Ngā Tauira Pātai me te Kōrero mō ngā Mara Hiko
He ariā taketake te papa hiko i roto i te ahupūngao e whakamārama ana i te pānga o tētahi mea e utua ana he hiko ki te wāhi e karapoti ana. Ko te papa hiko te kaha e pā ana ki ia pūwāhi o te wāhi e te aroaro o taua utu. Hei mārama ake i tēnei ariā, me mahi whakaharatau nui. Kei raro nei ngā tauira raruraru me ngā kōrero taipitopito mō ngā papa hiko.
Tauira Pātai 1: Te Tatau i te Rahi o te Papa Hiko i tētahi Pūwāhi
Pātai:
E rua ngā utu pūwāhi \( q_1 = +4 \mu C \) me \( q_2 = -8 \mu C \) kua whakanohoia ki ngā taunga (0, 0) me (0, 2) mita. Tātaihia te rahi me te ahunga o te papa hiko i te pūwāhi A kei (0, 1) mita.
Kōrero:
1. Tāutuhia te tawhiti i waenganui i te pūwāhi A me ngā utu e rua:
– Ko te tawhiti mai i \( q_1 \) ki te pūwāhi A he 1 mita.
– Ko te tawhiti mai i \( q_2 \) ki te pūwāhi A he 1 mita.
2. Tātaihia te āpure hiko e pā ana ki ia utu i te pūwāhi A:
Ko te āpure hiko e pā ana ki te utunga pūwāhi \( q \) i te tawhiti \( r \) ko:
\[ E = \frac{k \cdot |q|}{r^2} \]
mō \( q_1 \) me \( q_2 \):
\[ E_1 = \frac{9 \times 10^9 \cdot 4 \times 10^{-6}}{1^2} = 36 \times 10^3 \, \text{N/C} \]
\[ E_2 = \frac{9 \times 10^9 \cdot 8 \times 10^{-6}}{1^2} = 72 \times 10^3 \, \text{N/C} \]
3. Whakatauhia te ahunga o te papa hiko:
Nā te mea he utu pai a \( q_1 \), ka anga atu tōna papa hiko ki tawhiti i te utu, nō reira kei te ahunga-y pai a \( E_1 \) (ki runga).
Nā te mea he utu kino a \( q_2 \), kei te anga whakamua te mara hiko ki te utu, nō reira kei te ahunga-y kino a \( E_2 \) (ki raro).
4. Tātaihia te hua o te mara hiko:
Nā te mea kei runga a \( E_1 \) me \( E_2 \) i te rārangi tika kotahi, ka taea e tātou te tango i ngā mara hiko:
\[ E_{\text{tapeke}} = E_2 – E_1 \]
\[ E_{\kuputuhi{katoa}} = 72 \times 10^3 – 36 \times 10^3 \]
\[ E_{\text{tapeke}} = 36 \times 10^3 \, \text{N/C} \]
Ko te ahunga o te papa hiko e anga ana ki te tuaka-y kino (ki raro).
Tauira Pātai 2: Te Tātai i te Pūmanawa Hiko i tētahi Pūwāhi
Pātai:
E rua ngā utu pūwāhi \( q_1 = +2 \mu C \) me \( q_2 = +3 \mu C \) kua whakanohoia ki ngā taunga (0, 0) me (4, 0) mita. Tātaihia te pūmanawa hiko i te pūwāhi B kei (2, 0) mita.
Kōrero:
1. Tāutuhia te tawhiti i waenganui i te pūwāhi B me ngā utu e rua:
– E 1 mita te tawhiti mai i \( q_2 \) ki te pūwāhi B.
– E 2 mita te tawhiti mai i \( q_2 \) ki te pūwāhi B.
2. Tātaihia te pūmanawa hiko e pā ana ki ia utu i te pūwāhi B:
Ko te pūmanawa hiko e pā ana ki te utunga pūwāhi \( q \) i te tawhiti \( r \) ko:
\[ V = \frac{k \cdot q}{r} \]
mō \( q_1 \) me \( q_2 \):
\[ V_1 = \frac{9 \times 10^9 \cdot 2 \times 10^{-6}}{2} = 9 \times 10^3 \, \text{V} \]
\[ V_2 = \frac{9 \times 10^9 \cdot 3 \times 10^{-6}}{2} = 13.5 \times 10^3 \, \text{V} \]
3. Tātaihia te pūmanawa hiko katoa i te pūwāhi B:
He rahinga tauine te pūmanawa hiko, nō reira ko te pūmanawa katoa ko te tapeke o ngā pūmanawa:
\[ V_{\kuputuhi{katoa}} = V_1 + V_2 \]
\[ V_{\kuputuhi{katoa}} = 9 \times 10^3 + 13.5 \times 10^3 \]
\[ V_{\text{tapeke}} = 22.5 \times 10^3 \, \text{V} \]
Tauira 3: Papa Hiko i roto i tētahi Rauemi Whakakore Hiko
Pātai:
Mena ka whakanohoia he utu \( q = 5 \mu C \) ki waenganui o tētahi porowhita tuwhera he 3 mita te whānui e kī tonu ana i tētahi matū hiko me tētahi pūmau matū \( \kappa = 2 \). Tātaihia te āpure hiko i te tawhiti o te 2 mita mai i waenganui o te porowhita.
Kōrero:
1. Ko te tātai mō te papa hiko i roto i tētahi rauemi ārai-hiko:
Ko te papa hiko \( E \) i te tawhiti \( r \) i roto i tētahi rauemi dielectric ko:
\[ E = \frac{q}{4 \pi \epsilon_0 \kappa r^2} \]
ko \( \epsilon_0 = 8.85 \times 10^{-12} \) F/m.
2. Whakauruhia ngā uara kua hoatu:
\[ E = \frac{5 \times 10^{-6}}{4 \pi \cdot 8.85 \times 10^{-12} \cdot 2 \cdot (2)^2} \]
\[ E = \frac{5 \times 10^{-6}}{4 \pi \cdot 8.85 \times 10^{-12} \cdot 8} \]
\[ E = \frac{5 \times 10^{-6}}{8 \cdot 3.54 \times 10^{-10}} \]
\[ E = \frac{5 \times 10^{-6}}{28.32 \times 10^{-10}} \]
\[ E = 1.77 \whakareatia ki te 10^4 \, \kuputuhi{N/C} \]
Whakamutunga
Mā roto i ngā tauira i runga ake nei, ka mārama ake tātou ki te ariā o ngā mara hiko. Kei roto i tēnei ko te rahi o te mara hiko i tētahi pūwāhi nā ngā utu maha, te tatau i te pūmanawa hiko, me te mara hiko i roto i ngā rauemi dielectric. He mea nui te māramatanga pakari ki tēnei ariā nā te mea he maha ngā āhuatanga ā-tinana ka taea te whakamārama e ngā mara hiko, me ō rātou tono i roto i ngā hangarau hou. Me haere tonu te whakaharatau me ngā momo raruraru kia tino mōhio ai koe ki tēnei ariā.
