Nā nīnau hoʻohālike e kūkākūkā ana i nā kahua magnetic a puni kahi uea pololei
Pengantar
He kumuhana hoihoi mau nā kahua magnetic i ka physics, ʻoiai hoʻi i ke kūkākūkā ʻana i ke ʻano o ko lākou hoʻokumu ʻia ʻana a pehea lākou e launa pū ai me ke au uila. ʻO kahi ʻano koʻikoʻi o nā kahua magnetic ʻo ia ke kahua magnetic a puni kahi uea e lawe ana i ke au pololei. Ma kēia ʻatikala, e kūkākūkā mākou i ke kumumanaʻo kumu o kahi kahua magnetic a puni kahi uea pololei a hāʻawi i kekahi mau pilikia hoʻohālike a me nā hoʻonā e hoʻoikaika i ko mākou ʻike.
Kumumanaʻo Kumu o nā Kahua Magnetic a puni nā Uea Pololei
Ma mua o ko mākou luʻu ʻana i loko o ka pilikia hoʻohālike, he mea nui e hoʻomaopopo mua i ke kumumanaʻo kumu o nā kahua magnetic a puni kahi uea pololei. Wahi a ke kānāwai Biot-Savart a me ke kānāwai o Ampère, hiki ke hōʻike ʻia ke kahua magnetic a puni kahi uea pololei e lawe ana i kahi au uila e ka hoohalike:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
Ma hea,
– ʻO \( B \) ke kahua makeneka (Tesla),
– ʻO \( \mu_0 \) ka permeability vacuum \( (4\pi \times 10^{-7} T \cdot m/A) \),
– ʻO \( I \) ke au e kahe ana i loko o ke kaula (Ampere), a
– ʻO \( r \) ka mamao mai ke kaula a i kahi i ana ʻia ai ke kahua makeneka (mika).
Hoʻokumu kēia kahua makeneti i nā pōʻai concentric a puni ke kaula e like me ke kānāwai lima ʻākau. Inā hōʻike ka manamana nui i ke kuhikuhi o ke au, a laila hōʻike nā manamana lima e paʻa ana i ke kaula i ke kuhikuhi o ke kahua makeneti.
Nā Nīnau Laʻana a me ke Kūkākūkā
Nīnau 1:
He 10 A ke au uila o kahi uea lōʻihi a pololei. E helu i ka nui o ke kahua makeneka ma kahi mamao o 0,2 mika mai ke uea.
Kūkākūkā:
Hoʻohana mākou i ka hoohalike no ke kahua magnetic a puni kahi uea pololei:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
Ua ʻike ʻia:
\[ I = 10 \, A \]
\[ r = 0,2 \, m \]
\[ \mu_0 = 4 \pi \times 10^{-7} \, T \cdot m/A \]
E hoʻololi i kēia mau waiwai i loko o ka hoohalike:
\[ B = \frac{4 \pi \times 10^{-7} \times 10}{2 \pi \times 0,2} \]
\[ B = \frac{4 \pi \times 10^{-6}}{2 \pi \times 0,2} \]
\[ B = \frac{4 \times 10^{-6}}{0,2} \]
\[ B = 20 \times 10^{-6} \]
\[ B = 2 \times 10^{-5} \, T \]
\[ B = 20 \, \mu T \]
No laila, ʻo ka nui o ke kahua magnetic ma kahi mamao o 0,2 mika mai ke kaula he 20 μT (microTesla).
Nīnau 2:
ʻElua mau uea lōʻihi pololei e lawe ana i ke au like o 5 A akā ma nā ʻaoʻao ʻē aʻe, a ʻo ka mamao ma waena o lākou he 0,1 mika. E helu i ka nui o ke kahua magnetic ma kahi kiko ma waena o nā uea ʻelua.
Kūkākūkā:
Ma kahi kiko ma waena o nā uea ʻelua, ʻo ka mamao he \( r = 0,05 \, m \) mai kēlā me kēia uea. Hoʻomaulia mua mākou i ke kahua magnetic ma muli o hoʻokahi uea.
