I roto i te kaupapa o te Papa Hiko , kua matapakihia e tātou te whakamāramatanga me te tātai o te papa hiko ka taea te whakamahi hei tatau i te kaha o te papa hiko e puta mai ana i te utu hiko kotahi, i ētahi utu hiko, i te tohatoha rānei o ngā utu hiko. He ngāwari te whakatau i te kaha o te papa hiko e puta mai ana i te utu hiko kotahi, i ngā utu hiko e rua rānei mā te whakamahi i te tātai kaha o te papa hiko. Mēnā ko te kaha o te papa hiko e tatauhia ana e puta mai ana i te tohatoha utu hiko, he uaua ake te tatau mēnā ka whakamahia te tātai kaha o te papa hiko, engari he māmā ake mēnā ka whakamahia te ture a Gauss . I mua i te ako hohonu i te ture a Gauss, me mārama tuatahi ki te rerenga hiko nā te mea kei roto i te ture a Gauss te ariā o te rerenga hiko.
Te Mārama ki te Rerenga Hiko
I ahu mai te kupu rere i te kupu Latina, fluere , ko tōna tikanga he rere. Ko te tikanga o te rerenga hiko ko te rere o te papa hiko. Kāore te kupu rere i konei e tohu ana i te papa hiko e rere ana pērā i te wai e rere ana, engari e whakaahua ana i te aroaro o te papa hiko e tohu ana i tētahi ahunga. I roto i te kaupapa o ngā Raina Papa Hiko, i whakamāramahia ko ngā papa hiko ka whakaatuhia, ka whakaaturia rānei mā te whakamahi i ngā raina papa hiko, nō reira ka whakaaturia hoki te rere hei raina papa hiko. Nō reira, ko te rere ko ngā raina papa hiko e tika ana mā roto i tētahi horahanga mata, e ai ki te tauira i raro nei.
Tātai
I roto i te pāngarau, ko te rerenga hiko te hua o te papa hiko (E), te horahanga mata (A) me te kosinī o te koki i waenganui i 
ngā rārangi papa hiko me ngā rārangi noa e poutū ana ki te mata.
Φ = EA cos θ …………………. (Whārite 1)
Mena he poutū ngā rārangi mara hiko ki te horahanga mata e tika ana mā roto, pērā i te pikitia, ko te koki i waenganui i ngā rārangi mara hiko me te rārangi noa he 0.o, kei hea ko te cos 0o = 1. Nō reira, ko te tātai 
kua hurihia hei:
Φ = EA cos 0o = EA (1)
Φ = EA …………………. (Whārite 2)
I runga i te tātai rerenga i runga ake nei, he maha ngā mea ka taea te whakatau. Tuatahi , kei te uara mōrahi te rerenga ina he poutū te rārangi mara hiko ki te horahanga mata nā te mea i roto i taua āhuatanga ko te koki i waenga i te rārangi mara hiko me te rārangi noa ko te 0 o , ko te uara kosinī o te 0 o ko te 1. Tuarua , kei te uara mōrahi te rerenga ina he whakarara te rārangi mara hiko ki te horahanga mata nā te mea i roto i taua āhuatanga ko te koki i waenga i te rārangi mara hiko me te rārangi noa ko te 90 o , ko te uara kosinī o te 90 o ko te 0. Tuatoru , ka whakawhirinaki te rerenga ki te mara hiko (E) me te horahanga mata (A). Haunga te horahanga mata tapawhā rite ki te tauira i runga ake nei, ka taea hoki te porowhita te horahanga mata me ētahi atu.
Mata Taupokina
Ko te rerenga hiko i whakaahuatia i mua ake nei i whakamahi i te tauira o tētahi mata tuwhera (he mata tapawhā, he mata tapawhā rānei). Ā, me pēhea te rerenga i runga i tētahi mata kati pērā i te poraka, te poraka, te porowhita rānei? Me kī he rārangi āpure hiko e haere ana i roto i te poraka, pērā i te pikitia i raro nei.
Ka taurite ngā rārangi o te papa hiko kikorangi ki ngā mata o runga me raro o te hihi hei hanga i tētahi koki 90.o me ngā rārangi noa o ngā mata o runga me raro. Nō reira, ko te rerenga i runga i ngā mata o runga me raro o te kurupae ko Φ = EA cos 90o = EA (0) = 0.
