Imibuzo Eyisibonelo Exoxa Ngezinkundla Zikagesi Ezisezindizeni Ezihambisanayo
Insimu kagesi kumapuleti ahambisanayo ingumqondo oyisisekelo kufiziksi kagesi futhi ivame ukuhlolwa emazingeni ahlukahlukene ezemfundo, kokubili esikoleni samabanga aphezulu nasekolishi. Ukuqonda kahle lo mqondo kubalulekile, njengoba insimu kagesi kumapuleti ahambisanayo ihlobene kakhulu nezinhlelo zokusebenza ezahlukahlukene ezisebenzayo, okuhlanganisa ukwakheka kwama-capacitor namanye amadivayisi kagesi. Lesi sihloko sizohlinzeka ngezibonelo zezinkinga kanye nengxoxo eningiliziwe yensimu kagesi kumapuleti ahambisanayo ukusiza ukuqonda lo mqondo.
Umbono Oyisisekelo Wezinkundla Zikagesi Ezindizeni Ezihambisanayo
Amapuleti ahambisanayo angamapuleti amabili okuhambisa athwala amacala kagesi aphambene futhi ahlelwe ngokuhambisana ebangeni elithile. Kula mapuleti ahambisanayo, icala lizosatshalaliswa ngokulinganayo ebusweni bamapuleti. Ngokusekelwe emthethweni kaGauss, insimu kagesi \( E \) phakathi kwamapuleti amabili okuhambisa ahambisanayo anamacala aphambene ingachazwa kanje:
\[ E = \frac{\sigma}{\epsilon_0} \]
Kuphi:
– \( \sigma \) ukuminyana kweshaja ebusweni epuletini,
– \( \epsilon_0 \) yi-vacuum permittivity \((8.85 \times 10^{-12} \, \text{F/m})\).
Ngaphansi kwezimo ezifanele (ubukhulu bepuleti bukhulu uma buqhathaniswa nebanga eliphakathi kwawo), insimu kagesi phakathi kwamapuleti ibhekwa njengefanayo.
Imibuzo Nezingxoxo Eziyisibonelo
Umbuzo 1:
Amapuleti amabili ahambisanayo anendawo engu-A enkulu kakhulu uma kuqhathaniswa nebanga \( d \) phakathi kwawo ahlelwe ngendlela yokuthi ipuleti eliphezulu libe nokushaja \( +Q \) kanti ipuleti elingezansi libe nokushaja \( -Q \). Uma ibanga eliphakathi kwamapuleti amabili lingu-\( 2 \, \text{mm} \), indawo yepuleti ngalinye ingu-\( 1 \, \text{m}^2 \), kanti ukushaja \( Q \) kungu-\( 1 \, \mu \text{C} \), nquma insimu kagesi phakathi kwamapuleti ahambisanayo!
Izinyathelo Zokuxoxisana:
1. Ubuningi Beshaja Yomphezulu \( \sigma \) :
Ubuningi beshaja engaphezulu yinani leshaja ngeyunithi ngayinye endaweni epuletini. Lingabalwa kanje:
\[ \sigma = \frac{Q}{A} \]
Kuyaziwa:
– \( Q = 1 \, \mu \text{C} = 1 \times 10^{-6} \text{C} \)
– \( A = 1 \, \text{m}^2 \)
Ngakho-ke:
\[ \sigma = \frac{1 \times 10^{-6} \text{C}}{1 \text{m}^2} = 1 \times 10^{-6} \text{C/m}^2 \]
2. Inkundla Kagesi \(E \):
Insimu kagesi ephakathi kwamapuleti amabili ahambisanayo aneshaja ephambene yi-\( E = \frac{\sigma}{\epsilon_0} \).
Uma kunikezwe \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \), bese kuba:
\[ E = \frac{1 \times 10^{-6} \text{C/m}^2}{8.85 \times 10^{-12} \text{F/m}} \]
\[ E = 1.13 \izikhathi 10^5 \, \umbhalo{N/C} \]
Ngakho-ke, insimu kagesi phakathi kwamapuleti amabili ingu-\( 1.13 \times 10^5 \, \text{N/C} \).
Umbuzo 2:
I-capacitor yepuleti eliyisicaba inamapuleti amabili ahambisanayo anendawo engu-\(2 \, \text{m}^2 \) ngayinye futhi ahlukaniswe yibanga elingu-\(1 \, \text{mm} \). Uma amandla epuleti eliphezulu engu-\(200 \, \text{V} \) kanti epuletini elingezansi engu-0 V, nquma amandla ensimu kagesi phakathi kwamapuleti amabili!
