Tauira o ngā Pātai Kaha o te Papa Hiko
Ko te kaha o te mara hiko he ariā taketake i roto i te ahupūngao e whakaahua ana i te kaha o te mara hiko i tētahi wāhi motuhake o te wāhi. Ka puta ngā mara hiko i ngā utu hiko, ā, ka taea e rātou te awe i ētahi atu utu i roto i taua mara. Kia pai ake ai te mārama ki tēnei ariā, me titiro tātou ki ētahi tauira raruraru e pā ana ki te kaha o te mara hiko me pēhea te whakaoti i aua raruraru.
Ngā Kaupapa Taketake o ngā Mara Hiko
I mua i te urunga atu ki ngā tauira raruraru, me arotake tātou i te ariā taketake o ngā mara hiko. Ko te kaha o te mara hiko (\(E\)) i tētahi pūwāhi i te wāhi ka tautuhia ko te kaha (\(F\)) mō ia wae utu (\(q\)) e pāngia ana e tētahi utu whakamātautau iti i taua pūwāhi:
\[ E = \frac{F}{q} \]
Dimana:
– Ko te kaha o te mara hiko (N/C, V/m rānei) te \(E\),
– Ko te kaha hiko e pāngia ana e te utu (N) ko \(F\),
– Ko te rahi o te utu whakamātautau (C) ko \(q\).
Mena ko te pūtake o te papa hiko he utu pūwāhi \(Q\), ko te kaha o te papa hiko i te tawhiti \(r\) mai i te utu ka hoatuhia e te whārite:
\[ E = \frac{k \cdot |Q|}{r^2} \]
Dimana:
– Ko te pūmau Coulomb te \(k\) (\(8.99 \times 10^9 \, \text{N m}^2/\text{C}^2\)),
– Ko te utu pūtake (C) te \(Q\),
– Ko te \(r\) te tawhiti mai i te pūtake utu ki te pūwāhi tirotiro (m).
Tauira Pātai 1: Papa Hiko mā te Utu Pūwāhi
Pātai: Kei te pūtake (0,0) te utu \(Q\) o te \(5 \times 10^{-6} \, \text{C}\). Tātaihia te kaha o te papa hiko i te tawhiti o te 2 mita mai i te utu.
Otinga:
Mai i te whārite o te mara hiko mā te utu pūwāhi, ka taea e tātou te tatau i te kaha o te mara hiko penei:
\[ E = \frac{k \cdot |Q|}{r^2} \]
Tāuruhia ngā uara o \(k\), \(Q\), me \(r\):
\[ E = \frac{8.99 \times 10^9 \times 5 \times 10^{-6}}{2^2} \]
\[ E = \frac{8.99 \times 10^9 \times 5 \times 10^{-6}}{4} \]
\[ E = \frac{44.95 \times 10^3}{4} \]
\[ E = 11.2375 \whakareatia ki te 10^3 \]
\[ E = 11,237.5 \, \text{N/C} \]
Nō reira, ko te kaha o te papa hiko i te tawhiti o te 2 mita mai i te utu ko \(11,237.5 \, \text{N/C}\).
Tauira 2: Te Taupatupatu o ngā Papa Hiko
Pātai: E rua ngā utu hiko, \(Q_1 = 4 \times 10^{-6} \, \text{C}\) me \(Q_2 = -3 \times 10^{-6} \, \text{C}\) kua whakatakotoria ki te tawhiti o te 3 mita te tawhiti tetahi i tetahi. Tātaihia te kaha o te papa hiko i waenganui i ngā utu hiko e rua.
Otinga:
Tuatahi, ka tatauhia e tātou te āpure hiko e whakaputaina ana e ia utu i waenganui.
