Mienzaniso yeMibvunzo Inotaura NezveSimba reMagetsi
Tsanangudzo yesimba remagetsi isimba rinobva mukusangana pakati pemagetsi. Simba iri rinodzidzwa mufizikisi, kunyanya mubazi re electrodynamics. Mhedzisiro yesimba remagetsi inogona kuonekwa muzviitiko zvakawanda zvezuva nezuva, kubva pakukwesha zvimwe zvinhu pamwe chete kusvika pakushanda kwemidziyo yemagetsi. Chinyorwa chino chichakurukura mienzaniso yakati wandei yematambudziko esimba remagetsi nemhinduro dzawo, pamwe nepfungwa huru dzine chekuita nesimba remagetsi.
Nhanganyaya kuMasimba Emagetsi
Simba remagetsi riri pakati pemagetsi maviri rinopihwa neMutemo waCoulomb, uyo unoratidzwa ne equation:
$$ F = k_e \frac{|q_1 q_2|}{r^2} $$
di mana:
– \( F \) isimba remagetsi riri pakati pekuchaja mbiri.
– \( q_1 \) uye \( q_2 \) ndiwo hukuru hwemari dzinobhadharwa.
– \( r \) ndiyo daro riri pakati pemachaji maviri.
– \( k_e \) ndiyo constant yeCoulomb (inenge \(8.99 \times 10^9 \, N \cdot m^2 / C^2\)).
Mutemo waCoulomb wakafanana nemutemo waNewton wesimba rinokwevera pasi, asi simba rinokwevera pasi rinogara richikwezva nepo simba remagetsi richigona kukwezva kana kutsamwisa zvichienderana nechiratidzo chechaji.
Mibvunzo yemuenzaniso nekukurukurirana
Mubvunzo 1: Mari mbiri dzakaenzana
Mapoinzi maviri \( q_1 = 3 \, \mu C \) uye \( q_2 = -4 \, \mu C \) ari kure nemamita 0.5 kubva kune mumwe nemumwe. Verenga simba remagetsi rinoshanda pakati pemapoinzi maviri aya.
Kukurukurirana:
1. Kuzivikanwa kweMutoro neDaro:
– \( q_1 = 3 \, \mu C = 3 \kawa 10^{-6} \, C \)
– \( q_2 = -4 \, \mu C = -4 \kawa 10^{-6} \, C \)
– \( r = 0.5 \, m \)
2. Kutsiva Mutemo waCoulomb:
\[
F = k_e \frac{|q_1 q_2|}{r^2}
\]
\[
F = 8.99 \kawa 10^9 \, \frac{(3 \kawa 10^{-6})(4 \kawa 10^{-6})}{(0.5)^2}
\]
3. Verenga Mhedzisiro:
\[
F = 8.99 \kawa 10^9 \, \frac{12 \kawa 10^{-12}}{0.25}
\]
\[
F = 8.99 \kawa 10^9 \kawa 48 \kawa 10^{-12}
\]
\[
F = 431.52 \kawa 10^{-3} \, N
\]
\[
F \inenge 0.432 \, N
\]
Saka, simba remagetsi rinoshanda pakati pemachaji maviri aya rinosvika 0.432 Newtons.
Mubvunzo 2: Kubhadharisa Mari Dzakawanda
Mapoinzi matatu, \( q_1 = 2 \, \mu C \), \( q_2 = 3 \, \mu C \), uye \( q_3 = -1 \, \mu C \) akaiswa mumutsara wakatwasuka nedaro riri pakati pe \( q_1 \) ne \( q_2 \) riri 0.6 metres uye pakati pe \( q_2 \) ne \( q_3 \) riri 0.4 metres. Verenga simba rinobuda pa \( q_2 \).
Kukurukurirana:
1. Kuzivikanwa kweMutoro neDaro:
– \( q_1 = 2 \, \mu C = 2 \kawa 10^{-6} \, C \)
– \( q_2 = 3 \, \mu C = 3 \kawa 10^{-6} \, C \)
– \( q_3 = -1 \, \mu C = -1 \kawa 10^{-6} \, C \)
– Daro riri pakati pe(q_1 \) ne(q_2 \) i0.6 m
– Daro riri pakati pe(q_2 \) ne(q_3 \) i0.4 m
2. Kumanikidza \( q_1 \) kurwisa \( q_2 \):
\[
F_{12} = k_e \frac{|q_1 q_2|}{r_{12}^2}
\]
\[
F_{12} = 8.99 \kawa 10^9 \, \frac{(2 \kawa 10^{-6})(3 \kawa 10^{-6})}{(0.6)^2}
\]
\[
F_{12} = 8.99 \kawa 10^9 \, \frac{6 \kawa 10^{-12}}{0.36}
\]
\[
F_{12} = 8.99 \kawa 10^9 \kawa 16.67 \kawa 10^{-12}
\]
\[
F_{12} \inenge 0.15 \, N
\]
Kutungamira kwesimba \( F_{12} \) kuri kure ne \( q_1 \) (kurudyi).
