Mehlala ea Lipotso Tse Buisanang ka Molao oa Coulomb
Molao oa Coulomb ke molao-motheo oa motheo fisiks o hlalosang matla a pakeng tsa litefiso tse peli tsa motlakase. Ha o ithutoa ka har'a karoloana ea li-electrostatics, molao ona o hlalosa kamoo litefiso tsa motlakase li hohelanang kapa li ferekantseng. Molao ona o ile oa hlahisoa ka lekhetlo la pele ke setsebi sa fisiks sa Lefora Charles-Augustin de Coulomb lekholong la bo18 la lilemo. Sehlooho sena se tla tšohla Molao oa Coulomb ka ho hlahloba mehlala le litharollo tsa eona, kahoo se thusa babali ho utloisisa lits'ebetso tse sebetsang tsa molao-motheo ona oa motheo.
Motheo oa Khopolo-taba: Molao oa Coulomb ke eng?
Molao oa Coulomb o bolela hore boholo ba matla a motlakase \( F \) pakeng tsa litefiso tse peli tsa lintlha \( q_1 \) le \( q_2 \) bo lekana ka ho toba le sehlahisoa sa boholo ba litefiso tse peli 'me bo lekana ka tsela e fapaneng le sekwere sa sebaka \( r \) pakeng tsa tsona. Ka lipalo, foromo ea Molao oa Coulomb e ka hlalosoa tjena:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Di mana:
– \( F \) ke boholo ba matla a motlakase
– \( k_e \) ke ntho e sa fetoheng ya Coulomb (\( 8.9875 \times 10^9 \, N \cdot m^2 \cdot C^{-2} \))
– \( q_1 \) le \( q_2 \) ke boholo ba tjhaja ya motlakase
– \( r \) ke sebaka se pakeng tsa litefiso tse peli
Mohlala oa Potso ea 1
Potso:
Ho na le litefiso tse peli tsa lintlha: \( q_1 = 2 \times 10^{-6} \, C \) le \( q_2 = -3 \times 10^{-6} \, C \). Li arohane ka limithara tse 0,05. Bala boholo ba matla a motlakase a sebetsang lipakeng tsa litefiso tse peli.
Puisano:
Mohato oa pele ke ho ngola bocha mokhoa oa Molao oa Coulomb:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Jwale re nkela boleng bo tsejwang sebaka ka foromo:
\[ k_e = 8.9875 \ka makhetlo a 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[q_1 = 2 \makgetlo a 10^{-6} \, C \]
\[q_2 = -3 \makgetlo a 10^{-6} \, C \]
\[r = 0,05 \, m \]
Re hokela boleng bona ka foromong:
\[ F = 8.9875 \ka makhetlo a 10^9 \, \frac{|2 \ka makhetlo a 10^{-6} \cdot -3 \ka makhetlo a 10^{-6}|}{(0,05)^2} \]
\[ F = 8.9875 \ka makhetlo a 10^9 \, \frac{6 \ka makhetlo a 10^{-12}}{0,0025} \]
\[ F = 8.9875 \ka makhetlo a 10^9 \, \frac{6 \ka makhetlo a 10^{-12}}{2,5 \ka makhetlo a 10^{-3}} \]
\[ F = 8.9875 \makgetlo a 10^9 \, \makgetlo a 2,4 \makgetlo a 10^{-9} \]
\[ F = 21.57 \, N \]
Hobane tefiso \(q_2 \) e le mpe, matla a motlakase a sebetsang ke matla a hohelang, hobane ditefiso tse ntle le tse mpe lia hohelana.
Mohlala oa Potso ea 2
Potso:
Litefiso tse peli tsa motlakase \( q_1 = 5 \times 10^{-9} \, C \) le \( q_2 = 10 \times 10^{-9} \, C \) li arotsoe ka sebaka sa limithara tse 0,1. Bala boholo ba matla a motlakase a sebetsang ho \( q_1 \).
Puisano:
Sebelisa foromo ea Molao oa Coulomb hape:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[ k_e = 8.9875 \ka makhetlo a 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[q_1 = 5 \makgetlo a 10^{-9} \, C \]
\[q_2 = 10 \makgetlo a 10^{-9} \, C \]
\[r = 0,1 \, m \]
\[ F = 8.9875 \ka makhetlo a 10^9 \, \frac{(5 \ka makhetlo a 10^{-9}) (10 \ka makhetlo a 10^{-9})}{(0,1)^2} \]
\[ F = 8.9875 \ka makhetlo a 10^9 \, \frac{50 \ka makhetlo a 10^{-18}}{0,01} \]
\[ F = 8.9875 \makgetlo a 10^9 \, \makgetlo a 5 \makgetlo a 10^{-15} \]
\[ F = 44.9375 \, N \]
Matla a sebetsang ke matla a nyonyehang, hobane liqoso ka bobeli \(q_1 \) le \(q_2 \) li na le letšoao le tšoanang, e leng le letle.
