Mafunso ndi Zitsanzo za Magawo a Magetsi
Mphamvu yamagetsi ndi lingaliro lofunikira mu fizikiki lomwe limafotokoza momwe chinthu chodzazidwa ndi magetsi chimakhudzira malo ozungulira. Mphamvu yamagetsi ndi mphamvu yomwe imagwiritsidwa ntchito pamalo aliwonse mumlengalenga chifukwa cha mphamvuyo. Kuti mumvetse bwino lingaliro ili, nthawi zambiri pamafunika kuchita khama kwambiri. Pansipa pali zitsanzo za mavuto ndi zokambirana zatsatanetsatane zokhudza mphamvu yamagetsi.
Chitsanzo Funso 1: Kuwerengera Kukula kwa Magetsi Pamalo Ena
Funso:
Ma point charge awiri \( q_1 = +4 \mu C \) ndi \( q_2 = -8 \mu C \) amayikidwa pa ma coordinates (0, 0) ndi (0, 2) mamita. Werengani kukula ndi njira ya magetsi pa mfundo A yomwe ili pa (0, 1) mamita.
Kukambirana:
1. Dziwani mtunda pakati pa mfundo A ndi ma charge awiri:
– Mtunda wochokera ku (q_1 \) kupita ku mfundo A ndi mita imodzi.
– Mtunda wochokera ku (q_2 \) kupita ku mfundo A ndi mita imodzi.
2. Werengani mphamvu yamagetsi yomwe imabwera chifukwa cha mphamvu iliyonse pa mfundo A:
Mphamvu yamagetsi chifukwa cha mphamvu ya mfundo \( q \) patali \( r \) ndi:
\[ E = \frac{k \cdot |q|}{r^2} \]
kwa \( q_1 \) ndi \( q_2 \):
\[ E_1 = \frac{9 \times 10^9 \cdot 4 \times 10^{-6}}{1^2} = 36 \times 10^3 \, \text{N/C} \]
\[ E_2 = \frac{9 \times 10^9 \cdot 8 \times 10^{-6}}{1^2} = 72 \times 10^3 \, \text{N/C} \]
3. Dziwani komwe magetsi akupita:
Popeza \(q_1 \) ndi positive charge, malo ake amagetsi amaloza kutali ndi charge, kotero \(E_1 \) ali mu positive y-direction (mmwamba).
Popeza \(q_2 \) ndi chaji yoyipa, mphamvu yamagetsi imayang'ana chaji, kotero \(E_2 \) ili mu njira yoyipa ya y (pansi).
4. Werengani mphamvu yamagetsi yomwe yapezeka:
Popeza \( E_1 \) ndi \( E_2 \) ali pamzere wowongoka womwewo, titha kuchotsa minda yamagetsi:
\[ E_{\mawu{chiwerengero}} = E_2 – E_1 \]
\[ E_{\text{total}} = 72 \nthawi 10^3 – 36 \nthawi 10^3 \]
\[ E_{\text{total}} = 36 \times 10^3 \, \text{N/C} \]
Njira ya magetsi ikupita ku negative y-axis (pansi).
Chitsanzo Funso 2: Kuwerengera Mphamvu ya Magetsi Pamalo Ena
Funso:
Ma point charge awiri \( q_1 = +2 \mu C \) ndi \( q_2 = +3 \mu C \) amayikidwa pa ma coordinates (0, 0) ndi (4, 0) mamita. Werengani mphamvu yamagetsi pa point B yomwe ili pa (2, 0) mamita.
Kukambirana:
1. Dziwani mtunda pakati pa mfundo B ndi ma charge awiri:
– Mtunda wochokera ku (q_1 \) kupita ku mfundo B ndi mamita awiri.
– Mtunda wochokera ku (q_2 \) kupita ku mfundo B ndi mamita awiri.
2. Werengani mphamvu yamagetsi chifukwa cha chaji iliyonse pa mfundo B:
Mphamvu yamagetsi chifukwa cha kutchaja kwa mfundo \( q \) patali \( r \) ndi:
\[ V = \frac{k \cdot q}{r} \]
kwa \( q_1 \) ndi \( q_2 \):
\[ V_1 = \frac{9 \times 10^9 \cdot 2 \times 10^{-6}}{2} = 9 \times 10^3 \, \text{V} \]
\[ V_2 = \frac{9 \times 10^9 \cdot 3 \times 10^{-6}}{2} = 13.5 \times 10^3 \, \text{V} \]
3. Werengani mphamvu yonse yamagetsi pa mfundo B:
Mphamvu yamagetsi ndi kuchuluka kwa scalar, kotero mphamvu yonse ndi chiwerengero cha algebraic cha mphamvu izi:
\[ V_{\text{total}} = V_1 + V_2 \]
\[ V_{\text{total}} = 9 \nthawi 10^3 + 13.5 \nthawi 10^3 \]
\[ V_{\text{total}} = 22.5 \times 10^3 \, \text{V} \]
Chitsanzo 3: Malo Ogwiritsira Ntchito Magetsi mu Dielectric Material
Funso:
Ngati chaji \( q = 5 \mu C \) yayikidwa pakati pa bwalo lopanda kanthu lomwe lili ndi utali wa mamita atatu lomwe ladzazidwa ndi dielectric yokhala ndi dielectric constant \( \kappa = 2 \). Werengani munda wamagetsi pa mtunda wa mamita awiri kuchokera pakati pa bwalo.
Kukambirana:
1. Fomula ya gawo lamagetsi mu chinthu cha dielectric:
Munda wamagetsi \( E \) patali \( r \) mu chinthu cha dielectric ndi:
\[ E = \frac{q}{4 \pi \epsilon_0 \kappa r^2} \]
kumene \( \epsilon_0 = 8.85 \nthawi 10^{-12} \) F/m.
2. Lowetsani mfundo zomwe zaperekedwa:
\[ E = \frac{5 \times 10^{-6}}{4 \pi \cdot 8.85 \times 10^{-12} \cdot 2 \cdot (2)^2} \]
\[ E = \frac{5 \times 10^{-6}}{4 \pi \cdot 8.85 \times 10^{-12} \cdot 8} \]
\[ E = \frac{5 \times 10^{-6}}{8 \cdot 3.54 \times 10^{-10}} \]
\[ E = \frac{5 \times 10^{-6}}{28.32 \times 10^{-10}} \]
\[ E = 1.77 \nthawi 10^4 \, \malemba{N/C} \]
Mapeto
Kudzera mu zitsanzo zomwe zili pamwambapa, titha kumvetsetsa bwino lingaliro la magawo amagetsi. Izi zikuphatikizapo kukula kwa gawo lamagetsi panthawi inayake chifukwa cha ma charges angapo, kuwerengera mphamvu yamagetsi, ndi gawo lamagetsi muzinthu zamagetsi. Kumvetsetsa bwino lingaliro ili ndikofunikira chifukwa zochitika zambiri zakuthupi zitha kufotokozedwa ndi magawo amagetsi, komanso momwe amagwiritsidwira ntchito muukadaulo wamakono. Pitirizani kuchita ndi mavuto osiyanasiyana kuti mumvetse bwino lingaliro ili.