No kēlā me kēia uea:
\[ B_1 = \frac{\mu_0 I}{2 \pi r} \]
Ua ʻike ʻia:
\[ I = 5 \, A \]
\[ r = 0,05 \, m \]
\[ \mu_0 = 4 \pi \times 10^{-7} \, T \cdot m/A \]
E hoʻololi i kēia mau waiwai i loko o ka hoohalike:
\[ B_1 = \frac{4 \pi \times 10^{-7} \times 5}{2 \pi \times 0,05} \]
\[ B_1 = \frac{4 \pi \times 10^{-7} \times 5}{\pi \times 0,1} \]
\[ B_1 = \frac{20 \pi \times 10^{-7}}{\pi \times 0,1} \]
\[ B_1 = \frac{20 \times 10^{-7}}{0,1} \]
\[ B_1 = 200 \times 10^{-7} \]
\[ B_1 = 2 \times 10^{-5} \, T \]
ʻOiai ke kahe nei nā au o nā uea ʻelua i nā ʻaoʻao ʻē aʻe, hoʻopau nā kahua makeneti kekahi i kekahi ma ia wahi. ʻO ka huina o ke kahua makeneti ma ia wahi he ʻole.
Nīnau 3:
He 12 A ke au o kahi uea pololei lōʻihi A a ua kau ʻia ma ke ʻano like me kahi uea pololei lōʻihi B e lawe ana i ke au o 8 A ma ke kuhikuhi like. E helu i ka huina o ke kahua makeneka ma kahi kiko he 0,15 mika mai ka uea A a he 0,1 mika mai ka uea B.
Kūkākūkā:
E helu i ke kahua makeneka o kēlā me kēia uea ma ia wahi.
No ke kaula A:
\[ B_A = \frac{\mu_0 I_A}{2 \pi r_A} \]
Ua ʻike ʻia:
\[ I_A = 12 \, A \]
\[ r_A = 0,15 \, m \]
Hoʻololi waiwai:
\[ B_A = \frac{4 \pi \times 10^{-7} \times 12}{2 \pi \times 0,15} \]
\[ B_A = \frac{48 \pi \times 10^{-7}}{\pi \times 0,3} \]
\[ B_A = \frac{48 \times 10^{-7}}{0,3} \]
\[ B_A = 160 \times 10^{-7} \]
\[ B_A = 1,6 \times 10^{-5} \, T \]
No ke kaula B:
\[ B_B = \frac{\mu_0 I_B}{2 \pi r_B} \]
Ua ʻike ʻia:
\[ I_B = 8 \, A \]
\[ r_B = 0,1 \, m \]
Hoʻololi waiwai:
\[ B_B = \frac{4 \pi \times 10^{-7} \times 8}{2 \pi \times 0,1} \]
\[ B_B = \frac{32 \pi \times 10^{-7}}{\pi \times 0,2} \]
\[ B_B = \frac{32 \times 10^{-7}}{0,2} \]
\[ B_B = 160 \times 10^{-7} \]
\[ B_B = 1,6 \times 10^{-5} \, T \]
ʻOiai ke kahe nei ke au ma nā uea ʻelua ma ke kuhikuhi like, a ʻokoʻa nā mamao o nā kiko mai kēlā me kēia uea, e like ke kuhikuhi o ke kahua makeneka hopena. No laila, ʻo ke kahua makeneka holoʻokoʻa ka huina o kēia mau kahua makeneka ʻelua.
\[ B_{total} = B_A + B_B \]
\[ B_{total} = 1,6 \times 10^{-5} + 1,6 \times 10^{-5} \]
\[ B_{total} = 3,2 \times 10^{-5} \, T \]
No laila, ʻo ka huina o ke kahua magnetic ma kēlā wahi he 32 μT (microTesla).
Ka hopena
He mea koʻikoʻi ka hoʻomaopopo ʻana i ke kumumanaʻo o kahi kahua magnetic a puni kahi uea pololei no ka physics no ka mea he nui nā noi kūpono. Ma ka hoʻohana ʻana i nā laʻana a me nā kūkākūkā e like me ka mea ma luna, hiki iā mākou ke hoʻoikaika i ke kumumanaʻo kumu a hoʻonui i ko mākou ʻike pehea e hana ai nā kahua magnetic a puni kahi uea e lawe ana i ke au. E hoʻomanaʻo mau, he mea koʻikoʻi ka analytical regularity a me ka hoʻomaopopo ʻana i nā kānāwai kumu no ka hoʻoponopono ʻana i nā pilikia physics like ʻole.
