He tauira pātai kōrero mō te rahi o te EMF whakaohokia
Pendahuluan
Ko te kaha hiko whakaaweawe (EMF) he āhuatanga ā-tinana i kitea e Michael Faraday i te tau 1831. I kitea e Faraday ka taea e te hurihanga o te papa aukume i roto i te porowhita, i te koiri rānei o te ara iahiko te whakaputa i te iahiko hiko. Ka kiia tēnei āhuatanga ko te whakaaweawe hiko aukume, ā, koinei te pūtake mō ngā hangarau hou maha, pērā i ngā whakaputa hiko, ngā whakawhiti hiko, me ngā motuka hiko. Ka whakamāramahia e tēnei tuhinga ētahi tauira raruraru me te matapaki i te rahi o te EMF whakaaweawe, he mea tino whai hua, inā koa mō ngā ākonga e ako ana i te ahupūngao o te hiko me te aukume.
Ariā Taketake o te EMF Whakaoho
I mua i te ruku hohonu ki te tauira raruraru, he mea pai kia arotakehia te ariā taketake o te emf whakaoho. E kī ana te ture a Faraday ko te emf whakaoho i roto i te porowhita kawe he rite tonu ki te tere o te huringa o te rerenga aukume i roto i te porowhita. I roto i te pāngarau, ka taea te whakatakoto i te ture a Faraday penei:
\[ \mathcal{E} = – \frac{d\Phi}{dt} \]
kāore i te mana:
– Ko te EMF whakaoho (volts) te \( \mathcal{E} \)
– Ko te rerenga aukume (Weber, Wb) te \( \Phi \)
– Ko te wā (hēkona, s) ko te \( t \)
Ko te tohu kino i roto i te whārite e whakaata ana i te Ture a Lenz, e kī ana ko te ahunga o te iahiko i whakaohokia ka hanga he papa aukume e ātete ana ki te huringa o te rerenga aukume i puta ai.
Ngā Pātai Tauira me te Kōrero
Pātai 1: Koiri Kotahi
Pātai: Kua whakanohoia he koiri kotahi, he 0.02 m² te horahanga o te mata, ki roto i tētahi papa aukume ōrite he 0.5 T te rahi, e poutū ana ki te mata o te koiri. Ka taurite te kore o te papa aukume i roto i te 0.1 hēkona. Tātaihia te rahi o te EMF i puta mai i roto i te koiri.
Kōrero:
E mōhiotia ana:
– Te horahanga o te mata o te koiri \( A = 0.02 \, \text{m}^2 \)
– Te rahi o te papa aukume \( B = 0.5 \, \text{T} \)
– Te wā whakarerekētanga o te mara \( \Delta t = 0.1 \, \text{s} \)
Te huringa o te rerenga aukume:
\[ \Delta \Phi = B \ngā A \]
\[ \Delta \Phi = 0.5 \, \text{T} \times 0.02 \, \text{m}^2 \]
\[ \Delta \Phi = 0.01 \, \text{Wb} \]
Te rahi o te EMF i whakaohokia:
\[ \mathcal{E} = – \frac{\Delta \Phi}{\Delta t} \]
\[ \mathcal{E} = – \frac{0.01 \, \text{Wb}}{0.1 \, \text{s}} \]
\[ \mathcal{E} = -0.1 \, \text{V} \]
Nā te mea ko te rahi o te EMF te mea e pātaihia ana (me te kore e aro ki te tohu):
\[ |\mathcal{E}| = 0.1 \, \kuputuhi{V} \]
Pātai 2: Koiri me ngā Hurihanga N
Pātai: E 100 ngā hurihanga o tētahi koiri, ā, ko tōna horahanga mata he 0.03 m². Kei roto tēnei koiri i tētahi papa aukume ōrite o te 0.4 T e poutū ana ki te koiri. Mena ka piki te papa aukume ki te 1.2 T i roto i te 0.4 hēkona, tatauhia te emf whakaoho toharite i puta i roto i te koiri.
