Ifomula Engaba Khona Kagesi Yezinkokhelo Ezine Amaphuzu Amane
I-Pengantar
Amandla kagesi angumqondo obalulekile ku-physics kagesi osisiza siqonde ukuthi amashaja kagesi asebenzisana kanjani esikhaleni. Uma sikhuluma ngokushaja kwephuzu, sibhekisela ekushajeni okubhekwa njengokugxilile endaweni eyodwa esikhaleni. Kulesi sihloko, sizoxoxa ngamafomula amandla kagesi amashaja amane ahlukene, indlela yokuwabala, kanye nokusetshenziswa okusebenzayo kwalomqondo.
Umqondo Oyisisekelo Wamandla Kagesi
Amandla kagesi endaweni ethile esikhaleni amandla kagesi angasetshenziswa ngeyunithi ngayinye yokushaja okuzobonakala ngokushaja okuhle okubekwe kuleyo ndawo. Amandla kagesi avame ukulinganiswa ngama-volts (V). Ngokwezibalo, amandla kagesi \( V \) ngenxa yokushaja \( q \) okude \( r \) kusuka kuwo anikezwa ngefomula:
\[ V = \frac{kq}{r} \]
Di mana:
– \( V \) amandla kagesi (ama-volts),
– \( k \) yi-Coulomb constant (\( 8.99 \times 10^9 \, \text{N m}^2 \text{C}^{-2} \)),
– \( q \) yinkokhelo (coulomb),
– \(r \) ibanga elisuka ekushajweni kuya endaweni lapho amandla ebalwe khona (amamitha).
Amandla kagesi ezindleko zamaphuzu amane
Uma sinezinkokhelo zamaphuzu amane \( q_1 \), \( q_2 \), \( q_3 \), kanye \( q_4 \) ezitholakala ezindaweni \( (x_1, y_1) \), \( (x_2, y_2) \), \( (x_3, y_3) \), kanye \( (x_4, y_4) \) kuma-coordinates e-Cartesian, singabala amandla kagesi aphelele endaweni ethile \( P(x, y) \) ngokufingqa amandla kagesi ngenxa yokushaja ngakunye kuleyo ndawo.
Amandla kagesi aphelele \( V \) endaweni \( P \) anikezwa ngu:
\[ V = V_1 + V_2 + V_3 + V_4 \]
Di mana:
– \( V_1 \) amandla kagesi abangelwa \( q_1 \),
– \( V_2 \) amandla kagesi abangelwa \( q_2 \),
– \( V_3 \) amandla kagesi abangelwa \( q_3 \),
– \( V_4 \) amandla kagesi abangelwa \( q_4 \).
Amandla kagesi abangelwa ukushaja ngakunye endaweni \( P \) angabhalwa kanje:
\[ V_1 = \frac{k q_1}{r_1}, \quad V_2 = \frac{k q_2}{r_2}, \quad V_3 = \frac{k q_3}{r_3}, \quad V_4 = \frac{k q_4}{r_4} \]
Di mana:
– \( r_1 \) ibanga eliphakathi kokushaja \( q_1 \) kanye nephuzu \( P \),
– \( r_2 \) ibanga eliphakathi kokushaja \( q_2 \) kanye nephuzu \( P \),
– \( r_3 \) ibanga eliphakathi kokushaja \( q_3 \) kanye nephuzu \( P \),
– \( r_4 \) ibanga eliphakathi kokushaja \( q_4 \) kanye nephuzu \( P \).
Ibanga \( r \) phakathi kwamaphuzu amabili kuma-coordinate e-Cartesian lingabalwa kusetshenziswa ifomula:
\[r = \sqrt{(x – x_i)^2 + (y – y_i)^2} \]
Di mana:
– \( (x, y) \) yizixhumanisi zephuzu \( P \),
– \( (x_i, y_i) \) yizixhumanisi zokushaja \( q_i \) (i = 1, 2, 3, 4).
Ngakho-ke, singabala ibanga \( r \) lokushaja ngakunye bese sisebenzisa ifomula yamandla kagesi ukuthola amandla endaweni \( P \).
