Imibuzo Yezibonelo Nengxoxo Ngezinkundla Zikagesi
Insimu kagesi ingumqondo oyisisekelo ku-physics ochaza umphumela wento eshajwe ngogesi endaweni ezungezile. Insimu kagesi ingamandla asetshenziswa kuzo zonke izindawo esikhaleni ngokuba khona kwaleyo shaje. Ukuze uqonde lo mqondo ngokujulile, kuvame ukudingeka ukuzijwayeza okujulile. Ngezansi kunezinkinga eziyisibonelo kanye nezingxoxo ezinemininingwane mayelana namasimu kagesi.
Isibonelo Umbuzo 1: Ukubala Ubukhulu Bensimu Kagesi Ephuzwini Elithile
Umbuzo:
Amashaja amabili amaphuzu \( q_1 = +4 \mu C \) kanye \( q_2 = -8 \mu C \) abekwe kumamitha (0, 0) kanye (0, 2). Bala ubukhulu kanye nesiqondiso sensimu kagesi endaweni A engamamitha (0, 1).
Ingxoxo:
1. Thola ibanga phakathi kwephuzu A kanye namacala amabili:
– Ibanga elisuka ku-(q_1 \) kuya ephuzwini A liyimitha eli-1.
– Ibanga elisuka ku-(q_2 \) kuya ephuzwini A liyimitha eli-1.
2. Bala insimu kagesi ngenxa yokushaja ngakunye endaweni A:
Insimu kagesi ngenxa yokushaja kwephuzu \( q \) ekude \( r \) ithi:
\[ E = \frac{k \cdot |q|}{r^2} \]
kwe-\( q_1 \) kanye ne-\( q_2 \):
\[ E_1 = \frac{9 \times 10^9 \cdot 4 \times 10^{-6}}{1^2} = 36 \times 10^3 \, \text{N/C} \]
\[ E_2 = \frac{9 \times 10^9 \cdot 8 \times 10^{-6}}{1^2} = 72 \times 10^3 \, \text{N/C} \]
3. Thola indlela eya ensimini kagesi:
Njengoba i-\(q_1 \) iyishaja eqondile, insimu yayo kagesi ikhomba kude neshaja, ngakho-ke i-\(E_1 \) isendleleni eqondile ye-y (phezulu).
Njengoba i-\(q_2 \) iyishaja engemihle, insimu kagesi ibheke ekushajeni, ngakho-ke i-\(E_2 \) isendleleni engemihle ye-y (eya phansi).
4. Bala insimu kagesi ephumela:
Njengoba \( E_1 \) kanye \( E_2 \) zisemugqeni ofanayo oqondile, singasusa amasimu kagesi:
\[ E_{\text{total}} = E_2 – E_1 \]
\[ E_{\text{total}} = 72 \times 10^3 – 36 \times 10^3 \]
\[ E_{\text{total}} = 36 \times 10^3 \, \text{N/C} \]
Isiqondiso sensimu kagesi sibheke ku-axis y engemihle (phansi).
Isibonelo Umbuzo 2: Ukubala Amandla Kagesi Ephuzwini Elithile
Umbuzo:
Amashaja amabili amaphuzu \( q_1 = +2 \mu C \) kanye \( q_2 = +3 \mu C \) abekwe kuma-coordinates (0, 0) kanye namamitha (4, 0). Bala amandla kagesi endaweni B engamamitha (2, 0).
Ingxoxo:
1. Thola ibanga phakathi kwephuzu B kanye namacala amabili:
– Ibanga elisuka ku-(q_1 \) liye ephuzwini B lingama-2 amamitha.
– Ibanga elisuka ku-(q_2 \) liye ephuzwini B lingama-2 amamitha.
2. Bala amandla kagesi ngenxa yokushaja ngakunye endaweni B:
Amandla kagesi abangelwa ukushaja kwephuzu \( q \) kude \( r \) yilawa:
\[ V = \frac{k \cdot q}{r} \]
kwe-\( q_1 \) kanye ne-\( q_2 \):
\[ V_1 = \frac{9 \times 10^9 \cdot 2 \times 10^{-6}}{2} = 9 \times 10^3 \, \text{V} \]
\[ V_2 = \frac{9 \times 10^9 \cdot 3 \times 10^{-6}}{2} = 13.5 \times 10^3 \, \text{V} \]
3. Bala amandla kagesi aphelele endaweni B:
Amandla kagesi ayinani elilinganiselwe, ngakho-ke amandla aphelele ayisamba se-algebraic salezi zindlela:
\[ V_{\text{total}} = V_1 + V_2 \]
\[ V_{\text{total}} = 9 \times 10^3 + 13.5 \times 10^3 \]
\[ V_{\text{total}} = 22.5 \times 10^3 \, \text{V} \]
Isibonelo 3: Inkundla Kagesi Entweni Esebenzisa Ugesi
Umbuzo:
Uma ishaja \( q = 5 \mu C \) ibekwa enkabeni yesphere esingenalutho esinobubanzi obungamamitha ama-3 esigcwele ngokuphelele i-dielectric ene-dielectric constant \( \kappa = 2 \). Bala insimu kagesi ebangeni elingamamitha ama-2 ukusuka enkabeni yesphere.
Ingxoxo:
1. Ifomula yensimu kagesi ezintweni ze-dielectric:
Insimu kagesi \( E \) ekude \( r \) ezintweni ze-dielectric yile:
\[ E = \frac{q}{4 \pi \epsilon_0 \kappa r^2} \]
lapho \( \epsilon_0 = 8.85 \izikhathi ezingu-10^{-12} \) F/m.
2. Faka amanani anikeziwe:
\[ E = \frac{5 \times 10^{-6}}{4 \pi \cdot 8.85 \times 10^{-12} \cdot 2 \cdot (2)^2} \]
\[ E = \frac{5 \times 10^{-6}}{4 \pi \cdot 8.85 \times 10^{-12} \cdot 8} \]
\[ E = \frac{5 \times 10^{-6}}{8 \cdot 3.54 \times 10^{-10}} \]
\[ E = \frac{5 \times 10^{-6}}{28.32 \times 10^{-10}} \]
\[ E = 1.77 \izikhathi 10^4 \, \umbhalo{N/C} \]
Isiphetho
Ngezibonelo ezingenhla, singathola ukuqonda okucacile komqondo wezinkundla zikagesi. Lokhu kufaka phakathi ubukhulu benkundla kagesi ngesikhathi esithile ngenxa yokushaja okuningi, ukubalwa kwamandla kagesi, kanye nenkundla kagesi ezintweni ze-dielectric. Ukuqonda okuqinile kwalomqondo kubalulekile ngoba izinto eziningi ezibonakalayo zingachazwa ngezinkundla zikagesi, kanye nokusetshenziswa kwazo kubuchwepheshe besimanje. Qhubeka uzijwayeza ngezinkinga ezahlukahlukene ukuze uqonde lo mqondo ngokujulile.
