Zitsanzo za Mafunso Okhudza Mphamvu Yoyendetsa
Pendauluan
Fiziki ndi kuphunzira za zochitika zachilengedwe, kuphatikizapo mphamvu zomwe zimagwira ntchito pa zinthu. Mutu umodzi wosangalatsa womwe umakambidwa kawirikawiri ndi mphamvu yomwe imayendetsa mphamvu zoyenda, makamaka pankhani ya magetsi ndi maginito. Mphamvu yomwe imayendetsa mphamvu yoyenda mumagetsi kapena maginito imadziwika kuti mphamvu ya Lorentz. Nkhaniyi ikambirana zitsanzo zingapo za mavuto ndi kukambirana kwawo pankhani ya mphamvu yomwe imayendetsa mphamvu zoyenda.
Mphamvu ya Lorentz
Mphamvu ya Lorentz ndi kuphatikiza kwa mphamvu yamagetsi ndi mphamvu ya maginito yomwe imagwira ntchito pa mphamvu yoyenda mu gawo lamagetsi ndi gawo la maginito. Mwa masamu, mphamvu ya Lorentz (F) ikhoza kufotokozedwa ndi equation:
\[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \nthawi \mathbf{B}) \]
Kumene:
- \( \mathbf{F} \) ndi mphamvu ya Lorentz
– \( q \) ndiye mtengo
– \( \mathbf{E} \) ndi munda wamagetsi
– \( \mathbf{v} \) ndi liwiro la mphamvu
– \( \mathbf{B} \) ndi mphamvu ya maginito
Ndi equation iyi, titha kusanthula mphamvu zomwe zimagwira ntchito pa mphamvu yomwe ikuyenda mumagetsi ndi maginito.
Mafunso ndi Kukambirana Zitsanzo
Funso 1: Mphamvu Yolipiritsa Pamagetsi
Funso:
Mphamvu yabwino \( q = 2 \times 10^{-6} \, C \) ili mu gawo lamagetsi lofanana \( E = 5 \times 10^4 \, N/C \) yolunjika kumanja. Werengani mphamvu yomwe ikugwira ntchito pa mphamvuyo.
Kukambirana:
Pa mphamvu yamagetsi yomwe imapezeka popanda mphamvu ya maginito, mphamvu ya Lorentz imangokhala ndi mphamvu yamagetsi yokha:
\[ \mathbf{F} = q \mathbf{E} \]
Ndi \( q = 2 \times 10^{-6} \, C \) ndi \( \mathbf{E} = 5 \times 10^4 \, N/C \):
\[ \mathbf{F} = (2 \nthawi 10^{-6} \, C) \nthawi (5 \nthawi 10^4 \, N/C) \]
\[ \mathbf{F} = 0.1 \, N \]
Kulunjika kwa mphamvu \( \mathbf{F} \) kuli mbali imodzi ndi gawo lamagetsi chifukwa mphamvu ndi yabwino. Chifukwa chake, mphamvu yomwe ikugwira ntchito pa mphamvu ndi 0.1 N kumanja.
Funso 2: Mphamvu Yoyatsira Mphamvu Mu Magnetic Field
Funso:
Mphamvu yoipa \( q = -3 \times 10^{-6} \, C \) imayenda ndi liwiro \( \mathbf{v} = 2 \times 10^3 \, m/s \) motsatira x-axis mu mphamvu ya maginito yofanana \( \mathbf{B} = 0.5 \, T \) yolunjika motsatira z-axis. Werengani mphamvu yomwe ikugwira ntchito pa mphamvuyo.
Kukambirana:
Pa mphamvu yoyenda mu mphamvu ya maginito popanda mphamvu yamagetsi, mphamvu ya Lorentz imangokhala ndi zigawo za mphamvu ya maginito zokha:
\[ \mathbf{F} = q (\mathbf{v} \nthawi \mathbf{B}) \]
Ndi \( q = -3 \times 10^{-6} \, C \), \( \mathbf{v} = 2 \times 10^3 \, m/s \) mu x direction, ndi \( \mathbf{B} = 0.5 \, T \) mu z direction:
Kuwerengera \( \mathbf{v} \times \mathbf{B} \):
\[ \mathbf{v} = 2 \times 10^3 \, m/s \, \hat{i} \]
\[ \mathbf{B} = 0.5 \, T \, \chipewa{k} \]
\[ \mathbf{v} \times \mathbf{B} = (2 \times 10^3 \, m/s \, \hat{i}) \times (0.5 \, T \, \hat{k}) \]
\[ \mathbf{v} \times \mathbf{B} = 2 \times 10^3 \, m/s \times 0.5 \, T \, \hat{i} \times \hat{k} \]
\[ \hat{i} \times \hat{k} = -\hat{j} \]
\[ \mathbf{v} \times \mathbf{B} = – (1 \times 10^3 \, T \cdot m/s) \, \hat{j} \]
Choncho, mphamvu ya maginito:
\[ \mathbf{F} = q \mathbf{v} \nthawi \mathbf{B} \]
\[ \mathbf{F} = (-3 \times 10^{-6} C) \times ( -10^3 \, T \cdot m/s \, \hat{j}) \]
\[ \mathbf{F} = 3 \kanthawi 10^{-3} \, N \, \hat{j} \]
\[ \mathbf{F} = 0.003 \, N \, \chipewa{j} \]
Njira ya mphamvu \( \mathbf{F} \) ikupita ku positive y-axis. Chifukwa chake, mphamvu yomwe ikugwira ntchito pa charge ndi 0.003 N kupita mmwamba (mu positive y-axis).