Ka taurite ngā rārangi o te papa hiko he kōwhai te tae ki ngā mata o te taha matau me te taha maui o te hihi, ā, ka hanga he koki 90.o me ngā rārangi noa o ngā mata taha maui me te taha matau. Nō reira, ko te rerenga i runga i ngā mata taha matau me te taha maui o te poraka ko Φ = EA cos 90o = EA (0) = 0.
Ko ngā rārangi papa hiko whero e tū poutū ana ki ngā mata o mua me muri o te poraka, e hanga ana i te koki o te 0.o me ngā rārangi noa o ngā mata o mua me muri. Nō reira, ko te rerenga ko Φ = EA cos 0o = EA (1) = EA.
I te ahua i runga ake nei, ka kitea ngā rārangi mara hiko whero e neke ana ki roto i te poraka, kātahi ka neke atu i waho o te poraka. Ina neke ngā rārangi mara hiko ki roto i te poraka me te mea he utu kino kei roto i te poraka, ka kino te rerenga. I tetahi atu taha, ina neke ngā rārangi mara hiko ki waho o te poraka me te mea he utu pai kei roto i te poraka, ka pai te rerenga hiko. Mā te tikanga kounga, mā te kore tatau rānei, mēnā he rite te maha o ngā rārangi mara hiko e tomo ana ki te poraka ki te maha o ngā rārangi mara hiko e wehe atu ana i te poraka, ka kore te rerenga hua. Mā te tikanga tauanga, mā te whakamahi tatau rānei, ka tatauhia te rerenga hiko e puta ana i roto i te poraka penei: rerenga e haere mai ana = Φ 1 = – EA cos 0 o = – EA (1) = -EA me te rerenga e puta atu ana = Φ 2 = + EA cos 0 o = + EA (1) = +E A. Ko te rerenga katoa ko Φ = -Φ 1 + Φ 2 = -EA + EA = 0.
I runga i ngā tātaitanga i runga ake nei, ka whakatauhia ko te rerenga katoa e puta ana i roto i te poraka, e whakaaturia ana i te pikitia i runga ake nei, he kore. Ka taea te kī he kore te rerenga katoa nā te mea kāore he utu hiko i roto i te poraka. Nō reira, ki te kore he utu hiko i roto i tētahi mata kua kati pērā i te poraka, te poraka, te porowhita, tētahi atu mea rānei, he kore te rerenga katoa. He aha mēnā he utu hiko kei roto i te mata kua kati?
Me kī he utu hiko kei waenganui o te porowhita e whakaaturia ana i te pikitia i te taha matau. Ko ngā rārangi mara hiko e whā e whakaaturia ana e tohu ana i ētahi atu rārangi mara hiko e neke ana ki waho mai i waenganui o te porowhita kia poutū ki te mata o te porowhita. He poutū ia rārangi ki te mata o te porowhita e whiti ana, ka hanga he koki 0 ° me te rārangi noa kia poutū ki te mata o te porowhita.
Te rerenga hiko i roto i te porowhita:
Ko te tātai mō te kaha o te papa hiko ko E = k Q / r 2 , ā, ko te tātai mō te horahanga mata o te porowhita ko A = 4 π r 2, kia huri ai te tātai rerenga ki:
Mena ko te utu i waenganui o te porowhita he +2Q, ko te rerenga i roto i te porowhita he
I runga i te tātai i runga ake nei, ka whakatauhia mēnā he utu hiko kei roto i tētahi mata porowhita kua kati, kāore te uara rerenga i roto i te porowhita e whakawhirinaki ki te whānui, ki te pūtoro rānei o te porowhita. Ko te uara rerenga he 4πk whakareatia te utu hiko katoa i roto i te porowhita, he 1/ε o rānei te utu hiko katoa i roto i te porowhita.
Wāhanga Rere Hiko
Ko te tātai taketake mō te rerenga ko Φ = EA, ko E te kaha o te papa hiko, ā, ko A te horahanga mata. Ko te waeine o te papa hiko ko Newton ia Coulomb (N/C) ā, ko te waeine o te horahanga mata ko te mita tapawha (m² ) nō reira ko te waeine o te rerenga ko Newton mita tapawha ia Coulomb (Nm² / C).
