Mibvunzo Yemuenzaniso Kukurukura Minda Yemagetsi Pamapurati Akafanana
Simba remagetsi riri mumaplate akafanana ipfungwa huru mufizikisi yemagetsi uye rinowanzo edzwa padanho rakasiyana redzidzo, kuchikoro chesekondari nekukoreji. Kunzwisisa zvakadzama pfungwa iyi kwakakosha, sezvo simba remagetsi riri mumaplate akafanana rakabatana zvakanyanya nemashandisirwo akasiyana-siyana anoshanda, kusanganisira dhizaini yemacapacitor nezvimwe zvishandiso zvemagetsi. Chinyorwa chino chichapa mienzaniso yezvinetso uye hurukuro yakadzama yesimba remagetsi riri mumaplate akafanana kuti zvibatsire kunzwisisa pfungwa iyi.
Dzidziso Yekutanga yeMagetsi Emagetsi muParallel Plates
Maplate akafanana iplate mbiri dzinofambisa magetsi dzine machaji emagetsi akatarisana uye dzakarongwa dzakafanana pane imwe daro. Muplate idzi dzakafanana, chaji inowanzo kugoverwa zvakaenzana pamusoro peplate. Zvichibva pamutemo waGauss, munda wemagetsi \( E \) uri pakati peplate mbiri dzinofambisa magetsi dzakafanana dzine machaji akatarisana unogona kuratidzwa se:
\[ E = \frac{\sigma}{\epsilon_0} \]
di mana:
– \( \sigma \) ndiko kuwanda kwechaji pamusoro peplate,
– \( \epsilon_0 \) ndiyo mvumo yekubvisa vacuum \((8.85 \times 10^{-12} \, \text{F/m})\).
Mumamiriro ezvinhu akanaka (zviyero zveplate zvakakura zvichienzaniswa nedaro riri pakati pawo), simba remagetsi riri pakati peplates rinoonekwa serakaenzana.
Mibvunzo yemuenzaniso nehurukuro
Mubvunzo 1:
Maplate maviri akafanana ane nzvimbo A yakakura zvikuru kana tichienzanisa nedaro \( d \) pakati pawo akarongwa kuitira kuti plate yepamusoro ive nechaji \( +Q \) uye plate yepasi ive nechaji \( -Q \). Kana daro riri pakati peplate mbiri iri \( 2 \, \text{mm} \), nzvimbo yeplate yega yega iri \( 1 \, \text{m}^2 \), uye chaji \( Q \) iri \( 1 \, \mu \text{C} \), sarudza nzvimbo yemagetsi iri pakati peplate dzakafanana!
Matanho Ekukurukurirana:
1. Kuwanda kweChaji Yepamusoro \( \sigma \) :
Kuwanda kwechaji pamusoro penzvimbo ndiko huwandu hwechaji panzvimbo imwe neimwe iri mundiro. Inogona kuverengerwa ne:
\[ \sigma = \frac{Q}{A} \]
Zvinozivikanwa:
– \( Q = 1 \, \mu \text{C} = 1 \times 10^{-6} \text{C} \)
– \( A = 1 \, \text{m}^2 \)
Saka:
\[ \sigma = \frac{1 \times 10^{-6} \text{C}}{1 \text{m}^2} = 1 \times 10^{-6} \text{C/m}^2 \]
2. Munda weMagetsi \(E \):
Nzvimbo yemagetsi iri pakati pemaplate maviri akafanana ane chaji yakatarisana ndiyo \( E = \frac{\sigma}{\epsilon_0} \).
Zvapiwa \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \), zvino:
\[ E = \frac{1 \times 10^{-6} \text{C/m}^2}{8.85 \times 10^{-12} \text{F/m}} \]
\[ E = 1.13 \kawa 10^5 \, \mashoko{N/C} \]
Saka, nzvimbo yemagetsi iri pakati pemaplate maviri iyi \( 1.13 \times 10^5 \, \text{N/C} \).
Mubvunzo 2:
Capacitor yeplate yakatsetseka ine maplate maviri akafanana ane nzvimbo ye \(2 \, \text{m}^2 \) imwe neimwe uye yakaparadzaniswa nedaro re \(1 \, \text{mm} \). Kana potential iri pamusoro peplate iri \(200 \, \text{V} \) uye pasi peplate iri 0 V, sarudza simba remagetsi pakati pemaplate maviri!