Hei utu \(Q_1\):
\[ r_1 = \frac{3}{2} = 1.5 \, \text{m} \]
\[ E_1 = \frac{k \cdot |Q_1|}{r_1^2} \]
\[ E_1 = \frac{8.99 \times 10^9 \times 4 \times 10^{-6}}{1.5^2} \]
\[ E_1 = \frac{35.96 \times 10^3}{2.25} \]
\[ E_1 = 15.9822 \whakareatia ki te 10^3 \]
\[ E_1 = 15,982.2 \, \text{N/C} \]
Hei utu \(Q_2\):
\[ r_2 = 1.5 \, \kuputuhi{m} \]
\[ E_2 = \frac{k \cdot |Q_2|}{r_2^2} \]
\[ E_2 = \frac{8.99 \times 10^9 \times 3 \times 10^{-6}}{1.5^2} \]
\[ E_2 = \frac{26.97 \times 10^3}{2.25} \]
\[ E_2 = 11.9822 \whakareatia ki te 10^3 \]
\[ E_2 = 11,982.2 \, \text{N/C} \]
Nā te mea he pai a \(Q_1\) ā, he kino a \(Q_2\), ka hoki whakamuri ō rāua mara hiko i waenganui. Nō reira, ka tāpirihia e mātou ngā mara hiko e rua:
\[ E = E_1 + E_2 \]
\[ E = 15,982.2 + 11,982.2 \]
\[ E = 27,964.4 \, \text{N/C} \]
Nō reira, ko te kaha o te papa hiko i waenganui i ngā utu e rua ko \(27,964.4 \, \text{N/C}\).
Tauira 3: Papa Hiko e te Dipole
Pātai: E rua ngā utu o tētahi pou hiko \(\pm 4 \times 10^{-6} \, \text{C}\) he 1 cm te tawhiti. Tātaihia te kaha o te mara hiko i tētahi pūwāhi 1 mita mai i te pokapū o te pou i runga i te tuaka o te pou.
Otinga:
Ko te kaha o te papa hiko i te tuaka o te dipole (mō ngā tawhiti e nui ana te rahi ki te whakataurite ki te tawhiti i waenga i ngā utu dipole) ka hoatuhia e:
\[ E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{2p}{r^3} \]
Ko \(p\) te autō hiko rua-pole (\(p = q \cdot d\)), ko \(d\) te tawhiti i waenga i ngā utu rua-pole, ā, ko \(r\) te tawhiti mai i te pokapū o te rua-pole ki te pūwāhi tirotiro.
Tuatahi, tatauhia te wā rua-ira:
\[ p = q \cdot d \]
\[ p = 4 \times 10^{-6} \cdot 0.01 \]
\[ p = 4 \times 10^{-8} \, \text{C m} \]
Kātahi ka tatau i te kaha o te mara hiko:
\[ E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{2p}{r^3} \]
\[ E = \frac{8.99 \times 10^9}{1} \cdot \frac{2 \times 4 \times 10^{-8}}{1^3} \]
\[ E = 8.99 \times 10^9 \cdot 8 \times 10^{-8} \]
\[ E = 7.192 \whakareatia ki te 10^2 \]
\[ E = 719.2 \, \text{N/C} \]
Nō reira, ko te kaha o te papa hiko i te pūwāhi 1 mita mai i te pokapū o te rua i runga i te tuaka rua ko \(719.2 \, \text{N/C}\).
Whakamutunga
He mea nui te mārama ki te kaha o te mara hiko i roto i te ahupūngao me ōna tono. E whakaatu ana ngā tauira raruraru i runga ake nei me pēhea te whakamahi i ngā mātāpono taketake o ngā mara hiko hei tatau i ngā kaha o te mara i roto i ngā whirihoranga utu rerekē. He tino āwhina ngā raruraru whakaharatau pēnei i ēnei ki te mārama ki te ariā me te tono o te ture a Coulomb me te taupatupatu mara hiko. Mā te mārama me te whakaharatau i ētahi atu raruraru, ka taea e tātou te whakahōhonu ake i tō tātou māramatanga ki ngā taunekeneke hiko i roto i ngā pūnaha rerekē.
