Fomula Yothekera Yamagetsi Yogulira Ma Pointi Anayi
Pegantar
Mphamvu yamagetsi ndi lingaliro lofunika kwambiri mu sayansi yamagetsi lomwe limatithandiza kumvetsetsa momwe ma charge amagetsi amagwirizanirana mumlengalenga. Tikamalankhula za point charge, tikutanthauza charge yomwe imaonedwa kuti ndi yokhazikika pamalo amodzi mumlengalenga. M'nkhaniyi, tikambirana za ma formula a power potential a ma point charge anayi osiyanasiyana, momwe tingawawerengere, ndi momwe lingaliroli limagwiritsidwira ntchito.
Lingaliro Loyambira la Mphamvu Yamagetsi
Mphamvu yamagetsi pamalo enaake ndi mphamvu yamagetsi pa unit charge yomwe ingadziwike ndi positive test charge yomwe imayikidwa pamalowo. Mphamvu yamagetsi nthawi zambiri imayesedwa mu volts (V). Mwa masamu, mphamvu yamagetsi \( V \) chifukwa cha charge \( q \) yomwe ili patali \( r \) kuchokera pamenepo imaperekedwa ndi fomula iyi:
\[ V = \frac{kq}{r} \]
Kumene:
– \( V \) ndi mphamvu yamagetsi (volts),
– \( k \) ndi Coulomb yosasintha (\( 8.99 \times 10^9 \, \text{N m}^2 \text{C}^{-2} \)),
– \( q \) ndiye cholipiritsa (coulomb),
– \(r \) ndi mtunda wochokera pa chaji mpaka pomwe mphamvu imawerengedwa (mamita).
Mphamvu yamagetsi ya mapointi anayi
Ngati tili ndi ma point charge anayi \( q_1 \), \( q_2 \), \( q_3 \), ndi \( q_4 \) omwe ali pamalo \( (x_1, y_1) \), \( (x_2, y_2) \), \( (x_3, y_3) \), ndi \( (x_4, y_4) \) mu ma Cartesian coordinates, tikhoza kuwerengera mphamvu yonse yamagetsi pa mfundo \( P(x, y) \) powerengera mphamvu zamagetsi zomwe zimachokera ku mphamvu iliyonse pa mfundo imeneyo.
Mphamvu yonse yamagetsi \( V \) pamalo \( P \) imaperekedwa ndi:
\[ V = V_1 + V_2 + V_3 + V_4 \]
Kumene:
– \( V_1 \) ndi mphamvu yamagetsi chifukwa cha \( q_1 \),
– \( V_2 \) ndi mphamvu yamagetsi chifukwa cha \( q_2 \),
– \( V_3 \) ndi mphamvu yamagetsi chifukwa cha \( q_3 \),
– \( V_4 \) ndi mphamvu yamagetsi chifukwa cha \( q_4 \).
Mphamvu yamagetsi chifukwa cha chaji iliyonse pamalopo \( P \) ikhoza kulembedwa motere:
\[ V_1 = \frac{k q_1}{r_1}, \quad V_2 = \frac{k q_2}{r_2}, \quad V_3 = \frac{k q_3}{r_3}, \quad V_4 = \frac{k q_4}{r_4} \]
Kumene:
– \( r_1 \) ndi mtunda pakati pa cholipiritsa \( q_1 \) ndi mfundo \( P \),
– \( r_2 \) ndi mtunda pakati pa cholipiritsa \( q_2 \) ndi mfundo \( P \),
– \( r_3 \) ndi mtunda pakati pa cholipiritsa \( q_3 \) ndi mfundo \( P \),
– \( r_4 \) ndi mtunda pakati pa cholipiritsa \( q_4 \) ndi mfundo \( P \).
Mtunda \( r \) pakati pa mfundo ziwiri mu ma coordinates a Cartesian ukhoza kuwerengedwa pogwiritsa ntchito fomula iyi:
\[r = \sqrt{(x – x_i)^2 + (y – y_i)^2} \]
Kumene:
– \( (x, y) \) ndi ma coordinates a mfundo \( P \),
– \( (x_i, y_i) \) ndi ma coordinates a charge \( q_i \) (i = 1, 2, 3, 4).
