Nā nīnau hoʻohālike e kūkākūkā ana i ka ikaika ma ka hoʻouka neʻe ʻana
Pendahuluan
ʻO ke ʻano hana kino ke aʻo ʻana i nā hanana kūlohelohe, me nā mana e hana ana ma luna o nā mea. ʻO kahi kumuhana hoihoi e kūkākūkā pinepine ʻia nei, ʻo ia ka mana ma luna o nā uku e neʻe ana, ʻoi aku hoʻi ma ke ʻano o nā kahua uila a me nā kahua magnetic. ʻO ka mana e hana ana ma luna o kahi uku e neʻe ana i loko o kahi kahua uila a magnetic paha ua kapa ʻia ʻo ia ka mana Lorentz. E kūkākūkā kēia ʻatikala i kekahi mau pilikia hoʻohālike a me kā lākou kūkākūkā ʻana e pili ana i ka mana e hana ana ma luna o nā uku e neʻe ana.
Mana Lorentz
ʻO ka ikaika Lorentz ka hui pū ʻana o ka ikaika uila a me ka ikaika magnetic e hana ana ma luna o kahi uku e neʻe ana i loko o kahi kahua uila a me kahi kahua magnetic. Ma ke ʻano makemakika, hiki ke hōʻike ʻia ka ikaika Lorentz (F) e ka hoohalike:
\[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}) \]
Ma hea:
– \( \mathbf{F} \) ka ikaika Lorentz
– ʻo \( q \) ka uku
– ʻO \( \mathbf{E} \) ke kahua uila
– ʻO \( \mathbf{v} \) ka wikiwiki o ka hoʻouku ʻana
– ʻO \( \mathbf{B} \) ke kahua makeneka
Me kēia hoohalike, hiki iā mākou ke kālailai i nā mana e hana ana ma kahi hoʻouku e neʻe ana i loko o kahi kahua uila a me kahi kahua magnetic.
Nā Nīnau Laʻana a me ke Kūkākūkā
Nīnau 1: Ka ikaika ma luna o kahi hoʻopiʻi ma kahi kahua uila
Nīnau:
Aia kahi uku maikaʻi \( q = 2 \times 10^{-6} \, C \) i loko o kahi kahua uila like \( E = 5 \times 10^4 \, N/C \) i kuhikuhi ʻia i ka ʻākau. E helu i ka ikaika e hana ana ma ka uku.
Kūkākūkā:
No ka hoʻopiʻi ʻana i loko o kahi kahua uila me ka ʻole o ke kahua magnetic, ʻo ka ikaika Lorentz wale nō ka ʻāpana ikaika uila:
\[ \mathbf{F} = q \mathbf{E} \]
Me \( q = 2 \times 10^{-6} \, C \) a me \( \mathbf{E} = 5 \times 10^4 \, N/C \):
\[ \mathbf{F} = (2 \times 10^{-6} \, C) \times (5 \times 10^4 \, N/C) \]
\[ \mathbf{F} = 0.1 \, N \]
ʻO ke kuhikuhi o ka ikaika \( \mathbf{F} \) aia ma ke kuhikuhi like me ke kahua uila no ka mea he maikaʻi ka uku. No laila, ʻo ka ikaika e hana ana ma ka uku he 0.1 N ma ka ʻākau.
Nīnau 2: Ka ikaika ma luna o kahi hoʻopiʻi ma kahi kahua Magnetic
Nīnau:
Neʻe kahi uku maikaʻi ʻole \( q = -3 \times 10^{-6} \, C \) me ka wikiwiki \( \mathbf{v} = 2 \times 10^3 \, m/s \) ma ke axis-x i loko o kahi kahua magnetic like \( \mathbf{B} = 0.5 \, T \) i kuhikuhi ʻia ma ke axis-z. E helu i ka ikaika e hana ana ma ka uku.
Kūkākūkā:
No ka hoʻouku e neʻe ana i loko o kahi kahua magnetic me ke alo ʻole o kahi kahua uila, ʻo ka ikaika Lorentz wale nō nā ʻāpana ikaika magnetic:
\[ \mathbf{F} = q (\mathbf{v} \manawa \mathbf{B}) \]
Me \( q = -3 \times 10^{-6} \, C \), \( \mathbf{v} = 2 \times 10^3 \, m/s \) ma ke kuhikuhi x, a me \( \mathbf{B} = 0.5 \, T \) ma ke kuhikuhi z:
Ka Heluhelu \( \mathbf{v} \times \mathbf{B} \):
\[ \mathbf{v} = 2 \times 10^3 \, m/s \, \hat{i} \]
\[ \mathbf{B} = 0.5 \, T \, \ pāpale{k} \]
\[ \mathbf{v} \times \mathbf{B} = (2 \times 10^3 \, m/s \, \hat{i}) \times (0.5 \, T \, \hat{k}) \]
\[ \mathbf{v} \times \mathbf{B} = 2 \times 10^3 \, m/s \times 0.5 \, T \, \hat{i} \times \hat{k} \]
\[ \hat{i} \times \hat{k} = -\hat{j} \]
\[ \mathbf{v} \times \mathbf{B} = – (1 \times 10^3 \, T \cdot m/s) \, \hat{j} \]
No laila, ka mana magnetic:
\[ \mathbf{F} = q \mathbf{v} \manawa \mathbf{B} \]
\[ \mathbf{F} = (-3 \times 10^{-6} C) \times ( -10^3 \, T \cdot m/s \, \hat{j}) \]
\[ \mathbf{F} = 3 \manawa 10^{-3} \, N \, \hat{j} \]
\[ \mathbf{F} = 0.003 \, N \, \ pāpale{j} \]
ʻO ke kuhikuhi o ka ikaika \( \mathbf{F} \) e kū pono ana i ka axis-y maikaʻi. No laila, ʻo ka ikaika e hana ana ma ka hoʻouku ʻana he 0.003 N i luna (ma ke kuhikuhi axis-y maikaʻi).