Isibonelo Sokubala
Ake sithathe isibonelo esiqondile ngama-point charge amane kanje:
– \( q_1 = 2 \, \mu \text{C} \) ku-(0, 0),
– \( q_2 = -3 \, \mu \text{C} \) ku-(1, 0),
– \( q_3 = 4 \, \mu \text{C} \) ku-(0, 1),
– \( q_4 = -1 \, \mu \text{C} \) ku-(1, 1).
Sifuna ukubala amandla kagesi endaweni ethi \( P \) etholakala ku-(2, 2).
Okokuqala, sibala ibanga eliphakathi kwephuzu \( P \) kanye nenkokhelo ngayinye:
\[ r_1 = \sqrt{(2-0)^2 + (2-0)^2} = \sqrt{8} = 2\sqrt{2} \]
\[ r_2 = \sqrt{(2-1)^2 + (2-0)^2} = \sqrt{5} \]
\[ r_3 = \sqrt{(2-0)^2 + (2-1)^2} = \sqrt{5} \]
\[ r_4 = \sqrt{(2-1)^2 + (2-1)^2} = \sqrt{2} \]
Bese, sisebenzisa leli nani lebanga ukubala amandla kagesi ngenxa yokushaja ngakunye endaweni ethi \( P \):
\[ V_1 = \frac{8.99 \izikhathi ezingu-10^9 \izikhathi ezingu-2 \izikhathi ezingu-10^{-6}}{2\sqrt{2}} \cishe kube ngu-3.18 \izikhathi ezingu-10^3 \, \umbhalo{V} \]
\[ V_2 = \frac{8.99 \izikhathi ezingu-10^9 \izikhathi (-3) \izikhathi ezingu-10^{-6}}{\sqrt{5}} \cishe -3.81 \izikhathi ezingu-10^3 \, \umbhalo{V} \]
\[ V_3 = \frac{8.99 \izikhathi ezingu-10^9 \izikhathi ezingu-4 \izikhathi ezingu-10^{-6}}{\sqrt{5}} \cishe kube ngu-7.62 \izikhathi ezingu-10^3 \, \umbhalo{V} \]
\[ V_4 = \frac{8.99 \izikhathi ezingu-10^9 \izikhathi (-1) \izikhathi ezingu-10^{-6}}{\sqrt{2}} \cishe -6.36 \izikhathi ezingu-10^3 \, \umbhalo{V} \]
Amandla kagesi aphelele endaweni \( P \) ayisamba sawo wonke la mandla kagesi:
\[ V = 3.18 \izikhathi 10^3 – 3.81 \izikhathi 10^3 + 7.62 \izikhathi 10^3 – 6.36 \izikhathi 10^3 \cishe 0.63 \izikhathi 10^3 \, \umbhalo{V} \]
Ukusetshenziswa Kwe-Electric Potential
Ukuqonda amandla kagesi anoma yiliphi ishaja yephoyinti kubalulekile ezinhlotsheni ezahlukene zokusebenza, okuhlanganisa:
– Umklamo wesekethe ye-elekthronikhi: Onjiniyela kumele baqonde ukusatshalaliswa okungenzeka kwesekethe ukuqinisekisa ukuthi izingxenye zisebenza kahle.
– Amasimu kagesi ku-biology: Amandla kagesi adlala indima ekusebenzeni kwamaseli ezinzwa kanye nokudluliswa kwesignali emzimbeni.
– Ukucubungula izinto: Amandla kagesi asetshenziswa kumasu kagesi anjengokufakwa kwe-electrostatic kanye nokuhluzwa kwezinto.
Isiphetho
Ukubala amandla kagesi wamacala amaningana okushaja kudinga ukuqonda okuyisisekelo kokuthi amandla kagesi asebenza kanjani nokuthi ibanga eliphakathi kwamacala lithinta kanjani. Ngale mbono, singachaza futhi sakhe izinhlelo ezihilela ukusebenzisana kukagesi ngempumelelo. Amandla kagesi ayithuluzi elibalulekile elisisiza siqonde umhlaba wefiziksi kokubili emazingeni amancane namakhulu.
