I roto i ngā rauemi mō te ture a Coulomb, i akohia te kaha i waenga i ngā utu hiko. I roto i te arotake i ngā mara hiko, i matapakihia tētahi atu momo ture a Coulomb, i whakaaturia mā te whārite F = q E, ko F te kaha hiko, ko q te utu hiko, ā, ko E te mara hiko. Ka taea te kī ko te ture a Coulomb he ture ahupūngao e whakamārama ana i te whanaungatanga i waenga i te utu hiko (q) me te mara hiko (E).
Ko te ture a Gauss tētahi atu ture ahupūngao e whakamārama ana i te whanaungatanga i waenga i te utu hiko me te mara hiko. Nā Carl Friedrich Gauss (1777–1855), he tohunga ahupūngao ariā Tiamana, he tohunga pāngarau hoki, i titoa te ture a Gauss. Ka taea te tatau ngāwari i te mara hiko i hangaia e tētahi, neke atu rānei, ngā utu hiko mā te whakamahi i te ture a Coulomb, engari ka uaua ake te tatau mēnā kei te whakatauhia te mara hiko i hangaia e te tohatoha o ngā utu hiko. Mā te ture a Gauss ka māmā ake te whakatau i te mara hiko i hangaia e te tohatoha o ngā utu hiko. Hei tāpiri, mēnā e mōhiotia ana te mara hiko, ka taea te whakamahi i te ture a Gauss hei whakatau i te tohatoha o ngā utu hiko e whakaputa ana i te mara hiko. Ka matapakihia i raro nei te ariā me te tauira mō te ture a Gauss.
Whakaarohia he utu hiko pai kei waenganui o te pōro e whakaaturia ana i te pikitia ki te taha. Mena ko te radius o te pōro ko R, ko te kaha o te mara hiko i hangaia e te utu puta noa i te mata o te pōro ko E = k Q / R2 ā, ko te horahanga mata o te porowhita ko A = 4 π R2Hei whakaatu i te mara hiko, ka tuhia ngā rārangi mara hiko, engari e whā anake e whakaatuhia ana e te pikitia. Nā te mea he pai te utu hiko, ka tuhia ngā rārangi mara hiko e puta mai ana i waenganui o te porowhita kei reira te utu hiko, ā, ko ia rārangi mara hiko he poutū ki te mata o te porowhita e haere ana. Ko te tawhiti atu i te utu hiko, ko te iti ake o te mara hiko, nō reira ka piki ake te tawhiti i waenga i ngā rārangi mara hiko.
Ka tatauhia te rerenga hiko e uru ana ki te mata o te porowhita mā te whakamahi i te tātai e whai ake nei:
Whakaahuatanga: Φ = rerenga hiko, Q = utu hiko, k = 9 x 10 9 N m 2 /C 2 , ε o (te āheinga o te wāhi wātea) = 8,85 x 10 -12 C 2 /N m 2 , π = 3,14. I runga i tēnei whārite, ka whakatauhia ko te rerenga hiko ( Φ ) e tika ana kia puta i roto i tētahi mata porowhita he rite ki te nui o te utu hiko (Q) kei roto, ā, kāore e whakawhirinaki ki te radius o te porowhita (R).
E whakaatu ana te ahua i te taha matau i ngā mata e whā kua kati kei roto he utu hiko Q. He porowhita te mata tuatahi, ko ngā mata kē atu he āhua koretake. He pai te utu hiko kia tuhia ai ngā rārangi mara hiko e tohuhia ana e ngā pere e whā e puta mai ana i te utu. Ka haere ngā rārangi mara hiko e whā mā roto i te mata porowhita, ā, ko tētahi atu mata he āhua koretake. I roto i te arotake mō rerenga hiko e kīia ana Ko te rerenga hiko ko ngā rārangi papa hiko e uru ana ki tētahi mata kua whakaritea.He rite tonu ngā rārangi āpure hiko e uru ana ki ngā mata e whā, kia rite ai te uara o te rerenga hiko i runga i ngā mata e whā. Ko te rerenga hiko e uru ana ki tētahi mata porowhita he ōrite ki a Φ = Q/εo , nō reira, ko te rerenga hiko e uru ana ki ētahi atu mata he āhua koretake hoki, he rite tonu te uara, arā, Φ = Q/εo. I runga i tēnei whakamārama, ka taea te whakatau ko te rerenga hiko e uru ana ki tētahi mata kua kati kei roto he utu hiko kāore e whakawhirinaki ki te āhua o te mata, ā, ko tōna rahi ko Φ = 4 π k Q = Q/εo.
E whakaatu ana te ahua i te taha matau i ngā utu hiko e rua i roto i tētahi mata kua kati. Ko te utu Q1 me te Q2 he pai, ā, ki te whakaaturia, he rārangi āpure hiko kei ia utu e puta mai ana i roto i te mata. Ko te rerenga hiko katoa ko te tapeke o ngā rārangi āpure hiko e puta mai ana i tētahi mata kua kati. Nā te mea ko ngā rārangi āpure hiko o te utu Q1 he rite ki te rerenga hiko o Φ = Q1/εo me ngā rārangi utu hiko Q2 he rite ki te rerenga hiko o Φ = Q2/εo kātahi ka ōrite te tapeke o ngā rārangi āpure hiko ki te Q1/εo +Q2/εo = 1/εo (Q1 +Q2).
I runga i tēnei whakamārama, ka taea te whakatau ko te rerenga hiko katoa he 1/ε o te whakarea o te utu hiko katoa i roto i te mata kua kati. Ko tēnei kōrero ko te ture a Gauss. I roto i te pāngarau:
Φ tapeke = 1/ε o (Q tapeke ) ———- Te whārite ture a Gauss
Ko te Q katoa te tapeke o te utu hiko i roto i tētahi mata kua kati. Mena he utu hiko kei waho o te mata kua kati, kāore te utu e whakaarohia nā te mea he kore te rerenga hiko e puta mai ana. He kore te rerenga hiko nā te mea ka uru ngā rārangi mara hiko e ahu mai ana i te utu ki roto i te mata kua kati, kātahi ka puta anō kia kore ai te rerenga e puta mai ana. Ko te mata kua kati i roto i te ture a Gauss he mata pohewa e whakaatuhia ana hei tatau i te rerenga hiko e puta mai ana i ngā utu hiko. Arā, kāore e hiahiatia kia noho ngā utu hiko ki roto i tētahi mata kua kati tūturu. Ka taea te whakamahi i te ture a Gauss hei whakatau i te mara hiko mena e mōhiotia ana te tohatoha o ngā utu hiko, ka taea rānei te whakamahi hei whakatau i te tohatoha o ngā utu hiko mena e mōhiotia ana te mara hiko. Ko te whakamahinga o te ture a Gauss hei whakaoti rapanga maha e whakamāramahia ana i roto i te tuhinga e kīia nei ko te whakatau i te mara hiko mā te whakamahi i te ture a Gauss.