Nīnau 3: Ka ikaika ma ke kumukūʻai ma nā kahua uila a me nā kahua magnetic
Nīnau:
Neʻe kahi uku maikaʻi \( q = 1.5 \times 10^{-6} \, C \) me ka wikiwiki \( \mathbf{v} = 4 \times 10^3 \, m/s \) ma ke kuhikuhi-y ma kahi kahua uila \( \mathbf{E} = 3 \times 10^4 \, N/C \) ma ke kuhikuhi-x, a me kahi kahua magnetic \( \mathbf{B} = 0.2 \, T \) ma ke kuhikuhi-z. E helu i ka ikaika net e hana ana ma ka uku.
Kūkākūkā:
Ka huina o ka ikaika Lorentz:
\[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}) \]
ʻO ka mea mua, e helu \( \mathbf{v} \times \mathbf{B} \):
\[ \mathbf{v} = 4 \times 10^3 \, m/s \, \hat{j} \]
\[ \mathbf{B} = 0.2 \, T \, \ pāpale{k} \]
\[ \mathbf{v} \times \mathbf{B} = (4 \times 10^3 \, m/s \, \hat{j}) \times (0.2 \, T \, \hat{k}) \]
\[ \mathbf{v} \times \mathbf{B} = 4 \times 10^3 \, m/s \times 0.2 \, T \, \hat{j} \times \hat{k} \]
\[ \hat{j} \times \hat{k} = \hat{i} \]
\[ \mathbf{v} \times \mathbf{B} = (0.8 \times 10^3 \, T \cdot m/s) \, \hat{i} \]
\[ \mathbf{v} \times \mathbf{B} = 800 \, T \cdot m/s \, \hat{i} \]
A laila, ʻo ka ikaika uila:
\[ q \mathbf{E} = (1.5 \times 10^{-6} \, C) \times (3 \times 10^4 \, N/C \, \hat{i}) \]
\[ q \mathbf{E} = 0.045 \, N \, \hat{i} \]
Mana makeneka:
q (\mathbf{v} \times \mathbf{B}) = (1.5 \times 10^{-6} \, C) \times (800 \, T \cdot m/s \, \hat{i}) \]
\[ q (\mathbf{v} \manawa \mathbf{B}) = 0.0012 \, N \, \hat{i} \]
Kaila holoʻokoʻa:
\[ \mathbf{F} = q \mathbf{E} + q (\mathbf{v} \manawa \mathbf{B}) \]
\[ \mathbf{F} = 0.045 \, N \, \hat{i} + 0.0012 \, N \, \hat{i} \]
\[ \mathbf{F} = 0.0462 \, N \, \hat{i} \]
No laila, ʻo ka ikaika holoʻokoʻa e hana ana ma ka hoʻopiʻi he 0.0462 N ma ka ʻākau (axis-x maikaʻi).
Ka hopena
ʻO ka ikaika ma luna o nā uku e neʻe ana i nā kahua uila a me nā kahua makeneka e hilinaʻi nui ʻia i ke kuhikuhi a me ka nui o kēlā me kēia kahua a me ka wikiwiki a me ke ʻano o ka uku. Ma o nā nīnau hoʻohālike a me ke kūkākūkā ʻana ma luna, ua manaʻolana ʻia e hiki i ka poʻe heluhelu ke hoʻomaopopo maikaʻi i ke ʻano o ka hoʻopili ʻana i ke kumumanaʻo ikaika Lorentz i nā kūlana like ʻole. ʻAʻole wale kēia ʻike he mea nui i ke kumumanaʻo akā i nā noi hana i nā kahua ʻenehana a me ka ʻepekema e like me ka hoʻolālā ʻana o nā mīkini uila, ka hoʻomaopopo ʻana i ka hanana aurora, a me ka hana o nā ʻāpana i loko o nā mea hoʻolalelale ʻāpana.
