He tuhinga mō te ture a Gauss
Mō te ture a Coulomb , kua akohia te kaha i waenga i ngā utu hiko. I roto i tētahi arotake o te mara hiko, kua matapakihia tētahi atu momo o te ture a Coulomb, e whakaatuhia ana e 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 ngā utu hiko me ngā mara hiko. Nā Carl Friedrich Gauss (1777-1855), he tohunga ahupūngao ariā me te tohunga pāngarau Tiamana, i tito te ture a Gauss.
Ka taea te tatau ngāwari i te mara hiko i hangaia e te kotahi, e ētahi rānei o ngā utu hiko mā te whakamahi i te ture a Coulomb, engari ka uaua ake te tatau mēnā ko te mara hiko i hangaia e te tohatoha utu hiko te mea e whakatauhia ana. Mā te ture a Gauss ka whakaratohia he huarahi maori ake hei whakatau i te mara hiko i hangaia e te tohatoha utu hiko. Hei tāpiri, mēnā e mōhiotia ana he 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 arotakehia te ariā me te whārite o te ture a Gauss i raro nei.
Arotakehia tētahi utu hiko pai i waenganui o te pōro e whakaaturia ana i te pikitia i te taha. Mena ko te radius o te porowhita ko R, ko te kaha o te mara hiko i hangaia e te utu puta noa i te porowhita ko E = k Q/R2 ā, ko te horahanga mata o te porowhita ko A = 4 π r2.
Hei whakaatu i te papa hiko, ka tuhia ngā rārangi papa hiko, engari i roto i te pikitia, e whā noa iho ngā rārangi papa hiko e whakaaturia ana. He pai te utu hiko, nō reira ka tuhia ngā rārangi papa hiko mai i waenganui o te pōro kei reira te utu hiko,
ā, ko ia rārangi o te papa hiko e tū poutū ana ki te mata o te pōro e tika ana mā roto. Ka tawhiti atu i te utu hiko, ka iti haere te papa hiko, ā, ka tawhiti atu anō hoki te tawhiti i waenga i ngā rārangi papa hiko.
Ka tatauhia ngā rerenga hiko e uru ana ki te mata o te porowhita mā te whakamahi i te tātai e whai ake nei:
F = rerenga hiko, Q = utu hiko, k = 9 x 10 9 N m 2 /C 2 , ε o (te āheinga korehau) = 8.85 x 10 -12 C 2 /N m 2 , π = 3.14.
I runga i tēnei whārite, ka whakatauhia ko te rerenga hiko (F) e tika ana mā roto i tētahi mata porowhita he rite ki te nui o te utu hiko (Q) i roto, ā, kāore e whakawhirinaki ki te radius o te pōro (R).
E whakaatu ana te ahua i te taha i ngā mata e whā kua kati, kei roto he utu hiko Q. He porowhita te mata tuatahi, ko te mata kē he āhua koretake. He pai te utu hiko, ā, ka tangohia ngā rārangi mara hiko e tohuhia ana e ngā pere e whā mai i te utu. Ka haere ngā rārangi mara hiko e whā mā roto i tētahi mata porowhita, ā, ka haere anō hoki ētahi atu mata he āhua koretake ō rātou mā roto i ēnei rārangi e whā.
I roto i te arotake o te rerenga hiko, e kīia ana ko te rerenga hiko ko ngā rārangi o te papa hiko e uru ana ki tētahi horahanga mata motuhake.
He rite tonu ngā rārangi āpure hiko e uru ana ki ngā mata e whā, kia rite ai te kaha o te rerenga hiko i runga i ngā mata e whā. Ko te rerenga hiko e uru ana ki te mata porowhita ko Φ = Q/εo kia rite anō te kaha o te rerenga hiko e uru ana ki ētahi atu mata he āhua koretake, 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 reira he utu hiko, kāore e whakawhirinaki ki te āhua o te mata, ā, ko te rahi ko Φ = 4 π k Q = Q/ε o.
E whakaatu ana te ahua i te taha i ngā utu hiko e rua kei roto i tētahi mata kua kati. Q1 me te Q2 he pai, nō reira mēnā he 
I te mea kua tuhia, 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 te mata kua kati. Nā te mea ko ngā rārangi o te āpure hiko o te utu Q1 he ōrite ki te rerenga hiko Φ = Q1/εo me ngā rārangi o te papa hiko o te utu Q2
he rite ki te rerenga hiko Φ = Q 2 /ε o , ko te tapeke o ngā rārangi mara hiko he rite ki Q 1 /ε o + Q 2 /ε o = 1 / ε o (Q 1 + Q 2 ).
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 kupenga = 1/ε o (Q kupenga) ———- Whārite o te ture a Gauss
Ko te kupenga Q te tapeke o te utu hiko kei roto i tētahi mata kua kati. Mēnā he utu hiko kei waho o te mata kua kati, kāore te utu e tātaihia nā te mea he kore te rerenga hiko e puta mai ana. He kore te rerenga hiko nā te mea ka uru ngā rārangi o te mara hiko e puta mai ana i te utu ki roto i te mata kua kati, kātahi ka puta anō.
Ko te mata kati o te ture a Gauss ko te mata pohewa e whakaatuhia ana hei tatau i te rerenga hiko i puta mai i te utu hiko.
Ka taea te whakamahi i te ture a Gauss hei whakatau i tētahi mara hiko mēnā e mōhiotia ana te tohatoha o tētahi utu hiko, ka taea rānei te whakamahi hei whakatau i te tohatoha o ngā utu hiko mēnā e mōhiotia ana tētahi mara hiko. Kei roto i te tuhinga mō te whakamahinga o te ture a Gauss te whakamārama i te whakamahinga o te ture a Gauss hei whakaoti rapanga.