Motero, tikhoza kuwerengera mtunda \( r \) pa chaji iliyonse kenako tigwiritse ntchito njira yamagetsi ya potential kuti tipeze potential pamalo \( P \).
Chitsanzo cha Kuwerengera
Tiyeni titenge chitsanzo chenicheni cha ma point charge anayi motere:
– \( q_1 = 2 \, \mu \text{C} \) pa (0, 0),
– \( q_2 = -3 \, \mu \text{C} \) pa (1, 0),
– \( q_3 = 4 \, \mu \text{C} \) pa (0, 1),
– \( q_4 = -1 \, \mu \text{C} \) pa (1, 1).
Tikufuna kuwerengera mphamvu yamagetsi pamalo \( P \) omwe ali pa (2, 2).
Choyamba, timawerengera mtunda pakati pa mfundo \( P \) ndi cholipiritsa chilichonse:
\[ r_1 = \sqrt{(2-0)^2 + (2-0)^2} = \sqrt{8} = 2\sqrt{2} \]
\[ r_2 = \sqrt{(2-1)^2 + (2-0)^2} = \sqrt{5} \]
\[ r_3 = \sqrt{(2-0)^2 + (2-1)^2} = \sqrt{5} \]
\[ r_4 = \sqrt{(2-1)^2 + (2-1)^2} = \sqrt{2} \]
Kenako, timagwiritsa ntchito mtunda uwu kuti tiwerenge mphamvu yamagetsi chifukwa cha kuyitanitsa kulikonse pamalo \( P \):
\[ V_1 = \frac{8.99 \nthawi 10^9 \nthawi 2 \nthawi 10^{-6}}{2\sqrt{2}} \pafupifupi 3.18 \nthawi 10^3 \, \malemba{V} \]
\[ V_2 = \frac{8.99 \nthawi 10^9 \nthawi (-3) \nthawi 10^{-6}}{\sqrt{5}} \pafupifupi -3.81 \nthawi 10^3 \, \malemba{V} \]
\[ V_3 = \frac{8.99 \nthawi 10^9 \nthawi 4 \nthawi 10^{-6}}{\sqrt{5}} \pafupifupi 7.62 \nthawi 10^3 \, \malemba{V} \]
\[ V_4 = \frac{8.99 \nthawi 10^9 \nthawi (-1) \nthawi 10^{-6}}{\sqrt{2}} \pafupifupi -6.36 \nthawi 10^3 \, \malemba{V} \]
Mphamvu yonse yamagetsi pamalo \( P \) ndi chiwonkhetso cha mphamvu zonsezi:
\[ V = 3.18 \nthawi 10^3 – 3.81 \nthawi 10^3 + 7.62 \nthawi 10^3 – 6.36 \nthawi 10^3 \pafupifupi 0.63 \nthawi 10^3 \, \malemba{V} \]
Kugwiritsa Ntchito Mphamvu Zamagetsi
Kumvetsetsa mphamvu yamagetsi ya mphamvu iliyonse ya mfundo ndikofunikira pa ntchito zosiyanasiyana, kuphatikizapo:
– Kapangidwe ka ma circuit apakompyuta: Mainjiniya ayenera kumvetsetsa momwe magawidwe angagwirire ntchito mu circuit kuti atsimikizire kuti zigawo zikugwira ntchito bwino.
– Magawo amagetsi mu zamoyo: Mphamvu yamagetsi imagwira ntchito pa ntchito ya maselo amitsempha ndi kutumiza zizindikiro m'thupi.
– Kukonza zinthu: Mphamvu yamagetsi imagwiritsidwa ntchito mu njira zamagetsi monga kuyika zinthu zamagetsi ndi kukonza zinthu.
Mapeto
Kuwerengera mphamvu yamagetsi ya ma point charges angapo kumafuna kumvetsetsa koyambira momwe mphamvu yamagetsi imagwirira ntchito komanso momwe mtunda pakati pa ma charges umakhudzira. Ndi lingaliro ili, titha kufotokoza bwino ndikupanga machitidwe okhudzana ndi kuyanjana kwamagetsi. Mphamvu yamagetsi ndi chida chofunikira chomwe chimatithandiza kumvetsetsa dziko la fizikisi pamlingo wa microscopic ndi macroscopic.
