siffar cajin lantarki a saman fili, yayin da babu cajin lantarki a cikin fili. Idan saman Gaussian da aka zaɓa yana da zagaye kuma yankin Gaussian yana cikin rami mai rami, to babu cajin lantarki a cikin fili na Gaussian. Cajin lantarki sifili ne, don haka filin lantarki shi ma sifili ne. Saboda haka, filin lantarki da ke cikin rami mai rami sifili ne.
b) Filin lantarki a wajen ramin da babu komai
Swipe ɗin da ke cikin ramin yana da radius R, yayin da saman Gaussian da aka zaɓa shine swipe mai radius r, inda r > R.
Filin wutar lantarki da ke fitowa daga tsakiyar ƙwallon yana ratsawa a tsaye zuwa saman ƙwallon don haka tsarin kwararar wutar lantarki shine Φ = EA = E 4π r 2. Tsarin dokar Gauss shine Φ = Q / ε o.
Filin lantarki a wani wuri a nesa daga tsakiyar ramin shine:
Filin lantarki kusa da siririn waya mai caji da wutar lantarki
Waya siririya mai tsayin da ba ta da iyaka tana ɗauke da cajin lantarki mai kama da na λ . Cajin lantarki da ke kan wayar shine Q = λl. Kayyade ƙarfin filin lantarki a kusa da siririn wayar.
An zaɓi saman Gaussian ya zama silinda mai tsayin l da radius r. Akwai nau'i biyu na saman, wato saman zagaye mai radius r wanda ke a ƙarshen silinda biyu (faɗin saman shine .r2) da kuma saman silinda mai tsawon l (faɗin samansa shine 2πr l).
Cajin wutar lantarki yana da kyau, saboda haka filin wutar lantarki yana fitowa daga waya a tsaye a saman bututun don haka kwararar wutar lantarki tana da ƙimar Φ = EA = E 2πr l . A gefe guda kuma, filin wutar lantarki yana daidai da ƙarshen bututun biyu a siffar da'ira don haka kwararar wutar lantarki tana da ƙimar sifili.
Filin lantarki a wani wuri a nesa daga waya shine:
