Zitsanzo za Mafunso Okhudza Mphamvu Zamagetsi
Tanthauzo la mphamvu yamagetsi ndi mphamvu yomwe imachokera ku kuyanjana pakati pa magetsi. Mphamvu iyi imaphunziridwa mu fizikisi, makamaka mu gawo la electrodynamics. Zotsatira za mphamvu yamagetsi zitha kuwoneka m'zochitika zambiri za tsiku ndi tsiku, kuyambira kusakaniza zinthu zina mpaka kugwira ntchito kwa zida zamagetsi. Nkhaniyi ikambirana zitsanzo zingapo za mavuto a mphamvu yamagetsi ndi mayankho ake, komanso mfundo zazikulu zokhudzana ndi mphamvu yamagetsi.
Chiyambi cha Mphamvu Zamagetsi
Mphamvu yamagetsi pakati pa magetsi awiri imaperekedwa ndi Lamulo la Coulomb, lomwe limafotokozedwa ndi equation iyi:
$$ F = k_e \frac{|q_1 q_2|}{r^2} $$
Kumene:
– \( F \) ndi mphamvu yamagetsi pakati pa ma charge awiri.
– \( q_1 \) ndi \( q_2 \) ndi kukula kwa zolipiritsa.
– \( r \) ndi mtunda pakati pa ma charge awiriwa.
– \( k_e \) ndi Coulomb constant (pafupifupi \(8.99 \times 10^9 \, N \cdot m^2 / C^2\)).
Lamulo la Coulomb ndi lofanana ndi lamulo la Newton la mphamvu yokoka, koma mphamvu yokoka nthawi zonse imakhala yokongola pomwe mphamvu yamagetsi imatha kukhala yokongola kapena yonyansa kutengera chizindikiro cha mphamvuyo.
Mafunso ndi Kukambirana Zitsanzo
Funso 1: Malipiro Awiri Ofanana
Ma point charge awiri \( q_1 = 3 \, \mu C \) ndi \( q_2 = -4 \, \mu C \) ali pa mtunda wa mamita 0.5 kuchokera wina ndi mnzake. Werengani mphamvu yamagetsi yomwe ikugwira ntchito pakati pa ma charge awiriwa.
Kukambirana:
1. Kuzindikira Katundu ndi Mtunda:
– \( q_1 = 3 \, \mu C = 3 \nthawi 10^{-6} \, C \)
– \( q_2 = -4 \, \mu C = -4 \nthawi 10^{-6} \, C \)
– \( r = 0.5 \, m \)
2. Kulowa m'malo mwa lamulo la Coulomb:
\[
F = k_e \frac{|q_1 q_2|}{r^2}
\]
\[
F = 8.99 \nthawi 10^9 \, \frac{(3 \nthawi 10^{-6})(4 \nthawi 10^{-6})}{(0.5)^2}
\]
3. Werengani Zotsatira:
\[
F = 8.99 \nthawi 10^9 \, \frac{12 \nthawi 10^{-12}}{0.25}
\]
\[
F = 8.99 \nthawi 10^9 \nthawi 48 \nthawi 10^{-12}
\]
\[
F = 431.52 \nthawi 10^{-3} \, N
\]
\[
F \pafupifupi 0.432 \, N
\]
Kotero, mphamvu yamagetsi yomwe imagwira ntchito pakati pa ma charge awiriwa ndi pafupifupi 0.432 Newtons.
Funso 2: Kulipiritsa Ndalama Zosiyanasiyana
Ma point charge atatu, \( q_1 = 2 \, \mu C \), \( q_2 = 3 \, \mu C \), ndi \( q_3 = -1 \, \mu C \) amayikidwa pamzere wowongoka ndi mtunda pakati pa \( q_1 \) ndi \( q_2 \) kukhala mamita 0.6 ndipo pakati pa \( q_2 \) ndi \( q_3 \) kukhala mamita 0.4. Werengani mphamvu yochokera pa \( q_2 \).
Kukambirana:
1. Kuzindikira Katundu ndi Mtunda:
– \( q_1 = 2 \, \mu C = 2 \nthawi 10^{-6} \, C \)
– \( q_2 = 3 \, \mu C = 3 \nthawi 10^{-6} \, C \)
– \( q_3 = -1 \, \mu C = -1 \nthawi 10^{-6} \, C \)
– Mtunda pakati pa q_1 ndi q_2 ndi 0.6 m
– Mtunda pakati pa q_2 ndi q_3 ndi 0.4 m
2. Kukakamiza \( q_1 \) motsutsana \( q_2 \):
\[
F_{12} = k_e \frac{|q_1 q_2|}{r_{12}^2}
\]
\[
F_{12} = 8.99 \times 10^9 \, \frac{(2 \times 10^{-6})(3 \times 10^{-6})}{(0.6)^2}
\]
\[
F_{12} = 8.99 \times 10^9 \, \frac{6 \times 10^{-12}}{0.36}
\]
\[
F_{12} = 8.99 \nthawi 10^9 \nthawi 16.67 \nthawi 10^{-12}
\]
\[
F_{12} \pafupifupi 0.15 \, N
\]
Kulunjika kwa mphamvu \( F_{12} \) kuli kutali ndi \( q_1 \) (kumanja).