3. Kumanikidza \( q_3 \) kurwisa \( q_2 \):
\[
F_{32} = k_e \frac{|q_3 q_2|}{r_{32}^2}
\]
\[
F_{32} = 8.99 \kawa 10^9 \, \frac{(1 \kawa 10^{-6})(3 \kawa 10^{-6})}{(0.4)^2}
\]
\[
F_{32} = 8.99 \kawa 10^9 \, \frac{3 \kawa 10^{-12}}{0.16}
\]
\[
F_{32} = 8.99 \kawa 10^9 \kawa 18.75 \kawa 10^{-12}
\]
\[
F_{32} \inenge 0.17 \, N
\]
Kutungamira kwesimba \( F_{32} \) kuri kudhonza kuenda ku \( q_3 \) (kuruboshwe).
4. Simba Rinobuda:
Sezvo \( F_{12} \) iri kurudyi uye \( F_{32} \) iri kuruboshwe, simba rinobuda \( F_{res} = F_{32} – F_{12} \):
\[
F_{res} = 0.17 \,N – 0.15 \,N
\]
\[
F_{res} = 0.02 \, N (kuruboshwe)
\]
Saka, simba rinobuda pa \( q_2 \) i0.02 Newton kuruboshwe.
Mubvunzo 3: Sisitimu yekutakura zvinhu muTriangle
Mapoinzi matatu \( q_1 = 5 \, \mu C \), \( q_2 = -3 \, \mu C \), uye \( q_3 = 4 \, \mu C \) akaiswa pamakona matatu etriangle yakaenzana ine kureba kwemativi 0.2 metres. Verenga simba rese remagetsi rinoshanda pachaji \( q_1 \).
Kukurukurirana:
1. Kumanikidza \( q_2 \) kurwisa \( q_1 \):
\[
F_{12} = k_e \frac{|q_1 q_2|}{r^2}
\]
\[
F_{12} = 8.99 \kawa 10^9 \, \frac{(5 \kawa 10^{-6})(3 \kawa 10^{-6})}{(0.2)^2}
\]
\[
F_{12} = 8.99 \kawa 10^9 \, \frac{15 \kawa 10^{-12}}{0.04}
\]
\[
F_{12} = 8.99 \kawa 10^9 \kawa 375 \kawa 10^{-12}
\]
\[
F_{12} \inenge 3.37 \, N
\]
Kutungamira kwesimba \( F_{12} \) kunokwezva pakatarisana ne \( q_2 \).
2. Kumanikidza \( q_3 \) kurwisa \( q_1 \):
\[
F_{13} = k_e \frac{|q_1 q_3|}{r^2}
\]
\[
F_{13} = 8.99 \kawa 10^9 \, \frac{(5 \kawa 10^{-6})(4 \kawa 10^{-6})}{(0.2)^2}
\]
\[
F_{13} = 8.99 \kawa 10^9 \, \frac{20 \kawa 10^{-12}}{0.04}
\]
\[
F_{13} = 8.99 \kawa 10^9 \kawa 500 \kawa 10^{-12}
\]
\[
F_{13} \inenge 4.50 \, N
\]
Kutungamira kwesimba \( F_{13} \) kunosemesa kubva ku \( q_3 \).
3. Simba Rinobuda:
Tinofanira kushandisa nzira yevector kuti tiwane mhedzisiro ye \( F_{12} \) uye \( F_{13} \), nekuti kona iri pakati pemasimba i60 degrees (equilateral triangle).
Tichishandisa zvikamu zve x na y, tinogona kuona simba rose. Zvisinei, kuti zvive nyore, tichashandisa nzira dzemifananidzo kana kuverenga nhamba kuti tione kuti simba rose rakakura kupfuura 4.50 N uye riri pakati pemutsetse unobatanidza \( q_2 \) uye \( q_3 \) kusvika \( q_1 \).
Mhedziso
Kuburikidza nemuenzaniso wedambudziko nehurukuro iri pamusoro apa, tinogona kunzwisisa maverengero esimba remagetsi tichishandisa Mutemo waCoulomb. Nekuparadzanisa dambudziko kuita matanho ari nyore uye kushandisa fungidziro dzevector, tinogona kuona simba rese pachaji yega yega musystem. Simba remagetsi, kunyangwe riri nyore mukugadzirwa kwaro kwemasvomhu, rinogona kuva nemigumisiro yakakosha uye yakaoma mukushandiswa kwenyika chaiyo.
