Te Ture a Coulomb

I roto i te tuhinga mō utu hiko dan ngā momo utu hiko E whakamāramahia ana ko ngā utu hiko rite tonu ka pana tetahi i tetahi, ko ngā utu hiko rerekē ka kukume tetahi i tetahi. Arā, ka kukume ngā mea utu pai i ngā mea utu kino, ka pana ngā mea utu pai i ngā mea utu pai, ā, ka pana ngā mea utu kino i ngā mea utu kino. E whakaatu ana tēnei āhuatanga i te noho o te kaha hiko e pā ana ki ngā mea utu pai me ngā mea utu kino. He aha ngā āhuatanga e pā ana ki te nui o te kaha hiko i waenga i ngā mea utu hiko?

I whakahaerehia e te tohunga ahupūngao Wīwī a Charles Coulomb (1736–1806) he raupapa whakamātautau i ngā tau 1780 hei tirotiro i ngā āhuatanga e awe ana i te rahi o te kaha hiko i waenga i ngā mea e utua ana e te hiko. He rite te taputapu i whakamahia e Coulomb ki tā Cavendish i whakamahi ai hei tirotiro i te pūmau ā-papatipu, e kiia nei ko te taurite torsion. I tirotirohia e Coulomb te kaha hiko, nō reira i whakamahia e ia e rua ngā pōro whakarewa e utua ana e te hiko, i a Cavendish ia i tirotiro i te kaha ā-papatipu, nō reira i whakamahia e ia e rua ngā pōro papatipu kāore i utua e te hiko.

Te mahi a te tauine taipana  

 
E pā ana te mahi a te tauine taipana ki te kaupapa o te kaupapa taipana, te wā kaha rānei i roto i te upoko ngā hihiri hurihuri.
Ka whakamahia te mokowā i roto i te pauna takahuri hei ārai i te nekehanga o te hiko i runga i te pōro totoka ki te hau. Mā te tikanga e whai ake nei ka whakatauhia te nui o te hiko i runga i te pōro totoka. I te tīmatanga, ka whakakīia te pōro totoka A mā te arataki, mā te waku rānei. Ka honoa te pōro totoka A kua whakakīia te hiko ki te pōro totoka B e noho pūmau tonu ana mā te whakamahi i tētahi kaiārahi hiko kia wehea ōritetia te hiko o te pōro totoka A ki te pōro totoka B. Mena ko te nui o te hiko o te pōro totoka A he ½, ko te nui o te hiko o te pōro totoka B he ½. Muri iho, ka honoa te pōro totoka B me te pōro totoka C ki tētahi kaiārahi hiko kia wehea ōritetia te hiko o te pōro totoka B ki te pōro totoka C. Mena ko te nui o te hiko o te pōro totoka B he ¼, ko te nui o te hiko o te pōro totoka C he ¼. Mā tēnei ara ka whiwhihia te nui o te hiko me te momo hiko o te pōro totoka 1 me te pōro totoka 2.

He mea utu hiko te porowhita totoka 1 me te porowhita totoka 2, ā, ka panaia tetahi ki tetahi mēnā he rite te utu hiko o ngā porowhita e rua, ka kukumea rānei tetahi ki tetahi mēnā he rerekē ngā utu hiko o ngā porowhita e rua. Mā te noho o tētahi kaha kukume, kaha pana rānei i waenganui i ngā porowhita totoka e rua e utu hiko ana ka huri te porowhita totoka 2. Ka inehia te koki haere o te porowhita totoka 2 hei whakatau i te kaha hiko e pā ana ki ngā porowhita totoka e rua.

Ngā āhuatanga e pā ana ki te kaha hiko

I runga i ngā whakamātautau i whakahaerehia mā te whakamahi i te pauna torsion, i kitea e Coulomb ētahi mea.
– I tēnei whakamātautau, he rite tonu te tawhiti i waenganui i ngā pōro totoka e rua. Ina ko te nui o te utu hiko i runga i te pōro totoka 1 he 1, ā, ko te nui o te utu hiko i runga i te pōro totoka 2 he 1, ko te kaha hiko e pā ana ki ngā pōro totoka e rua he 1. Ina ko te nui o te utu hiko i runga i te pōro totoka 1 he 2, ā, ko te nui o te utu hiko i runga i te pōro totoka 2 he 4, ko te kaha hiko e pā ana ki ngā pōro totoka e rua. I whakatau a Coulomb ko te rahi o te kaha hiko e pā ana ki ngā pōro totoka e rua he rite ki te hua o te nui o te utu i runga i ngā pōro totoka e rua (F ≈ q₁ q₂).
– I tēnei whakamātautau, he rite tonu te nui o te utu i runga i ngā pōro totoka e rua. Mena ko te tawhiti i waenganui i ngā pōro totoka e rua he 1, ko te kaha hiko e pā ana ki ngā pōro totoka e rua he 1. Mena ko te tawhiti i waenganui i ngā pōro totoka e rua he 2, ko te kaha hiko e pā ana ki ngā pōro totoka e rua he ¼. I whakatau a Coulomb ko te rahi o te kaha hiko e pā ana ki ngā pōro totoka e rua he rite whakamuri ki te tapawhā o te tawhiti (F ≈ 1 / r²)

Te Ture a Coulomb

Ko te ture a Coulomb he ture ahupūngao e whakamārama ana i te whanaungatanga i waenga i te kaha hiko, te utu hiko, me te tawhiti i waenga i ngā utu. I titoa tēnei ture i runga i ngā whakamātautau a Coulomb, e ai ki te whakamārama i te tuhinga o mua.

Te Ture a Coulomb e kī ana ko te rahi o te kaha e pā ana ki tētahi matūriki e utua ana e te hiko ki tētahi atu matūriki e utua ana e te hiko he rite tonu ki te hua o te tapeke o ngā utu o ngā matūriki e rua, ā, he rite whakamuri ki te tapawhā o te tawhiti i waenganui i ngā matūriki e rua e utua ana e te hiko. Ka mahi tēnei kaha i runga i tētahi rārangi tika e hono ana i ngā matūriki e rua. He mea whakahē te kaha hiko mēnā he ōrite ngā utu hiko o ngā matūriki e rua, ā, he mea kukume te kaha hiko mēnā kāore i te ōrite ngā utu hiko o ngā matūriki e rua.

Ka taea te whakaatu i te ture a Coulomb i roto i te whārite pāngarau:
Whakaahuatanga tātai:
F₁₂ = te kaha hiko i waenganui i te matūriki 1 me te matūriki 2
q₁ = te maha o ngā utu matūriki 1
q₂ = te maha o ngā utu hiko o te matūriki 2
r₁₂ = te tawhiti i waenganui i te matūriki 1 me te matūriki 2
(pānuihia: epsilon kore) = 8,854 x 10^-12 C²/Nm²
k = (Te pūmau o Coulomb) = 9 x 10⁹ Nm²/C²
F₂₁ ko te kaha i tukuna e te utu q₂ i te utu q₁, ko F ia₁₂ ko te kaha i tukuna e te utu q₁ i te utu q₂. F₂₁ me F₁₂ te pana tetahi i tetahi ina ko te utu he q₁ me te q₂ he rite, ā, ka kukume tetahi i tetahi ina ko te utu he q₁ me te q₂ ehara i te momo kotahi.
F₂₁ me F₁₂ he ōrite te uara, he rerekē te ahunga, ā, he rerekē te pānga ki ngā mea, nō reira he takirua kaha mahi-tauhohenga ēnei kaha e rua.