Ngā Tauira Pātai e Matapaki ana i te Kaha Aukume i runga i te Waea Kawe-Au
He āhuatanga ā-tinana te kaha aukume e pā ana ki te taunekeneke i waenga i te papa aukume me te iahiko hiko. E whakaahuatia ana tēnei āhuatanga e te ture a Ampère, e kī ana ka taea e te iahiko e rere ana i roto i te waea te whakaputa i tētahi papa aukume. Ka whakamāramahia e tēnei tuhinga ngā tauira me te matapaki i te kaha aukume i roto i te waea e kawe ana i te iahiko, hei āwhina i a koe ki te mārama ake ki tēnei ariā.
Pendahuluan
Kua mōhiotia te āhuatanga o te aukumetanga mai anō i ngā wā onamata, engari kāore i kitea he whakamārama pūtaiao mō te taunekeneke i waenga i ngā iahiko hiko me ngā papa aukume tae noa ki te rautau 19. Ko Hans Christian Ørsted te tuatahi ki te kite ka taea e ngā iahiko te whakaputa papa aukume. Nō muri mai, ka tautokona e André-Marie Ampère tēnei kitenga mā te whakatakoto i te mea e mōhiotia nei ko te Ture a Ampère.
Ngā Ariā Taketake
1. Te Ture Biot-Savart
Ka taea te tatau i te papa aukume i hangaia e tētahi huānga hiko iti mā te whakamahi i te ture Biot-Savart:
\[
dB = \frac{\mu_0}{4\pi} \cdot \frac{I \cdot (d\mathbf{l} \times \mathbf{r})}{r^3}
\]
Kei hea:
– \(dB\) = huānga papa aukume
– \(\mu_0\) = te uruhanga korehau \((4\pi \times 10^{-7} \text{Tm/A})\)
– \(I\) = Iahiko hiko (A)
– \(d\mathbf{l}\) = huānga roa waea (m)
– \(\mathbf{r}\) = te ine tūnga whanaunga i waenga i te huānga o nāianei me te pūwāhi tirotiro (m)
2. Te kaha o Lorentz
Ka pāngia te waea e mau ana i te iahiko \(I\) ka whakanohoia ki roto i te papa aukume \(B\) e te kaha \(F\) e homai ana e:
\[
\mathbf{F} = I \cdot (\mathbf{L} \times \mathbf{B})
\]
Kei hea:
– \(\mathbf{F}\) = Te kaha aukume (N)
– \(I\) = Iahiko hiko (A)
– \(\mathbf{L}\) = Te roa o te waea i roto i te papa aukume (m)
– \(\mathbf{B}\) = Papa aukume (T)
Ngā Pātai Tauira me te Kōrero
Pātai 1:
Kua whakanohoia he waea tika, 0.5 mita te roa, ki roto i tētahi papa aukume ōrite o te 0.2 Tesla. Mēnā he iahiko hiko kei te waea o te 3 A, ā, he poutū te ahunga o te iahiko ki te papa aukume, tatauhia te rahi o te kaha Lorentz e pā ana ki te waea.
Otinga:
Mā te whakamahi i te whārite kaha Lorentz, ka whiwhi tātou:
\[
\mathbf{F} = I \cdot (\mathbf{L} \times \mathbf{B})
\]
Ka taea e tātou te tautuhi i te ahunga o te iahiko \(I\) e whakarara ana ki \(\mathbf{L}\) me te papa aukume \(B\) e poutū ana ki \(\mathbf{L}\).
\[
|\mathbf{F}| = I \cdot L \cdot B \cdot \sin\theta
\]
Nā te mea he poutū te iahiko me te papa aukume (\(\theta = 90^\circ\)), kāti \(\sin 90^\circ = 1\), nō reira:
\[
|\mathbf{F}| = 3 \, \text{A} \cdot 0.5 \, \text{m} \cdot 0.2 \, \text{T} \cdot 1 = 0.3 \, \text{N}
\]
Pātai 2:
He waea porowhita, he 0.1 mita te whānui, e mau ana i te iahiko hiko o te 2 A. Tāutuhia te papa aukume kei waenganui o te porowhita.
Otinga:
Mā te whakamahi i te tātai aukume i waenganui o te porowhita porowhita:
\[
B = \frac{\mu_0 I}{2R}
\]
me:
– \(\mu_0 = 4\pi \times 10^{-7} \, \text{Tm/A}\)
– \(I = 2 \, \kuputuhi{A}\)
– \(R = 0.1 \, \kuputuhi{m}\)
Nā reira:
\[
B = \frac{(4\pi \times 10^{-7} \, \text{Tm/A} \times 2 \, \text{A})}{2 \times 0.1 \, \text{m}}
= \frac{4\pi \times 10^{-7} \times 2}{0.2} \, \text{T}
= 4\pi \times 10^{-6} \, \text{T}
tata ki te 1.26 wā 10^{-5}
\]
Pātai 3:
E rua ngā waea tika whakarara, he roa \(L\) kei te tawhiti \(d\) tetahi i tetahi. Mēnā he iahiko \(I\) kei ia waea i te taha whakamuri, tātaihia te kaha mō ia wae roa e mahi ana i waenganui i ngā waea e rua.
Otinga:
Te kaha mō ia wae roa i waenganui i ngā waea whakarara e rua e kawe ana i te iahiko:
\[
f = \frac{\mu_0 I_1 I_2}{2\pi d}
\]
Nā te mea he ōrite ngā ia, ā, he rerekē te ahunga:
\[
f = \frac{\mu_0 I^2}{2\pi d}
\]
Hei tauira:
– \(\mu_0 = 4\pi \times 10^{-7} \, \text{Tm/A}\)
– \(I_1 = I_2 = I\)
– Ko te \(d\) te tawhiti i waenganui i ngā waea.
Mā te whakakapi i ngā uara ki te tātai, ka whiwhi tātou:
\[
f = \frac{(4\pi \times 10^{-7}) \, I^2}{2\pi d}
= \frac{2 \times 10^{-7} I^2}{d} \, \text{N/m}
\]
Whakamutunga
He mea nui te mārama ki te taunekeneke i waenga i ngā papa aukume me ngā iahiko hiko ki ngā hangarau hou maha, mai i ngā motuka hiko ki ngā whakaputa hiko. Mā te mārama ki ngā ariā o te kaha Lorentz, te ture Biot-Savart, me te whakamahinga o ngā tātai papa aukume, ka taea e tātou te whakamahi i tēnei mōhiotanga ki ngā momo raruraru me ngā āhuatanga o ia rā. Ko te kaupapa o tēnei tuhinga he whakarato i tētahi turanga pakari mō te mārama me te whakaoti rapanga e pā ana ki ngā kaha aukume i roto i ngā waea e kawe ana i te iahiko.
