Mafunso Okhudza Malamulo a Coulomb
Lamulo la Coulomb ndi mfundo yofunikira mu fizikisi yomwe imafotokoza mphamvu pakati pa ma charge awiri amagetsi. Lophunziridwa mkati mwa gawo laling'ono la ma electrostatics, lamuloli limafotokoza momwe ma charge amagetsi amakokerana kapena kuthamangitsana. Lamuloli linaperekedwa koyamba ndi katswiri wa sayansi ya zaku France Charles-Augustin de Coulomb m'zaka za m'ma 18. Nkhaniyi ikambirana za Lamulo la Coulomb pofufuza zitsanzo ndi mayankho ake, motero kuthandiza owerenga kumvetsetsa momwe mfundo yofunikirayi imagwirira ntchito.
Maziko a Chiphunzitso: Kodi Lamulo la Coulomb ndi Chiyani?
Lamulo la Coulomb limati kukula kwa mphamvu yamagetsi \( F \) pakati pa ma point charges awiri \( q_1 \) ndi \( q_2 \) kuli kofanana mwachindunji ndi zomwe zapezeka pa kukula kwa ma charges awiriwa ndipo motsutsana ndi sikweya ya mtunda \( r \) pakati pawo. Mwa masamu, njira ya Lamulo la Coulomb ikhoza kufotokozedwa motere:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Kumene:
– \( F \) ndi kukula kwa mphamvu yamagetsi
– \( k_e \) ndi nthawi zonse ya Coulomb (\( 8.9875 \times 10^9 \, N \cdot m^2 \cdot C^{-2} \))
– \( q_1 \) ndi \( q_2 \) ndi kukula kwa mphamvu yamagetsi
– \( r \) ndi mtunda pakati pa zolipiritsa ziwiri
Chitsanzo cha Funso 1
Funso:
Pali ma point charges awiri: \( q_1 = 2 \times 10^{-6} \, C \) ndi \( q_2 = -3 \times 10^{-6} \, C \). Ali kutali mamita 0,05. Werengani kukula kwa mphamvu yamagetsi yomwe ikugwira ntchito pakati pa ma charges awiriwa.
Kukambirana:
Gawo loyamba ndi kulembanso njira ya Coulomb's Law:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Tsopano tikusintha mfundo zodziwika bwino kukhala fomula:
\[ k_e = 8.9875 \times 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[q_1 = 2 \nthawi 10^{-6} \, C \]
\[q_2 = -3 \nthawi 10^{-6} \, C \]
\[r = 0,05 \, m \]
Timayika mfundo izi mu fomula:
\[ F = 8.9875 \nthawi 10^9 \, \frac{|2 \nthawi 10^{-6} \cdot -3 \nthawi 10^{-6}|}{(0,05)^2} \]
\[ F = 8.9875 \nthawi 10^9 \, \frac{6 \nthawi 10^{-12}}{0,0025} \]
\[ F = 8.9875 \nthawi 10^9 \, \frac{6 \nthawi 10^{-12}}{2,5 \nthawi 10^{-3}} \]
\[ F = 8.9875 \nthawi 10^9 \, \nthawi 2,4 \nthawi 10^{-9} \]
\[ F = 21.57 \, N \]
Chifukwa chakuti mphamvu \(q_2 \) ndi yoipa, mphamvu yamagetsi yomwe imagwira ntchito ndi mphamvu yokoka, chifukwa mphamvu zabwino ndi zoyipa zimakokerana.
Chitsanzo cha Funso 2
Funso:
Ma charge awiri amagetsi \( q_1 = 5 \times 10^{-9} \, C \) ndi \( q_2 = 10 \times 10^{-9} \, C \) amalekanitsidwa ndi mtunda wa mamita 0,1. Werengani kukula kwa mphamvu yamagetsi yomwe imagwira ntchito pa \( q_1 \).
Kukambirana:
Gwiritsaninso ntchito njira ya Coulomb's Law:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
M'malo mwa mfundo zodziwika bwino:
\[ k_e = 8.9875 \times 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[q_1 = 5 \nthawi 10^{-9} \, C \]
\[q_2 = 10 \nthawi 10^{-9} \, C \]
\[r = 0,1 \, m \]
\[ F = 8.9875 \nthawi 10^9 \, \frac{(5 \nthawi 10^{-9}) (10 \nthawi 10^{-9})}{(0,1)^2} \]
\[ F = 8.9875 \nthawi 10^9 \, \frac{50 \nthawi 10^{-18}}{0,01} \]
\[ F = 8.9875 \nthawi 10^9 \, \nthawi 5 \nthawi 10^{-15} \]
\[ F = 44.9375 \, N \]
Mphamvu yomwe imagwira ntchito ndi mphamvu yonyansa, chifukwa ma charge onse \( q_1 \) ndi \( q_2 \) ali ndi chizindikiro chofanana, chomwe ndi chabwino.
