Nā nīnau hoʻohālike e kūkākūkā ana i nā kahua magnetic
ʻO ke kahua magnetic kahi manaʻo nui i ka physics e wehewehe ana i ke ʻano o ka launa pū ʻana o nā mana magnetic me nā mea magnetized a i ʻole nā uku uila e neʻe ana. He mea nui loa ke aʻo ʻana e pili ana i nā kahua magnetic no ka mea he nui nā noi, mai nā mea uila a i ka lāʻau lapaʻau a i ka mokulele. E kūkākūkā kēia ʻatikala i kekahi mau laʻana o ke aʻo ʻana i nā nīnau e pili ana i nā kahua magnetic me kā lākou kūkākūkā a me nā hoʻonā, a ke manaʻolana nei mākou e kōkua iā ʻoe e hoʻomaopopo maikaʻi i kēia manaʻo.
Ke Hoʻomaopopo nei i nā Kahua Magnetic
Ma keʻano laulā, hiki ke hoʻoulu ʻia kahi kahua magnetic e kahi magnet mau a i ʻole ke au uila e kahe ana i loko o kahi uea. Hoʻomaulia ʻia ka ikaika o ke kahua magnetic ma kahi kiko me ka hoʻohana ʻana i ke kānāwai Biot-Savart a i ʻole ke kānāwai o Ampère, ma muli o nā kūlana kikoʻī. Hōʻike ʻia ke kahua magnetic e ka vector B a he mau anakahi o Tesla (T).
Nā Nīnau Laʻana a me ke Kūkākūkā
Nīnau 1: Ke Kahua Makeneka ma ke Kikowaena o kahi Pōʻai e Lawe Ana i ke Au
Nīnau: E helu i ka nui o ke kahua makeneka ma ke kikowaena o kahi loop uea poepoe me ka radius R a e lawe ana i ke au I.
Kūkākūkā:
Hiki ke helu ʻia ke kahua makeneka ma ke kikowaena o kahi loop wire poepoe me ka hoʻohana ʻana i ke kānāwai Biot-Savart e ʻōlelo nei:
\[ B = \frac{\mu_0 I}{2R} \]
Ma hea:
– \( \mu_0 \) = ka hiki ke komo i loko o ka hakahaka ( \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \) )
– I = ke au uila i loko o ka loop
– R = radius o ke apo
Manaʻo ʻia ʻo R = 0,1 m a ʻo I = 5 A, a laila ʻo ka nui o ke kahua magnetic ma ke kikowaena o ka loop penei:
\[ B = \frac{4\pi \times 10^{-7} \times 5}{2 \times 0,1} = \frac{2\pi \times 10^{-6}}{0,1} = 2\pi \times 10^{-5} \, \text{T} \]
No laila, ʻo ka nui o ke kahua magnetic ma ke kikowaena o ka loop ma kahi o \( 6,28 \times 10^{-5} \, \text{T} \).
Nīnau 2: Kahua Magnetic ma kahi Uea Holo Pololei o ke Au
Nīnau: E hoʻoholo i ke kahua magnetic ma kahi mamao d mai kahi uea pololei lōʻihi e lawe ana i ke au I.
Kūkākūkā:
No ka hōʻoia ʻana i ke kahua magnetic a puni kahi uea e lawe pololei ana i ke au, hoʻohana mākou i ke kānāwai o Ampere, i ʻōlelo ʻia penei:
\[ B = \frac{\mu_0 I}{2\pi d} \]
Ma hea:
– \( \mu_0 \) = ka hiki ke komo i ka hakahaka
– I = ke au uila i loko o ke kaula
– d = ka mamao mai ke kaula
Manaʻo ʻia ʻo I = 10 A a me d = 0,02 m, a laila:
\[ B = \frac{4\pi \times 10^{-7} \times 10}{2\pi \times 0,02} = \frac{4 \times 10^{-6} \times 10}{0,02} = 2 \times 10^{-4} \, \text{T} \]
No laila, ʻo ka nui o ke kahua makeneka ma kahi mamao o 0,02 mika mai ke kaula he \( 2 \times 10^{-4} \, \text{T} \).