Izinyathelo Zokuxoxisana:
1. Ukubalwa Komehluko Ongaba Khona \( V \):
Kuyaziwa ukuthi ipuleti eliphezulu line-potential \( V_{\text{top}} = 200 \, \text{V} \) kanye nepuleti elingezansi \( V_{\text{bottom}} = 0 \, \text{V} \). Ngakho-ke, umehluko okhona \( V \) phakathi kwamapuleti amabili uthi:
\[ V = V_{\text{top}} – V_{\text{bottom}} = 200 \, \text{V} – 0 \, \text{V} = 200 \, \text{V} \]
2. Amandla Ensimu Kagesi \( E \):
Insimu kagesi ku-capacitor yepuleti elihambisanayo ingabalwa ngokuhlukanisa umehluko ongaba khona \( V \) ngebanga \( d \):
\[ E = \frac{V}{d} \]
Uma ubheka ibanga \( d = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} \), bese kuba:
\[ E = \frac{200 \, \text{V}}{1 \times 10^{-3} \, \text{m}} = 2 \times 10^5 \, \text{V/m} \]
Ngakho-ke, amandla ensimu kagesi phakathi kwamapuleti amabili angu-\( 2 \times 10^5 \, \text{V/m} \).
Umbuzo 3:
I-capacitor yepuleti elihambisanayo inamapuleti anendawo engu-\( 0.5 \, \text{m}^2 \) kanye nebanga phakathi kwamapuleti angu-\( 0.5 \, \text{cm} \). Uma le capacitor ishajwa ngokushaja okungu-\( 2 \, \mu \text{C} \), bala umthamo wayo kanye nensimu kagesi phakathi kwamapuleti!
Izinyathelo Zokuxoxisana:
1. Umthamo \(C \) :
I-capacitance ye-capacitor yepuleti elihambisanayo ingabalwa kusetshenziswa ifomula:
\[ C = \epsilon_0 \frac{A}{d} \]
Kuyaziwa:
– \( \epsilon_0 = 8.85 \izikhathi ezingu-10^{-12} \, \umbhalo{F/m} \)
– \( A = 0.5 \, \text{m}^2 \)
– \( d = 0.5 \, \text{cm} = 0.5 \times 10^{-2} \, \text{m} \)
Ngakho-ke:
\[ C = 8.85 \izikhathi 10^{-12} \, \umbhalo{F/m} \izikhathi \frac{0.5 \, \umbhalo{m}^2}{0.5 \izikhathi 10^{-2} \, \umbhalo{m}} \]
\[ C = 8.85 \izikhathi 10^{-12} \izikhathi 10 \, \umbhalo{F} \]
\[ C = 88.5 \izikhathi 10^{-12} \, \umbhalo{F} \]
\[C = 88.5 \, \umbhalo{pF} \]
2. Inkundla Kagesi \(E \):
Ukuze sibale insimu kagesi, kumele siqale sazi umehluko ongaba khona \( V \). Umehluko ongaba khona \( V \) ungabalwa kanje:
\[ V = \frac{Q}{C} \]
Kuyaziwa:
– \( Q = 2 \, \mu \text{C} = 2 \times 10^{-6} \text{C} \)
– \( C = 88.5 \izikhathi 10^{-12} \umbhalo{F} \)
Ngakho-ke:
\[ V = \frac{2 \times 10^{-6} \, \text{C}}{88.5 \times 10^{-12} \, \text{F}} \]
\[ V = 22.6 \izikhathi ezingu-10^3 \, \umbhalo{V} \]
\[ V = 22.6 \, \umbhalo{kV} \]
Okulandelayo, kusetshenziswa ifomula \( E = \frac{V}{d} \), insimu kagesi yile:
\[ E = \frac{22.6 \, \text{kV}}{0.5 \times 10^{-2} \, \text{m}} \]
\[ E = 22.6 \izikhathi 10^3 \, \frac{\text{V}}{0.5 \izikhathi 10^{-2} \, \text{m}} \]
\[ E = 4.52 \izikhathi 10^6 \, \umbhalo{V/m} \]
Ngakho-ke, umthamo we-capacitor ngu-\( 88.5 \, \text{pF} \) kanti insimu kagesi ephakathi kwamapuleti ingu-\( 4.52 \times 10^6 \, \text{V/m} \).
Isiphetho
Ukuqonda insimu kagesi kumapuleti ahambisanayo kubalulekile hhayi kuphela ezivivinyweni zemfundo kodwa futhi nasekusetshenzisweni okusebenzayo emikhakheni ehlukahlukene yobunjiniyela kanye nefiziksi. Ngezinkinga eziyisibonelo kanye nezingxoxo ezingenhla, kunethemba lokuthi abafundi bazothola ukuqonda okungcono komqondo kanye nokusetshenziswa kwawo, okubenza bakwazi ukuwufinyelela ngokuzethemba okukhulu ezimweni zangempela kanye nezivivinyo.
