Tauira o tētahi Pātai Kōrero mō tētahi Waea Porowhita e Kawe Ana i te Ia Hiko
Pendahuluan
He mea nui te waea takai e mau ana i te au hiko i roto i ngā mahi maha o te ahupūngao me te miihini hiko. He mea nui te mārama ki ngā mātāpono me ngā tataunga taketake o ngā papa aukume e whakaputaina ana e tēnei waea i roto i ngā momo mara, mai i te hoahoa motuka hiko ki ngā pūoko papa aukume. Ka tūhuratia e tēnei tuhinga ētahi tauira raruraru me ā rātou otinga hei āwhina i ngā kaipānui ki te mārama ki ngā mātāpono taketake o te waea takai e mau ana i te au hiko.
Papa Aukume e te Waea Pōkai
Ture Biot-Savart
Ko te ture Biot-Savart te pūtake mō te tatau i te papa aukume huri noa i te waea e kawe ana i te iahiko. Ko te whakatakotoranga taketake o te ture Biot-Savart e whai ake nei:
\[
d\mathbf{B} = \frac{\mu_0}{4\pi} \cdot \frac{I d\mathbf{l} \times \mathbf{\hat{r}}}{r^2}
\]
kāore i te mana:
– Ko te papa aukume te \( \mathbf{B} \)
– Ko te uruhanga korehau \( \mu_0 \) (\( 4\pi \times 10^{-7} \ \text{H/m} \))
– Ko te iahiko hiko te \( I \)
– Ko te \( d\mathbf{l} \) he wāhanga iti o te waea
– Ko \( \mathbf{\hat{r}} \) he whārite wae i te ahunga mai i te huānga waea ki te pūwāhi tirotiro
– Ko te \( r \) te tawhiti i waenganui i te huānga waea me te pūwāhi tirotiro
Waea Takai Kotahi
Ko te papa aukume i waenganui o te koropiko waea porowhita me te radius \( R \) me te au \( I \) ko:
\[
B = \frac{\mu_0 I}{2R}
\]
Tauira Pātai 1
Pātai: Tātaihia te papa aukume kei waenganui o tētahi koropiko waea he 10 cm te whānui e kawe ana i te iahiko o te 5 A.
Kōrero:
Whakamahia te tātai āpure aukume mō te porowhita kotahi,
\[
B = \frac{\mu_0 I}{2R}
\]
Kei hea:
– \( \mu_0 = 4\pi \times 10^{-7} \ \text{H/m} \)
– \( I = 5 \ \kuputuhi{A} \)
– \( R = 0.1 \ \text{m} \) (nā te mea 10 cm = 0.1 m)
Mā te whakakapi i ēnei uara,
\[
B = \frac{4\pi \times 10^{-7} \times 5}{2 \times 0.1}
\]
\[
B = \frac{20\pi \times 10^{-7}}{0.2}
\]
\[
B = 2\pi \times 10^{-6} \ \text{T}
\]
\[
B = 6.28 \times 10^{-6} \ \text{T}
\]
Nō reira, ko te papa aukume i waenganui o te koropiko waea ko \( 6.28 \ \mu T \).
Tauira Pātai 2
Pātai: He pōkai e 20 ngā takahuri, ā, he 10 cm te whānui o te pōkai, e mau ana i te iahiko o te 5 A. Tātaihia te papa aukume kei waenganui o te pōkai.
Kōrero:
Ko te papa aukume mō te koiri o ngā hurihanga N ko:
\[
B = \frac{\mu_0 NI}{2R}
\]
Kei hea:
– \( N = 20 \)
– \( I = 5 \ \kuputuhi{A} \)
– \( R = 0.1 \ \kuputuhi{m} \)
– \( \mu_0 = 4\pi \times 10^{-7} \ \text{H/m} \)
Mā te whakakapi i ēnei uara,
\[
B = \frac{4\pi \times 10^{-7} \times 20 \times 5}{2 \times 0.1}
\]
\[
B = \frac{400\pi \times 10^{-7}}{0.2}
\]
\[
B = 20\pi \times 10^{-6} \ \text{T}
\]
\[
B = 62.8 \times 10^{-6} \ \text{T}
\]
Nō reira, ko te papa aukume i waenganui o te koiri ko \( 62.8 \ \mu T \).
Waea Porowhita i tētahi Koki
Ki te tapahia he koropiko waea e kawe ana i te iahiko i tētahi koki, ka puta he papa aukume rerekē i taua wāhanga o te koropiko. Hei tauira, mō te haurua porowhita, ko te papa aukume he haurua o te papa aukume katoa, me whakauru atu anō mō ngā otinga uaua.
Tauira Pātai 3
Pātai: Tātaihia te papa aukume kei waenganui o tētahi waea porowhita e huri noa ana i te haurua porowhita (180 nekehanga), me te radius o te 10 cm me te iahiko o te 5 A.
Kōrero:
Mō te haurua porowhita, ko te papa aukume i waenganui ko te haurua o te papa aukume katoa:
\[
B = \frac{1}{2} \cdot \frac{\mu_0 I}{2R}
\]
Kei hea:
– \( \mu_0 = 4\pi \times 10^{-7} \ \text{H/m} \)
– \( I = 5 \ \kuputuhi{A} \)
– \( R = 0.1 \ \kuputuhi{m} \)
Mā te whakakapi i ēnei uara,
\[
B = \frac{1}{2} \cdot \frac{4\pi \times 10^{-7} \times 5}{2 \times 0.1}
\]
\[
B = \frac{1}{2} \times 2\pi \times 10^{-6} \ \text{T}
\]
\[
B = \pi \times 10^{-6} \ \text{T}
\]
\[
B = 3.14 \times 10^{-6} \ \text{T}
\]
Nō reira, ko te papa aukume i waenganui o te waea haurua porowhita ko \( 3.14 \ \mu T \).
Te Katinga
Mā ngā tauira i runga ake nei, ko te tumanako ka pai ake te māramatanga o ngā kaipānui ki te tatau i te papa aukume e puta mai ana i tētahi waea takai e mau ana i te iahiko hiko. He tino whai hua tēnei māramatanga i roto i ngā tono hangarau me ngā rangahau pūtaiao, inā koa i roto i ngā mara o te aukume hiko me te miihini hiko.