Matanho Ekukurukurirana:
1. Kuverengwa kweMusiyano Ungangodaro \( V \):
Zvinozivikanwa kuti ndiro yepamusoro ine mukana \( V_{\text{top}} = 200 \, \text{V} \) uye ndiro yepasi \( V_{\text{bottom}} = 0 \, \text{V} \). Saka, musiyano uripo \( V \) pakati pemaplate maviri ndewekuti:
\[ V = V_{\text{top}} – V_{\text{bottom}} = 200 \, \text{V} – 0 \, \text{V} = 200 \, \text{V} \]
2. Simba reMunda weMagetsi \( E \):
Munda wemagetsi uri mu capacitor yeplate yakafanana unogona kuverengerwa nekukamura musiyano wepotenti \( V \) nedaro \( d \):
\[ E = \frac{V}{d} \]
Zvichienderana nedaro \( d = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} \), zvino:
\[ E = \frac{200 \, \text{V}}{1 \times 10^{-3} \, \text{m}} = 2 \times 10^5 \, \text{V/m} \]
Saka, simba remagetsi pakati pemaplate maviri iri \( 2 \times 10^5 \, \text{V/m} \).
Mubvunzo 3:
Capacitor yeplate yakafanana ine maplate ane nzvimbo ye \( 0.5 \, \text{m}^2 \) uye chinhambwe pakati pemaplate e \( 0.5 \, \text{cm} \). Kana capacitor iyi yakachajwa nechaji ye \( 2 \, \mu \text{C} \), verenga capacitance yayo uye munda wemagetsi uri pakati pemaplate!
Matanho Ekukurukurirana:
1. Kugona \(C \) :
Kukwanisa kwe capacitor yeplate yakafanana kunogona kuverengerwa uchishandisa fomura:
\[ C = \epsilon_0 \frac{A}{d} \]
Zvinozivikanwa:
– \( \epsilon_0 = 8.85 \kawa 10^{-12} \, \text{F/m} \)
– \( A = 0.5 \, \text{m}^2 \)
– \( d = 0.5 \, \text{cm} = 0.5 \times 10^{-2} \, \text{m} \)
Saka:
\[ C = 8.85 \nguva 10^{-12} \, \text{F/m} \nguva \frac{0.5 \, \text{m}^2}{0.5 \nguva 10^{-2} \, \text{m}} \]
\[ C = 8.85 \kawa 10^{-12} \kawa 10 \, \text{F} \]
\[ C = 88.5 \kawa 10^{-12} \, \text{F} \]
\[ C = 88.5 \, \text{pF} \]
2. Munda weMagetsi \(E \):
Kuti tiverenge munda wemagetsi, tinofanira kutanga taziva musiyano wezvinogona kuitika \( V \). Musiyano wezvinogona kuitika \( V \) unogona kuverengerwa seizvi:
\[ V = \frac{Q}{C} \]
Zvinozivikanwa:
– \( Q = 2 \, \mu \text{C} = 2 \times 10^{-6} \text{C} \)
– \( C = 88.5 \kawa 10^{-12} \chinyorwa{F} \)
Saka:
\[ V = \frac{2 \times 10^{-6} \, \text{C}}{88.5 \times 10^{-12} \, \text{F}} \]
\[ V = 22.6 \kawa 10^3 \, \mashoko{V} \]
\[ V = 22.6 \, \text{kV} \]
Tevere, uchishandisa fomura \( E = \frac{V}{d} \), munda wemagetsi ndewekuti:
\[ E = \frac{22.6 \, \text{kV}}{0.5 \times 10^{-2} \, \text{m}} \]
\[ E = 22.6 \kawa 10^3 \, \frac{\text{V}}{0.5 \kawa 10^{-2} \, \text{m}} \]
\[ E = 4.52 \kawa 10^6 \, \mashoko{V/m} \]
Saka, capacitance ye capacitor ndeye \( 88.5 \, \text{pF} \) uye munda wemagetsi uri pakati pemaplates ndeye \( 4.52 \times 10^6 \, \text{V/m} \).
Mhedziso
Kunzwisisa simba remagetsi mumaplate akafanana kwakakosha kwete chete pabvunzo dzedzidzo asiwo pakushandisa zvinhu zvinoshanda muzvikamu zvakasiyana-siyana zveinjiniya nefizikisi. Nemuenzaniso wematambudziko nehurukuro dziri pamusoro apa, zvinotarisirwa kuti vaverengi vachanzwisisa zviri nani pfungwa iyi nekushandiswa kwayo, zvichivabatsira kuti vaiswedere pedyo nayo vaine chivimbo chakawanda mumamiriro ezvinhu chaiwo uye bvunzo.