Nīnau 3: Kahua Magnetic ma waena o ʻelua mau uea e lawe ana i ke au like
Nīnau: Ua hoʻokaʻawale ʻia ʻelua mau uea e lawe ana i ke au like e kahi mamao d a lawe kēlā me kēia i nā au I1 a me I2. E hoʻoholo i ke kahua magnetic ma ka waena ma waena o nā uea ʻelua.
Kūkākūkā:
No ka helu ʻana i ke kahua makeneka ma ka waena ma waena o nā uaea ʻelua, pono mākou e noʻonoʻo i ke kuhikuhi a me ka nui o ke kahua makeneka i hana ʻia e kēlā me kēia uaea.
Manaʻo ʻia ʻo I1 = 5 A a ʻo I2 = 10 A, a ʻo ka mamao ma waena o nā uea ʻelua he 0,1 m. A laila ʻo ka mamao mai ke kikowaena a i kēlā me kēia uea he 0,05 m. Ma muli o ke kānāwai o Ampere:
Ke kahua makeneka o ka uea 1 (B1) ma ke kikowaena:
\[ B_1 = \frac{\mu_0 I_1}{2\pi (d/2)} = \frac{4\pi \times 10^{-7} \times 5}{2\pi \times 0,05} = 2 \times 10^{-5} \, \text{T} \]
Ke kahua makeneka o ka uea 2 (B2) ma ke kikowaena:
\[ B_2 = \frac{\mu_0 I_2}{2\pi (d/2)} = \frac{4\pi \times 10^{-7} \times 10}{2\pi \times 0,05} = 4 \times 10^{-5} \, \text{T} \]
ʻOiai aia nā kahua makeneka ʻelua ma nā ʻaoʻao ʻē aʻe ma ke kikowaena, ʻo ka nui o ke kahua makeneka holoʻokoʻa ma ke kikowaena ka ʻokoʻa ma waena o B2 a me B1:
\[ B_{\text{total}} = B_2 – B_1 = 4 \times 10^{-5} – 2 \times 10^{-5} = 2 \times 10^{-5} \, \text{T} \]
No laila, ʻo ka nui o ke kahua makeneka ma ka waena ma waena o nā uea ʻelua he \( 2 \times 10^{-5} \, \text{T} \).
Nīnau 4: Kahua Magnetic i loko o ka ʻIwi o kahi Solenoid
Nīnau: E helu i ke kahua magnetic i loko o kahi solenoid lōʻihi nona nā huli n no kēlā me kēia anakahi lōʻihi a lawe i kahi au I.
Kūkākūkā:
No kahi solenoid lōʻihi, kokoke mau ke kahua magnetic i loko o ka solenoid a ua helu ʻia me ka hoʻohana ʻana i ka hoohalike:
\[ B = \mu_0 n I \]
Ma hea:
– \( \mu_0 \) = ka hiki ke komo i ka hakahaka
– n = ka helu o nā huli no ka mika
– I = au uila
Manaʻo ʻia he 1000 mau huli no ka mika ka solenoid a ke kahe nei ke au o 2 A, a laila:
\[ B = 4\pi \times 10^{-7} \times 1000 \times 2 = 8\pi \times 10^{-4} \, \text{T} \]
\[ B = 8 \times 3.14 \times 10^{-4} = 25.12 \times 10^{-4} \, \text{T} \]
No laila, ʻo ke kahua makeneka i loko o ka solenoid ma kahi o \( 2.51 \times 10^{-3} \, \text{T} \).
Ka hopena
ʻO ka hoʻomaopopo ʻana i nā kahua magnetic he kī ia i nā noi ʻenehana hou he nui. Ma o kēia mau laʻana, e loaʻa i ka poʻe heluhelu kahi ʻike maikaʻi aʻe i ke ʻano o ka hana ʻana o nā kahua magnetic i nā ʻano like ʻole, e like me ke kaula uea poepoe, kahi uea pololei, ʻelua mau uea like, a me kahi solenoid. ʻO ka hoʻomaʻamaʻa mau ʻana me nā pilikia a me nā kūlana like ʻole e hoʻoikaika hou i kēia manaʻo.
