Mienzaniso yeMibvunzo Inotsanangura Mutemo waCoulomb
Mutemo waCoulomb ipfungwa huru mufizikisi inotsanangura simba riri pakati pemachaji maviri emagetsi. Wakadzidzwa mukati mechikamu che electrostatics, mutemo uyu unotsanangura kuti machaji emagetsi anokwezvana kana kudzingana sei. Mutemo uyu wakatanga kutaurwa nenyanzvi yefizikisi yekuFrance Charles-Augustin de Coulomb muzana remakore rechi18. Chinyorwa chino chichakurukura Mutemo waCoulomb nekuongorora mienzaniso nemhinduro dzawo, nokudaro zvichibatsira vaverengi kunzwisisa mashandisirwo anoshanda epfungwa iyi huru.
Hwaro hwedzidziso: Chii chinonzi Mutemo waCoulomb?
Mutemo waCoulomb unoti hukuru hwesimba remagetsi \( F \) pakati pemapoinzi maviri \( q_1 \) uye \( q_2 \) hwakaenzana zvakananga nechibereko chehukuru hwemapoinzi maviri uye hwakafanana nechikamu chedaro \( r \) riri pakati pawo. Pamasvomhu, fomura yeMutemo waCoulomb inogona kuratidzwa seizvi:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Di mana:
– \( F \) ndiko kukura kwesimba remagetsi
– \( k_e \) ishoko rekuti Coulomb risingaperi (\( 8.9875 \times 10^9 \, N \cdot m^2 \cdot C^{-2} \))
– \( q_1 \) uye \( q_2 \) ndiwo hukuru hwechaji yemagetsi
– \( r \) ndiyo daro riri pakati pezvinopomerwa zviviri
Muenzaniso Mubvunzo 1
Mubvunzo:
Kune mapoinzi maviri ekuchaja: \( q_1 = 2 \times 10^{-6} \, C \) uye \( q_2 = -3 \times 10^{-6} \, C \). Iwo akaparadzana nemamita 0,05. Verenga hukuru hwesimba remagetsi rinoshanda pakati pemachaji maviri.
Kukurukurirana:
Danho rekutanga nderekunyora patsva fomura yeMutemo waCoulomb:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Zvino tinotsiva tsika dzinozivikanwa mufomura:
\[ k_e = 8.9875 \kawa 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[ q_1 = 2 \kawa 10^{-6} \, C \]
\[ q_2 = -3 \kawa 10^{-6} \, C \]
\[r = 0,05 \, m \]
Tinoisa izvi mufomura:
\[ F = 8.9875 \nguva 10^9 \, \frac{|2 \nguva 10^{-6} \cdot -3 \nguva 10^{-6}|}{(0,05)^2} \]
\[ F = 8.9875 \kawa 10^9 \, \frac{6 \kawa 10^{-12}}{0,0025} \]
\[ F = 8.9875 \kawa 10^9 \, \frac{6 \kawa 10^{-12}}{2,5 \kawa 10^{-3}} \]
\[ F = 8.9875 \kawa 10^9 \, \kawa 2,4 \kawa 10^{-9} \]
\[ F = 21.57 \, N \]
Nekuti chaji \(q_2 \) haina kunaka, simba remagetsi rinoshanda isimba rinokwezva, nekuti chaji dzakanaka nedzisina kunaka dzinokwezvana.
Muenzaniso Mubvunzo 2
Mubvunzo:
Machaji maviri emagetsi \( q_1 = 5 \times 10^{-9} \, C \) uye \( q_2 = 10 \times 10^{-9} \, C \) akaparadzaniswa nedaro remamita 0,1. Verenga hukuru hwesimba remagetsi rinoshanda pa \( q_1 \).
Kukurukurirana:
Shandisa fomura yeMutemo waCoulomb zvakare:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Tsiva tsika dzinozivikanwa:
\[ k_e = 8.9875 \kawa 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[ q_1 = 5 \kawa 10^{-9} \, C \]
\[ q_2 = 10 \kawa 10^{-9} \, C \]
\[r = 0,1 \, m \]
\[ F = 8.9875 \kawa 10^9 \, \frac{(5 \kawa 10^{-9}) (10 \kawa 10^{-9})}{(0,1)^2} \]
\[ F = 8.9875 \kawa 10^9 \, \frac{50 \kawa 10^{-18}}{0,01} \]
\[ F = 8.9875 \kawa 10^9 \, \kawa 5 \kawa 10^{-15} \]
\[ F = 44.9375 \, N \]
Simba rinoshanda isimba rinodzinga, nekuti machaja ese \( q_1 \) uye \( q_2 \) ane chiratidzo chimwe chete, icho chiri chekuti zvakanaka.