3. Kukakamiza \( q_3 \) motsutsana \( q_2 \):
\[
F_{32} = k_e \frac{|q_3 q_2|}{r_{32}^2}
\]
\[
F_{32} = 8.99 \times 10^9 \, \frac{(1 \times 10^{-6})(3 \times 10^{-6})}{(0.4)^2}
\]
\[
F_{32} = 8.99 \times 10^9 \, \frac{3 \times 10^{-12}}{0.16}
\]
\[
F_{32} = 8.99 \nthawi 10^9 \nthawi 18.75 \nthawi 10^{-12}
\]
\[
F_{32} \pafupifupi 0.17 \, N
\]
Njira ya mphamvu \( F_{32} \) ikukoka kupita ku \( q_3 \) (kumanzere).
4. Mphamvu Yotsatira:
Popeza \( F_{12} \) ili kumanja ndipo \( F_{32} \) ili kumanzere, mphamvu yochokera \( F_{res} = F_{32} – F_{12} \):
\[
F_{res} = 0.17 \,N – 0.15 \,N
\]
\[
F_{res} = 0.02 \, N (kumanzere)
\]
Kotero, mphamvu yochokera pa \( q_2 \) ndi 0.02 Newton kumanzere.
Funso 3: Kachitidwe Kokweza mu Katatu
Ma point charge atatu \( q_1 = 5 \, \mu C \), \( q_2 = -3 \, \mu C \), ndi \( q_3 = 4 \, \mu C \) amayikidwa pamakona atatu a triangle yofanana ndi kutalika kwa mbali kwa mamita 0.2. Werengani mphamvu yonse yamagetsi yomwe ikugwira ntchito pa charge \( q_1 \).
Kukambirana:
1. Kukakamiza \( q_2 \) motsutsana \( q_1 \):
\[
F_{12} = k_e \frac{|q_1 q_2|}{r^2}
\]
\[
F_{12} = 8.99 \times 10^9 \, \frac{(5 \times 10^{-6})(3 \times 10^{-6})}{(0.2)^2}
\]
\[
F_{12} = 8.99 \times 10^9 \, \frac{15 \times 10^{-12}}{0.04}
\]
\[
F_{12} = 8.99 \nthawi 10^9 \nthawi 375 \nthawi 10^{-12}
\]
\[
F_{12} \pafupifupi 3.37 \, N
\]
Kulunjika kwa mphamvu \( F_{12} \) ndikokongola poyang'ana \( q_2 \).
2. Kukakamiza \( q_3 \) motsutsana \( q_1 \):
\[
F_{13} = k_e \frac{|q_1 q_3|}{r^2}
\]
\[
F_{13} = 8.99 \times 10^9 \, \frac{(5 \times 10^{-6})(4 \times 10^{-6})}{(0.2)^2}
\]
\[
F_{13} = 8.99 \times 10^9 \, \frac{20 \times 10^{-12}}{0.04}
\]
\[
F_{13} = 8.99 \nthawi 10^9 \nthawi 500 \nthawi 10^{-12}
\]
\[
F_{13} \pafupifupi 4.50 \, N
\]
Kulunjika kwa mphamvu \( F_{13} \) ndi konyansa kuchokera ku \( q_3 \).
3. Mphamvu Yotsatira:
Tifunika kugwiritsa ntchito njira ya vekitala kuti tipeze zotsatira za \( F_{12} \) ndi \( F_{13} \), chifukwa ngodya pakati pa mphamvu ndi madigiri 60 (katatu kofanana).
Pogwiritsa ntchito zigawo za x ndi y, titha kudziwa mphamvu yonse. Komabe, kuti tipeze mosavuta, tigwiritsa ntchito njira zojambula kapena kuwerengera manambala kuti tipeze kuti mphamvu yonse ndi yoposa 4.50 N ndipo ili pakati pa mzere wolumikiza \( q_2 \) ndi \( q_3 \) mpaka \( q_1 \).
Mapeto
Kudzera mu chitsanzo cha funso ndi kukambirana pamwambapa, titha kumvetsetsa momwe tingawerengere mphamvu yamagetsi pogwiritsa ntchito Lamulo la Coulomb. Mwa kugawa vutoli m'magawo osavuta ndikugwiritsa ntchito malingaliro a vector, titha kudziwa mphamvu yonse pa mphamvu iliyonse mu dongosolo. Mphamvu yamagetsi, ngakhale kuti ndi yosavuta mu kapangidwe kake ka masamu, imatha kukhala ndi zotsatira zofunikira komanso zovuta kwambiri pakugwiritsa ntchito zenizeni.
