Chitsanzo cha Funso Lokambirana pa Waya Wozungulira Wonyamula Mphamvu Yamagetsi
Pendauluan
Waya wozungulira wonyamula magetsi ndi chinthu chofunikira kwambiri pa ntchito zambiri mu fizikisi ndi uinjiniya wamagetsi. Kumvetsetsa mfundo zoyambira ndi kuwerengera mphamvu zamaginito zomwe zimapangidwa ndi waya uwu ndikofunikira m'magawo osiyanasiyana, kuyambira pakupanga mota yamagetsi mpaka masensa amagetsi. Nkhaniyi ikufotokoza mavuto angapo ndi mayankho awo kuti athandize owerenga kumvetsetsa mfundo zoyambira za waya wozungulira wonyamula magetsi.
Mphamvu ya Maginito Yogwiritsidwa Ntchito ndi Waya Wozungulira
Lamulo la Biot-Savart
Lamulo la Biot-Savart limapereka maziko owerengera mphamvu ya maginito yozungulira waya wonyamula magetsi. Kapangidwe koyambira ka lamulo la Biot-Savart ndi motere:
\[
d\mathbf{B} = \frac{\mu_0}{4\pi} \cdot \frac{I d\mathbf{l} \nthawi \mathbf{\hat{r}}}{r^2}
\]
Kumene:
– \( \mathbf{B} \) ndi mphamvu ya maginito
– \( \mu_0 \) ndi vacuum permeability (\( 4\pi \times 10^{-7} \ \text{H/m} \))
– \( I \) ndi mphamvu yamagetsi
– \( d\mathbf{l} \) ndi chinthu chaching'ono cha waya
– \( \mathbf{\hat{r}} \) ndi vekitala ya unit yomwe imachokera ku waya kupita ku malo owonera
– \( r \) ndi mtunda pakati pa chinthu cha waya ndi malo owonera
Waya Wozungulira Wokha
Mphamvu ya maginito pakati pa waya wozungulira wokhala ndi radius \( R \) ndi current \( I \) ndi:
\[
B = \frac{\mu_0 I}{2R}
\]
Chitsanzo cha Funso 1
Funso: Werengani mphamvu ya maginito pakati pa waya wozungulira wokhala ndi utali wa masentimita 10 wokhala ndi mphamvu ya 5 A.
Kukambirana:
Gwiritsani ntchito njira ya maginito ya kuzungulira kamodzi,
\[
B = \frac{\mu_0 I}{2R}
\]
Kumene:
– \( \mu_0 = 4\pi \nthawi 10^{-7} \ \malemba{H/m} \)
– \( I = 5 \ \malemba{A} \)
– \( R = 0.1 \ \text{m} \) (chifukwa 10 cm = 0.1 m)
Mwa kusintha mfundo izi,
\[
B = \frac{4\pi \times 10^{-7} \times 5}{2 \times 0.1}
\]
\[
B = \frac{20\pi \times 10^{-7}}{0.2}
\]
\[
B = 2\pi \nthawi 10^{-6} \ \malemba{T}
\]
\[
B = 6.28 \nthawi 10^{-6} \ \malemba{T}
\]
Kotero, mphamvu ya maginito pakati pa waya wozungulira ndi \( 6.28 \ \mu T \).
Chitsanzo cha Funso 2
Funso: Chozungulira chokhala ndi ma turns 20 ndi radius ya 10 cm chimakhala ndi current ya 5 A. Werengani mphamvu ya maginito pakati pa chozunguliracho.
Kukambirana:
Mphamvu ya maginito ya coil ya N turns ndi:
\[
B = \frac{\mu_0 NI}{2R}
\]
Kumene:
– \( N = 20 \)
– \( I = 5 \ \malemba{A} \)
– \( R = 0.1 \ \malemba{m} \)
– \( \mu_0 = 4\pi \nthawi 10^{-7} \ \malemba{H/m} \)
Mwa kusintha mfundo izi,
\[
B = \frac{4\pi \nthawi 10^{-7} \nthawi 20 \nthawi 5}{2 \nthawi 0.1}
\]
\[
B = \frac{400\pi \times 10^{-7}}{0.2}
\]
\[
B = 20\pi \nthawi 10^{-6} \ \malemba{T}
\]
\[
B = 62.8 \nthawi 10^{-6} \ \malemba{T}
\]
Kotero, mphamvu ya maginito pakati pa coil ndi \( 62.8 \ \mu T \).
Waya Wozungulira pa Ngodya Yina
Ngati waya wonyamula magetsi wadulidwa pa ngodya, ndiye kuti gawo limenelo la waya lidzapanga mphamvu yosiyana ya maginito. Mwachitsanzo, pa semicircle, mphamvu ya maginito ndi theka la mphamvu yonse ya maginito, zomwe zimafuna kuphatikiza kwina kuti pakhale njira zovuta zothetsera mavuto.
Chitsanzo cha Funso 3
Funso: Werengani mphamvu ya maginito pakati pa waya wozungulira womwe umangozungulira theka la bwalo (madigiri 180), wokhala ndi utali wa masentimita 10 ndi mphamvu yamagetsi ya 5 A.
Kukambirana:
Pa semicircle, mphamvu ya maginito yomwe ili pakati ndi theka la mphamvu yonse ya maginito:
\[
B = \frac{1}{2} \cdot \frac{\mu_0 I}{2R}
\]
Kumene:
– \( \mu_0 = 4\pi \nthawi 10^{-7} \ \malemba{H/m} \)
– \( I = 5 \ \malemba{A} \)
– \( R = 0.1 \ \malemba{m} \)
Mwa kusintha mfundo izi,
\[
B = \frac{1}{2} \cdot \frac{4\pi \times 10^{-7} \times 5}{2 \times 0.1}
\]
\[
B = \frac{1}{2} \times 2\pi \times 10^{-6} \ \text{T}
\]
\[
B = \pi \nthawi 10^{-6} \ \malemba{T}
\]
\[
B = 3.14 \nthawi 10^{-6} \ \malemba{T}
\]
Kotero, mphamvu ya maginito pakati pa waya wozungulira ndi \( 3.14 \ \mu T \).
Kutseka
Kudzera mu zitsanzo zomwe zili pamwambapa, tikuyembekeza kuti owerenga amvetsetsa bwino momwe angawerengere mphamvu ya maginito yopangidwa ndi waya wozungulira womwe umanyamula magetsi. Kumvetsetsa kumeneku ndikothandiza kwambiri pakugwiritsa ntchito ukadaulo ndi kafukufuku wasayansi, makamaka m'magawo a maginito amagetsi ndi uinjiniya wamagetsi.