Mohlala oa Potso ea 3
Potso:
Litefiso tse tharo tsa lintlha li moleng o otlolohileng. Tefiso ea pele ke \( q_1 = 2 \mu C \), tefiso ea bobeli ke \( q_2 = -1 \mu C \), 'me tefiso ea boraro ke \( q_3 = 3 \mu C \). Sebaka se pakeng tsa \( q_1 \) le \( q_2 \) ke 0,1 m, ha sebaka se pakeng tsa \( q_2 \) le \( q_3 \) e le 0,2 m. Bala boholo le tataiso ea matla a felletseng a motlakase a sebetsang ho \( q_2 \).
Puisano:
Taba ea pele, re bala matla a motlakase pakeng tsa \(q_1 \) le \(q_2 \):
\[ F_{12} = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
\[ k_e = 8.9875 \ka makhetlo a 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[q_1 = 2 \makgetlo a 10^{-6} \, C \]
\[q_2 = -1 \makgetlo a 10^{-6} \, C \]
\[r = 0,1 \, m \]
\[ F_{12} = 8.9875 \ka makhetlo a 10^9 \, \frac{(2 \ka makhetlo a 10^{-6}) (-1 \ka makhetlo a 10^{-6})}{(0,1)^2} \]
\[ F_{12} = 8.9875 \ka makhetlo a 10^9 \, \frac{2 \ka makhetlo a 10^{-12}}{0,01} \]
\[ F_{12} = 8.9875 \makgetlo a 10^9 \, \makgetlo a 2 \makgetlo a 10^{-10} \]
\[ F_{12} = 1.7975 \, N \]
Kaha \(q_1 \) e ntle mme \(q_2 \) e mpe, matla \(F_{12} \) ke matla a hohelang a lebisitsweng ho \(q_1 \).
Ea bobeli, re bala matla a motlakase pakeng tsa \( q_2 \) le \( q_3 \):
\[ F_{23} = k_e \frac{|q_2 \cdot q_3|}{r^2} \]
\[q_2 = -1 \makgetlo a 10^{-6} \, C \]
\[q_3 = 3 \makgetlo a 10^{-6} \, C \]
\[r = 0,2 \, m \]
\[ F_{23} = 8.9875 \ka makhetlo a 10^9 \, \frac{(-1 \ka makhetlo a 10^{-6}) (3 \ka makhetlo a 10^{-6})}{(0,2)^2} \]
\[ F_{23} = 8.9875 \ka makhetlo a 10^9 \, \frac{3 \ka makhetlo a 10^{-12}}{0,04} \]
\[ F_{23} = 8.9875 \makgetlo a 10^9 \, \makgetlo a 7.5 \makgetlo a 10^{-11} \]
\[ F_{23} = 0.67406 \, N \]
Kaha \(q_2 \) ke ntho e mpe mme \(q_3 \) ke ntho e ntle, matla \(F_{23} \) ke matla a hohelang a lebisitsweng ho \(q_3 \).
Qetellong, re kopanya mabotho ka bobeli ho fumana sephetho sa ho qetela:
Matla ohle ho \(q_2 \):
\[ F_{\text{total}} = F_{12} – F_{23} \]
\[ F_{\text{total}} = 1.7975 \, N – 0.67406\, N \]
\[ F_{\text{total}} = 1.12344 \, N \]
Tsela eo matla ohle a lebileng ho yona e lebile ho (q_1 \) hobane matla \( F_{12} \) a maholo ho feta \( F_{23} \).
Qetello
Molao oa Coulomb o fana ka temohisiso ea bohlokoa mabapi le likamano lipakeng tsa litefiso tsa motlakase, tse khahlang le tse nyonyehang. Mehlala e tšohloang e bontša ts'ebeliso ea molao ona ho baleng matla a motlakase ka ho ela hloko boholo ba litefiso le sebaka se pakeng tsa tsona. Kutloisiso e batsi ea Molao oa Coulomb e ka re thusa ho utloisisa liketsahalo tse fapaneng tsa motlakase le makenete tse etsahalang ho re potoloha.