Funso 3: Mphamvu Yoyatsira mu Magetsi ndi Magineti
Funso:
Mphamvu yabwino \( q = 1.5 \times 10^{-6} \, C \) imayenda ndi liwiro \( \mathbf{v} = 4 \times 10^3 \, m/s \) munjira ya y mu gawo lamagetsi \( \mathbf{E} = 3 \times 10^4 \, N/C \) munjira ya x, ndi mphamvu ya maginito \( \mathbf{B} = 0.2 \, T \) munjira ya z. Werengani mphamvu ya neti yomwe ikugwira ntchito pa mphamvuyo.
Kukambirana:
Mphamvu yonse ya Lorentz:
\[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \nthawi \mathbf{B}) \]
Choyamba, werengerani \( \mathbf{v} \times \mathbf{B} \):
\[ \mathbf{v} = 4 \times 10^3 \, m/s \, \hat{j} \]
\[ \mathbf{B} = 0.2 \, T \, \chipewa{k} \]
\[ \mathbf{v} \times \mathbf{B} = (4 \times 10^3 \, m/s \, \hat{j}) \times (0.2 \, T \, \hat{k}) \]
\[ \mathbf{v} \times \mathbf{B} = 4 \times 10^3 \, m/s \times 0.2 \, T \, \hat{j} \times \hat{k} \]
\[ \hat{j} \times \hat{k} = \hat{i} \]
\[ \mathbf{v} \times \mathbf{B} = (0.8 \times 10^3 \, T \cdot m/s) \, \hat{i} \]
\[ \mathbf{v} \times \mathbf{B} = 800 \, T \cdot m/s \, \hat{i} \]
Kenako, mphamvu yamagetsi:
\[ q \mathbf{E} = (1.5 \nthawi 10^{-6} \, C) \nthawi (3 \nthawi 10^4 \, N/C \, \hat{i}) \]
\[q \mathbf{E} = 0.045 \, N \, \chipewa{i} \]
Mphamvu ya maginito:
\[ q (\mathbf{v} \times \mathbf{B}) = (1.5 \times 10^{-6} \, C) \times (800 \, T \cdot m/s \, \hat{i}) \]
\[q (\mathbf{v} \nthawi \mathbf{B}) = 0.0012 \, N \, \hat{i} \]
Kalembedwe konse:
\[ \mathbf{F} = q \mathbf{E} + q (\mathbf{v} \nthawi \mathbf{B}) \]
\[ \mathbf{F} = 0.045 \, N \, \chipewa{i} + 0.0012 \, N \, \chipewa{i} \]
\[ \mathbf{F} = 0.0462 \, N \, \chipewa{i} \]
Kotero, mphamvu yonse yomwe ikugwira ntchito pa mphamvu ndi 0.0462 N kumanja (positive x-axis).
Mapeto
Mphamvu ya ma charges yomwe imayenda m'magetsi ndi maginito imadalira kwambiri komwe ikupita komanso kukula kwa gawo lililonse komanso liwiro ndi mtundu wa charge. Kudzera mu zitsanzo za mafunso ndi zokambirana pamwambapa, tikukhulupirira kuti owerenga amvetsetsa bwino momwe angagwiritsire ntchito mfundo ya mphamvu ya Lorentz m'mikhalidwe yosiyanasiyana. Kumvetsetsa kumeneku sikuti ndikofunikira kokha m'malingaliro komanso m'magwiritsidwe ntchito m'magawo aukadaulo ndi sayansi monga pakupanga ma mota amagetsi, kumvetsetsa chochitika cha aurora, ndi ntchito ya tinthu tating'onoting'ono mu ma accelerator a tinthu.
