Mehlala ea Lipotso Tse Buisanang ka Matla a Motlakase a Hlahang
Motlakase ke mofuta oa matla o bohlokoa bophelong ba rona ba letsatsi le letsatsi. E 'ngoe ea likhopolo tsa motheo fisiks ea motlakase ke matla a Coulomb, a hlalosang tšebelisano-'moho lipakeng tsa litefiso tsa motlakase. Ho utloisisa matla a motlakase a hlahang ho bohlokoa lits'ebetsong tse ngata, ho tloha theknoloji ea elektroniki ho ea ho utloisiseng liketsahalo bokahohleng. Se latelang ke puisano e tebileng ea mathata a mehlala le mokhoa oa ho fumana matla a motlakase a hlahang.
Selelekela sa Khopolo ea Matla a Coulomb
Pele re kena bothateng ba mohlala, ha re hlahlobeng molao oa Coulomb. Molao oa Coulomb o re matla a motlakase a pakeng tsa litefiso tsa lintlha tse peli a lekana le sehlahisoa sa boholo ba tsona 'me a lekana ka mokhoa o fapaneng le sekwere sa sebaka se pakeng tsa tsona. Ka lipalo, matla a Coulomb \( F \) a ka hlalosoa e le:
\[ F = k_e \frac{|q_1 q_2|}{r^2} \]
Di mana:
– \( F \) ke boholo ba matla a motlakase a sa fetoheng.
– \( k_e \) ke phetolelo ya Coulomb e sa fetoheng, \( k_e \hoo e ka bang 8,99 \ka makhetlo a 10^9 \, \text{Nm}^2/\text{C}^2 \).
– \( q_1 \) le \( q_2 \) ke boholo ba ditefiso.
– \( r \) ke sebaka se pakeng tsa ditefiso.
Lipotso tsa Mehlala le Puisano
Potso ea 1: Litefiso tse peli Moleng o Otlolohileng
Litefiso tse peli tsa lintlha \( q_1 = 4 \mu C \) le \( q_2 = -3 \mu C \) li fumaneha bohōle ba 3 cm ho tloha ho e mong. Bala boholo le tataiso ea matla a Coulomb lipakeng tsa litefiso tsena tse peli.
Puisano:
Mohato oa pele ke ho fetolela tjhaja le sebaka ho diyuniti tsa SI:
– \( q_1 = 4 \makgetlo a 10^{-6} C \)
– \( q_2 = -3 \makgetlo a 10^{-6} C \)
– \( r = 3 \makgetlo a 10^{-2} m \)
Ho sebelisoa equation ea molao ea Coulomb:
\[ F = k_e \frac{|q_1 q_2|}{r^2} \]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[ F = (8,99 \makgetlo a 10^9) \frac{(4 \makgetlo a 10^{-6})(3 \makgetlo a 10^{-6})}{(3 \makgetlo a 10^{-2})^2} \]
Bala boholo ba matla:
\[ F = (8,99 \makgetlo a 10^9) \frac{12 \makgetlo a 10^{-12}}{9 \makgetlo a 10^{-4}} \]
\[ F = (8,99 \makgetlo a 10^9) \makgetlo (1,33 \makgetlo a 10^{-8}) \]
\[ F = 1,197 \makgetlo a 10^2 \]
\[ F = 119,7 \, N \]
Tsela ea matla: Kaha \(q_1 \) e ntle 'me \(q_2 \) e mpe, matla aa hohela. Kahoo, matla a ho \(q_1 \) a lebisitsoe ho \(q_2 \) 'me ka tsela e fapaneng.
Potso ea 2: Litefiso tse tharo Khutlotharong e Lekanang
Lichaja tse tharo, e 'ngoe le e 'ngoe \( q = 2 \mu C \), li behiloe lintlheng tsa khutlotharo e lekanang ka mahlakore a bolelele ba 5 cm. Bala matla a hlahang a sebetsang ho tjhaja e 'ngoe le e 'ngoe.
Puisano:
Fetola tjhaja le sebaka ho diyuniti tsa SI:
– \( q = 2 \makgetlo a 10^{-6} C \)
– \( r = 5 \makgetlo a 10^{-2} m \)
Matla pakeng tsa liqoso tse peli:
\[ F = k_e \frac{q^2}{r^2} \]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[ F = (8,99 \ka makhetlo a 10^9) \frac{(2 \ka makhetlo a 10^{-6})^2}{(5 \ka makhetlo a 10^{-2})^2} \]
\[ F = (8,99 \makgetlo a 10^9) \frac{4 \makgetlo a 10^{-12}}{25 \makgetlo a 10^{-4}} \]
\[ F = (8,99 \makgetlo a 10^9) \makgetlo (1,6 \makgetlo a 10^{-10}) \]
\[ F = 1,4384 N \]
Matla ana a sebetsa hodima para e 'ngoe le e 'ngoe ea litefiso tse ka har'a khutlotharo. Ho fumana matla a hlahang a sebetsang holim'a tefo e 'ngoe le e 'ngoe, hoa hlokahala ho sekaseka li-vector tsa matla a mabeli a sebetsang holim'a tefo e 'ngoe le e 'ngoe ka mahlakoreng a otlolohileng le a oblique a khutlotharo.
A re re tlhaselo ho \( A \) e fumana matla ho tsoa ho \( B \) le \( C \):
– Matla a tlohang ho \( B \) ho isa ho \( A \) ke \( F_{AB} = 1,4384 \, N \).
– Matla a tlohang ho (C \) ho isa ho (A \) ke \( F_{AC} = 1,4384 \, N \).
Kaha matla ana a mabedi a bopa sekhutlo sa 60° ka ho fapana (ka lebaka la khutlotharo e lekanang), re ka sebedisa tlhahlobo ya karolo ya vekthara ho fumana sephetho.
Likarolo tsa matla ho x-axis le y-axis:
\[ F_{Ax} = F_{AB} \cos 30^\circ + F_{AC} \cos 30^\circ \]
\[ F_{Ay} = F_{AB} \sebe 30^\circ – F_{AC} \sebe 30^\circ \]
Leha ho le jwalo, kaha matla ka bobedi a lekana hantle mme a lekana hantle mahlakoreng ka bobedi, dikarolo tsohle tsa y di tla hlakolwa mme ka katleho, tjhaja \( A \) e angwa feela ke matla a rapameng a sebetsang bohareng.
\[
F_{Ax} = 2F_{AB} \cos 30^\circ \\
= 2(1,4384 \ N \cdot \ 0,866) \\
= 2 \cdot 1.2467 \\
= 2.4934N
]
Kahoo matla a motlakase a hlahang ho e 'ngoe ea litefiso ke \( F = 2.4934 N.
Qetello
Ho fumana matla a motlakase a hlahang tsamaisong ea litefiso tsa lintlha ho hloka kutloisiso e batsi ea molao oa Coulomb le bokhoni ba ho arola vector ea matla ka likarolo tsa eona. Maemong a rarahaneng haholoanyane a nang le litefiso tse tharo kapa ho feta, tlhahlobo ea vector hangata ke sesebelisoa sa bohlokoa bakeng sa ho fumana liphetho tse nepahetseng. Ka mathata a ho itloaetsa a kang ana, re ka utloisisa le ho sebelisa likhopolo tsa fisiks ka katleho e kholo.
