Ngā Tauira Pātai e Matapaki ana i te Rerenga Aukume
He ariā nui te rerenga aukume i roto i te ahupūngao, inā koa i roto i te māramatanga ki te taunekeneke i waenga i ngā papa aukume me ngā kaiārahi hiko. Ka ine te rerenga aukume i te nui o te papa aukume e haere ana i roto i tētahi wāhi kua whakaritea, ā, ka whakaatuhia i roto i ngā waeine Weber (Wb). I roto i tēnei tuhinga, ka matapakihia e mātou ētahi tauira raruraru e pā ana ki te rerenga aukume me ā rātou otinga hei āwhina i te hōhonu ake o tō māramatanga ki tēnei ariā.
1. Te Mārama ki te Rerenga Aukume
Mā te pāngarau, ka taea te whakatakoto i te rerenga aukume (\(\Phi\)) e puta ana i tētahi horahanga (\(A\)) penei:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]
Kei hea:
– Ko te rerenga aukume i roto i a Weber (Wb) ko \(\Phi\),
– Ko te kiato rerenga aukume, te papa aukume rānei i Tesla (T), ko \(B\),
– Ko te horahanga i pāhia e te papa aukume i roto i ngā mita pūrua (m²),
– Ko te \(\theta\) te koki i waenganui i te papa aukume me te pūmau ki te horahanga.
Mena he poutū te papa aukume ki te papa (koki \(\theta = 0^\circ\)), kāti:
\[ \Phi = B \cdot A \]
Mena he whakarara te papa aukume ki te papa (koki \(\theta = 90^\circ\)), kāti:
\[ \Phi = 0 \]
2. Ngā Tauira Pātai me te Kōrero
Pātai 1: Te Rerenga Aukume i roto i te Papa e Tūhono ana ki te Papa Aukume
Pātai:
Kua whakatakotoria he porowhita waea porowhita, he 0,1 mita te whānui, poutū ki tētahi papa aukume ōrite o te 0,5 Tesla. Tātaihia te rerenga aukume e puta ana i te porowhita waea.
Kōrero:
E mōhiotia ana:
– \( r = 0.1 \, \kuputuhi{m} \)
– \( B = 0.5 \, \kuputuhi{T} \)
– \(\theta = 0^\circ\) (nā te mea he poutū)
Te horahanga o te porowhita porowhita:
\[ A = \pi r^2 = \pi (0.1)^2 = 0.01\pi \, \text{m}^2 \]
Te rerenga aukume:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]
\[ \Phi = 0.5 \, \kuputuhi{T} \times 0.01\pi \, \kuputuhi{m}^2 \times \cos(0^\circ) \]
\[ \Phi = 0.5 \whakareatia ki te 0.01\pi \whakareatia ki te 1 \]
\[ \Phi = 0.005\pi \, \text{Wb} \]
Nō reira, ko te rerenga aukume i roto i te koropiko waea he \(0.005\pi \, \text{Weber}\) tata ki te 0.0157 Weber rānei.
Pātai 2: Te Rerenga Aukume i tētahi Koki
Pātai:
He mata papatahi, e 2 mita pūrua te horahanga, kua whakatakotoria ki te koki o te 60 nekehanga ki tētahi papa aukume ōrite o te 0.3 Tesla. Tātaihia te rerenga aukume e puta ana i te mata.
Kōrero:
E mōhiotia ana:
– \( A = 2 \, m^2 \)
– \( B = 0.3 \, T \)
– \( \theta = 60^\circ \)
Te rerenga aukume:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]
\[ \Phi = 0.3 \, \text{T} \times 2 \, \text{m}^2 \times \cos(60^\circ) \]
\[ \Phi = 0.3 \times 2 \times \frac{1}{2} \]
\[ \Phi = 0.3 \, \text{Wb} \]
Nō reira, ko te rerenga aukume i roto i te papa ko \(0.3 \, \text{Weber}\).
Pātai 3: Ngā Huringa o te Rerenga Aukume me te Kaha Hiko Whakaoho (EMF)
Pātai:
Ka whakanohoia he waea tapawhā, he 0,5 mita te roa o te taha, ki roto i tētahi papa aukume ōrite o te 0,8 Tesla. Mēnā ka huri te papa aukume mai i te 0,8 Tesla ki te 0 Tesla i roto i te 2 hēkona, tatauhia te kaha hiko i puta mai i te nekehanga (EMF) i hangaia i roto i te waea.
Kōrero:
E mōhiotia ana:
– \( L = 0.5 \, m \) (roa taha)
– \( B_1 = 0.8 \, T \)
– \( B_2 = 0 \, T \)
– \( \Delta t = 2 \, s \)
Te horahanga o te porowhita tapawhā:
\[ A = L^2 = (0.5)^2 = 0.25 \, m^2 \]
Te huringa o te rerenga aukume (\(\Delta \Phi\)):
\[ \Delta \Phi = \Phi_2 – \Phi_1 \]
\[ \Phi_1 = B_1 \cdot A = 0.8 \, T \times 0.25 \, m^2 = 0.2 \, Wb \]
\[ \Phi_2 = B_2 \cdot A = 0 \times 0.25 \, m^2 = 0 \, Wb \]
\[ \Delta \Phi = 0 – 0.2 = -0.2 \, Wb \]
Ko te EMF whakaoho (\(\epsilon\)) i hangaia:
\[ \epsilon = – \frac{\Delta \Phi}{\Delta t} \]
\[ \epsilon = – \frac{-0.2 \, Wb}{2 \, s} \]
\[ \epsilon = 0.1 \, V \]
Nō reira, ko te EMF i whakaputahia i roto i te waea he 0.1 Volt.
Pātai 4: Kore Rerenga Aukume
Pātai:
Kei te whakatakotoria he porowhita waea, he 0,05 mita pūrua te horahanga, whakarara ki tētahi papa aukume ōrite o te 1,0 Tesla. Tātaihia te rerenga aukume e puta ana i te porowhita waea.
Kōrero:
E mōhiotia ana:
– \( A = 0.05 \, m^2 \)
– \( B = 1.0 \, T \)
– \(\theta = 90^\circ\) (nā te mea he whakarara)
Nā te mea he whakarara te papa aukume ki te papa, kāti:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]
\[ \Phi = 1.0 \, T \times 0.05 \, m^2 \times \cos(90^\circ) \]
\[ \Phi = 1.0 \whakareatia ki te 0.05 \whakareatia ki te 0 \]
\[ \Phi = 0 \, Wb \]
Nō reira, ko te rerenga aukume i roto i te koropiko waea ko \(0 \, \text{Weber}\).
Whakamutunga
He mea nui te mārama ki te ariā me te tatau i te rerenga aukume i roto i te ahupūngao, inā koa i roto i te ako i te hiko aukume. Ka ine te rerenga aukume i te kaha o te papa aukume e haere ana i roto i tētahi rohe, ā, ka pāngia e te rahi o te papa aukume, te horahanga o te rohe, me te koki i waenganui i te papa aukume me te āhua noa ki te horahanga. Mā te matapaki i ngā tauira i runga ake nei, e tūmanakohia ana ka pai ake tō māramatanga ki te tatau me te tātari i te rerenga aukume i raro i ngā āhuatanga rerekē. Mā te mahi tonu ka āwhina i te hohonu ake o tō māramatanga ki tēnei ariā.