Kōrero:
E mōhiotia ana:
– Te maha o ngā takahuri \( N = 100 \)
– Te horahanga o te mata o te koiri \( A = 0.03 \, \text{m}^2 \)
– Te huringa o te papa aukume \( \Delta B = 1.2 \, \text{T} – 0.4 \, \text{T} \)
– Te wā whakarerekētanga o te mara \( \Delta t = 0.4 \, \text{s} \)
Te huringa o te rerenga aukume i ia hurihanga:
\[ \Delta \Phi = A \times \Delta B \]
\[ \Delta \Phi = 0.03 \, \text{m}^2 \times (1.2 \, \text{T} – 0.4 \, \text{T}) \]
\[ \Delta \Phi = 0.03 \, \text{m}^2 \times 0.8 \, \text{T} \]
\[ \Delta \Phi = 0.024 \, \text{Wb} \]
Te huringa rerenga katoa mō ngā hurihanga N:
\[ \Delta \Phi_{\kuputuhi{katoa}} = N \ngā \Delta \Phi \]
\[ \Delta \Phi_{\kuputuhi{katoa}} = 100 \times 0.024 \, \kuputuhi{Wb} \]
\[ \Delta \Phi_{\kuputuhi{katoa}} = 2.4 \, \kuputuhi{Wb} \]
Te rahi o te EMF i whakaohokia:
\[ \mathcal{E} = – \frac{\Delta \Phi_{\text{tapeke}}}{\Delta t} \]
\[ \mathcal{E} = – \frac{2.4 \, \text{Wb}}{0.4 \, \text{s}} \]
\[ \mathcal{E} = -6 \, \text{V} \]
Nā te mea ko te rahi o te EMF te mea e pātaihia ana (me te kore e aro ki te tohu):
\[ |\mathcal{E}| = 6 \, \kuputuhi{V} \]
Pātai 3: Te Nekehanga o te Koiri i roto i te Papa Aukume
Pātai: He porowhita tapawhā rite, e 50 ngā hurihanga, e 4 cm te roa, e 2 cm te whānui, kua whakanohoia ki roto i tētahi papa aukume ōrite o te 0.3 T e whakarara ana ki te roa o te porowhita. Mena ka neke te porowhita i waho o te papa aukume i te tere pumau o te 5 cm/s, he aha te EMF i puta mai i roto i te porowhita?
Kōrero:
E mōhiotia ana:
– Te maha o ngā takahuri \( N = 50 \)
– Roa \( l = 0.04 \, \text{m} \)
– Whānui \( w = 0.02 \, \text{m} \)
– Te rahi o te papa aukume \( B = 0.3 \, \text{T} \)
– Te tere putanga o te papa aukume \( v = 0.05 \, \text{m/s} \)
Ko te kaha hikohiko i runga i te koiri e neke ana i roto i te papa aukume ka hoatuhia e:
\[ \mathcal{E} = B lv \]
Nā te mea e N ngā hurihanga o te koiri, ko te tapeke o te EMF i puta ko:
\[ \mathcal{E}_{\text{total}} = NB lv \]
\[ \mathcal{E}_{\text{tapeke}} = 50 \times 0.3 \, \text{T} \times 0.04 \, \text{m} \times 0.05 \, \text{m/s} \]
\[ \mathcal{E}_{\text{total}} = 50 \times 0.0006 \, \text{V} \]
\[ \mathcal{E}_{\text{tapeke}} = 0.03 \, \text{V} \]
Whakamutunga
Mā te matapakinga o ngā tauira raruraru i runga ake nei ka whakaatuhia te huarahi e taea ai te tatau i te emf whakaaweawe mai i ngā huringa o te rerenga aukume, mai i te nekehanga rānei o te koiri i roto i te papa aukume. He mea nui tēnei ariā ki te hiko aukume, ā, he maha ngā whakamahinga i roto i te hangarau. Mā te mārama ki te tatau tika i te emf whakaaweawe mā roto i ngā raruraru mahi ka tino āwhina i ngā ākonga ki te mōhio ki tēnei rauemi me te whakamahi i roto i ngā mara maha.