Chitsanzo cha Funso 3
Funso:
Ma point charge atatu ali pamzere wowongoka. Ma charge oyamba ndi \( q_1 = 2 \mu C \), ma charge achiwiri ndi \( q_2 = -1 \mu C \), ndipo ma charge achitatu ndi \( q_3 = 3 \mu C \). Mtunda pakati pa \( q_1 \) ndi \( q_2 \) ndi 0,1 m, pomwe mtunda pakati pa \( q_2 \) ndi \( q_3 \) ndi 0,2 m. Werengani kukula ndi malangizo a mphamvu yonse yamagetsi yomwe ikugwira ntchito pa \( q_2 \).
Kukambirana:
Choyamba, timawerengera mphamvu yamagetsi pakati pa \( q_1 \) ndi \( q_2 \):
\[ F_{12} = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
\[ k_e = 8.9875 \times 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[q_1 = 2 \nthawi 10^{-6} \, C \]
\[q_2 = -1 \nthawi 10^{-6} \, C \]
\[r = 0,1 \, m \]
\[ F_{12} = 8.9875 \nthawi 10^9 \, \frac{(2 \nthawi 10^{-6}) (-1 \nthawi 10^{-6})}{(0,1)^2} \]
\[ F_{12} = 8.9875 \nthawi 10^9 \, \frac{2 \nthawi 10^{-12}}{0,01} \]
\[ F_{12} = 8.9875 \nthawi 10^9 \, \nthawi 2 \nthawi 10^{-10} \]
\[ F_{12} = 1.7975 \, N \]
Popeza \( q_1 \) ndi yabwino ndipo \( q_2 \) ndi yoipa, mphamvu \( F_{12} \) ndi mphamvu yokoka yolunjika ku \( q_1 \).
Chachiwiri, timawerengera mphamvu yamagetsi pakati pa \( q_2 \) ndi \( q_3 \):
\[ F_{23} = k_e \frac{|q_2 \cdot q_3|}{r^2} \]
\[q_2 = -1 \nthawi 10^{-6} \, C \]
\[q_3 = 3 \nthawi 10^{-6} \, C \]
\[r = 0,2 \, m \]
\[ F_{23} = 8.9875 \nthawi 10^9 \, \frac{(-1 \nthawi 10^{-6}) (3 \nthawi 10^{-6})}{(0,2)^2} \]
\[ F_{23} = 8.9875 \nthawi 10^9 \, \frac{3 \nthawi 10^{-12}}{0,04} \]
\[ F_{23} = 8.9875 \nthawi 10^9 \, \nthawi 7.5 \nthawi 10^{-11} \]
\[ F_{23} = 0.67406 \, N \]
Popeza \( q_2 \) ndi yoipa ndipo \( q_3 \) ndi yabwino, mphamvu \( F_{23} \) ndi mphamvu yokoka yolunjika ku \( q_3 \).
Pomaliza, timagwirizanitsa mphamvu zonse ziwiri kuti tipeze zotsatira zomaliza:
Mphamvu yonse pa \( q_2 \):
\[ F_{\text{total}} = F_{12} – F_{23} \]
\[ F_{\text{total}} = 1.7975 \, N – 0.67406\, N \]
\[ F_{\text{total}} = 1.12344 \, N \]
Kulunjika kwa mphamvu yonse kuli ku \( q_1 \) chifukwa mphamvu \( F_{12} \) ndi yayikulu kuposa \( F_{23} \).
Mapeto
Lamulo la Coulomb limapereka chidziwitso chofunikira pa kuyanjana pakati pa ma charge amagetsi, okongola komanso onyansa. Zitsanzo zomwe zafotokozedwazi zikuwonetsa kugwiritsa ntchito lamuloli powerengera mphamvu zamagetsi poganizira kukula kwa ma charge ndi mtunda pakati pawo. Kumvetsetsa bwino Lamulo la Coulomb kungatithandize kumvetsetsa zochitika zosiyanasiyana zamagetsi ndi maginito zomwe zimachitika mozungulira ife.