Muenzaniso Mubvunzo 3
Mubvunzo:
Mapoinzi matatu ari mumutsetse wakatwasuka. Chaji yekutanga ndi \( q_1 = 2 \mu C \), chaji yechipiri ndi \( q_2 = -1 \mu C \), uye chaji yechitatu ndi \( q_3 = 3 \mu C \). Daro riri pakati pa \( q_1 \) na \( q_2 \) i0,1 m, nepo dariro riri pakati pa \( q_2 \) na \( q_3 \) iri 0,2 m. Verenga hukuru negwara resimba rese remagetsi rinoshanda pa \( q_2 \).
Kukurukurirana:
Kutanga, tinoverenga simba remagetsi pakati pe \( q_1 \) uye \( q_2 \):
\[ F_{12} = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
\[ k_e = 8.9875 \kawa 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[ q_1 = 2 \kawa 10^{-6} \, C \]
\[ q_2 = -1 \kawa 10^{-6} \, C \]
\[r = 0,1 \, m \]
\[ F_{12} = 8.9875 \nguva 10^9 \, \frac{(2 \nguva 10^{-6}) (-1 \nguva 10^{-6})}{(0,1)^2} \]
\[ F_{12} = 8.9875 \kawa 10^9 \, \frac{2 \kawa 10^{-12}}{0,01} \]
\[ F_{12} = 8.9875 \kawa 10^9 \, \kawa 2 \kawa 10^{-10} \]
\[ F_{12} = 1.7975 \, N \]
Sezvo \( q_1 \) iri yakanaka uye \( q_2 \) iri yakaipa, simba \( F_{12} \) isimba rinokwezva rakanangidzirwa ku \( q_1 \).
Chechipiri, tinoverenga simba remagetsi pakati pe \( q_2 \) ne \( q_3 \):
\[ F_{23} = k_e \frac{|q_2 \cdot q_3|}{r^2} \]
\[ q_2 = -1 \kawa 10^{-6} \, C \]
\[ q_3 = 3 \kawa 10^{-6} \, C \]
\[r = 0,2 \, m \]
\[ F_{23} = 8.9875 \kawa 10^9 \, \frac{(-1 \kawa 10^{-6}) (3 \kawa 10^{-6})}{(0,2)^2} \]
\[ F_{23} = 8.9875 \kawa 10^9 \, \frac{3 \kawa 10^{-12}}{0,04} \]
\[ F_{23} = 8.9875 \kawa 10^9 \, \kawa 7.5 \kawa 10^{-11} \]
\[ F_{23} = 0.67406 \, N \]
Sezvo \( q_2 \) iri negative uye \( q_3 \) iri positive, simba \( F_{23} \) isimba rinokwezva rakanangidzirwa ku \( q_3 \).
Pakupedzisira, tinobatanidza masimba ese maviri kuti tiwane mhedzisiro yekupedzisira:
Simba rose pa \( q_2 \):
\[ F_{\text{total}} = F_{12} – F_{23} \]
\[ F_{\text{total}} = 1.7975 \, N – 0.67406\, N \]
\[ F_{\text{total}} = 1.12344 \, N \]
Kutungamira kwesimba rose kuri kuenda ku \( q_1 \) nekuti simba \( F_{12} \) rakakura kupfuura \( F_{23} \).
Mhedziso
Mutemo waCoulomb unopa ruzivo rwakakosha pamusoro pekudyidzana kuripo pakati pemari dzemagetsi, dzinokwezva nedzinosemesa. Mienzaniso yakakurukurwa inoratidza kushandiswa kwemutemo uyu pakuverenga masimba emagetsi nekufunga nezvehukuru hwemari uye daro riri pakati pawo. Kunzwisisa zvakakwana Mutemo waCoulomb kunogona kutibatsira kunzwisisa zviitiko zvakasiyana-siyana zvemagetsi nemagineti zvinoitika zvakatikomberedza.
