Laʻana o kahi Nīnau Kūkākūkā ma luna o kahi Uea Pōʻai e Lawe Ana i ke Au Uila
Pendahuluan
He mea koʻikoʻi ka uea ʻōwili e lawe ana i kahi au uila i nā noi he nui i ka physics a me ka ʻenekinia uila. He mea nui ka hoʻomaopopo ʻana i nā kumumanaʻo kumu a me nā helu ʻana o nā kahua magnetic i hana ʻia e kēia uea i nā ʻano kahua like ʻole, mai ka hoʻolālā ʻana o ka motika uila a hiki i nā mea ʻike kahua magnetic. Ke nānā nei kēia ʻatikala i kekahi mau pilikia hoʻohālike a me kā lākou mau hoʻonā e kōkua i ka poʻe heluhelu e hoʻomaopopo i nā kumumanaʻo kumu o kahi uea ʻōwili e lawe ana i kahi au uila.
Kahua Magnetic e kahi Uea ʻōwili
Ke Kānāwai Biot-Savart
ʻO ke kānāwai Biot-Savart ke kumu no ka helu ʻana i ke kahua magnetic a puni kahi uea e lawe ana i ke au. ʻO ke ʻano kumu o ke kānāwai Biot-Savart penei:
\[
d\mathbf{B} = \frac{\mu_0}{4\pi} \cdot \frac{I d\mathbf{l} \times \mathbf{\hat{r}}}{r^2}
\]
Ma hea:
– ʻO \( \mathbf{B} \) ke kahua makeneka
– ʻO \( \mu_0 \) ka permeability vacuum (\( 4\pi \times 10^{-7} \ \text{H/m} \))
– ʻO \( I \) ke au uila
– ʻO \( d\mathbf{l} \) kahi ʻāpana liʻiliʻi o ka uea
– ʻO \( \mathbf{\hat{r}} \) he vector unit ma ke kuhikuhi mai ka element wire a i ke kiko nānā
– ʻO \( r \) ka mamao ma waena o ka ʻāpana uea a me ke kiko nānā
Uea ʻōwili hoʻokahi
ʻO ke kahua makeneka ma ke kikowaena o kahi loop uea poepoe me ka radius \( R \) a me ke au \( I \) penei:
\[
B = \frac{\mu_0 I}{2R}
\]
Laʻana Nīnau 1
Nīnau: E helu i ke kahua makeneka ma ke kikowaena o kahi loop uea me ka radius o 10 cm e lawe ana i ke au o 5 A.
Kūkākūkā:
E hoʻohana i ke ʻano hana kahua magnetic no kahi loop hoʻokahi,
\[
B = \frac{\mu_0 I}{2R}
\]
Ma hea:
– \( \mu_0 = 4\pi \times 10^{-7} \ \text{H/m} \)
– \( I = 5 \ \kikokikona{A} \)
– \( R = 0.1 \ \text{m} \) (no ka mea, 10 kenimika = 0.1 m)
Ma ke pani ʻana i kēia mau waiwai,
\[
B = 4/10^-7/5}{2/0.1
\]
\[
B = \frac{20\pi \times 10^{-7}}{0.2}
\]
\[
B = 2\pi \times 10^{-6} \ \text{T}
\]
\[
B = 6.28 \times 10^{-6} \ \text{T}
\]
No laila, ʻo ke kahua makeneka ma ke kikowaena o ke apo uea he \( 6.28 \ \mu T \).
Laʻana Nīnau 2
Nīnau: He wili i loaʻa he 20 mau huli me ka radius o 10 cm ke kahe nei i ke au o 5 A. E helu i ke kahua makeneka ma ke kikowaena o ka wili.
Kūkākūkā:
ʻO ke kahua magnetic no kahi coil o N mau huli:
\[
B = \frac{\mu_0 NI}{2R}
\]
Ma hea:
– \( N = 20 \)
– \( I = 5 \ \kikokikona{A} \)
– \( R = 0.1 \ \text{m} \)
– \( \mu_0 = 4\pi \times 10^{-7} \ \text{H/m} \)
Ma ke pani ʻana i kēia mau waiwai,
\[
B = 4/10^-7 me 20 me 5}{2 me 0.1
\]
\[
B = \frac{400\pi \times 10^{-7}}{0.2}
\]
\[
B = 20\pi \times 10^{-6} \ \text{T}
\]
\[
B = 62.8 \times 10^{-6} \ \text{T}
\]
No laila, ʻo ke kahua makeneka ma ke kikowaena o ke wili he \( 62.8 \ \mu T \).
Uea Pōʻai ma kekahi Kihi
Inā ʻoki ʻia kahi loop uea e lawe ana i ke au ma kahi kihi, a laila e hana kēlā ʻāpana o ka loop i kahi kahua magnetic ʻokoʻa. No ka laʻana, no ka hapalua pōʻai, ʻo ke kahua magnetic ka hapalua o ke kahua magnetic piha, e koi ana i ka hoʻohui hou ʻana no nā hoʻonā paʻakikī.
Laʻana Nīnau 3
Nīnau: E helu i ke kahua makeneka ma ke kikowaena o kahi uea poepoe e wili wale ana i ka hapalua o ka pōʻai (180 degere), me ka radius o 10 cm a me ke au o 5 A.
Kūkākūkā:
No ka hapalua pōʻai, ʻo ke kahua makeneka ma ke kikowaena he hapalua ia o ke kahua makeneka piha:
\[
B = \frac{1}{2} \cdot \frac{\mu_0 I}{2R}
\]
Ma hea:
– \( \mu_0 = 4\pi \times 10^{-7} \ \text{H/m} \)
– \( I = 5 \ \kikokikona{A} \)
– \( R = 0.1 \ \text{m} \)
Ma ke pani ʻana i kēia mau waiwai,
\[
B = \frac{1}{2} \cdot \frac{4\pi \times 10^{-7} \times 5}{2 \times 0.1}
\]
\[
B = \frac{1}{2} \times 2\pi \times 10^{-6} \ \text{T}
\]
\[
B = \pi \times 10^{-6} \ \text{T}
\]
\[
B = 3.14 \times 10^{-6} \ \text{T}
\]
No laila, ʻo ke kahua makeneka ma ke kikowaena o ka uea hapapoʻai he \( 3.14 \ \mu T \).
Pani
Ma o nā hiʻohiʻona ma luna, ua manaʻolana ʻia e loaʻa i ka poʻe heluhelu kahi ʻike maikaʻi aʻe i ke ʻano o ka helu ʻana i ke kahua magnetic i hana ʻia e kahi uea wili e lawe ana i kahi au uila. He mea pono loa kēia ʻike i nā noi ʻenehana like ʻole a me ka noiʻi ʻepekema, ʻoi aku hoʻi ma nā kahua o ka electromagnetism a me ka ʻenekinia uila.
