Mehlala ea Lipotso Tse Buang ka Matla a Motlakase
Tlhaloso ea matla a motlakase ke matla a hlahang ka lebaka la tšebelisano-'moho lipakeng tsa litefiso tsa motlakase. Matla ana a ithutoa fisiks, haholo-holo lekaleng la electrodynamics. Litlamorao tsa matla a motlakase li ka bonoa liketsahalong tse ngata tsa letsatsi le letsatsi, ho tloha ho hohla lintho tse itseng hammoho ho ea ts'ebetsong ea lisebelisoa tsa elektroniki. Sehlooho sena se tla tšohla mehlala e 'maloa ea mathata a matla a motlakase le litharollo tsa ona, hammoho le likhopolo-taba tse kholo tse amanang le matla a motlakase.
Selelekela ho Matla a Motlakase
Matla a motlakase pakeng tsa litefiso tse peli tsa motlakase a fanoa ke Molao oa Coulomb, o hlalosoang ke equation:
$$ F = k_e \frac{|q_1 q_2|}{r^2} $$
Moo:
– \( F \) ke matla a motlakase pakeng tsa litefiso tse peli.
– \( q_1 \) le \( q_2 \) ke boholo ba ditefiso.
– \( r \) ke sebaka se pakeng tsa litefiso tse peli.
– \( k_e \) ke constant ya Coulomb (hoo e ka bang \(8.99 \makgetlo a 10^9 \, N \cdot m^2 / C^2\)).
Molao oa Coulomb o tšoana le molao oa Newton oa matla a khoheli, empa matla a khoheli a lula a hohela athe matla a motlakase a ka hohela kapa a nyonyeha ho latela letšoao la tjhaja.
Lipotso tsa Mehlala le Puisano
Potso ea 1: Litefiso tse peli tse lekanang
Litefiso tse peli tsa lintlha \( q_1 = 3 \, \mu C \) le \( q_2 = -4 \, \mu C \) li hole ka limithara tse 0.5. Bala matla a motlakase a sebetsang lipakeng tsa litefiso tse peli.
Puisano:
1. Tlhaloso ea Mojaro le Sebaka:
– \( q_1 = 3 \, \mu C = 3 \makgetlo a 10^{-6} \, C \)
– \( q_2 = -4 \, \mu C = -4 \makgetlo a 10^{-6} \, C \)
– \( r = 0.5 \, m \)
2. Ho nkeloa sebaka ke Molao oa Coulomb:
\[
F = k_e \frac{|q_1 q_2|}{r^2}
\]
\[
F = 8.99 \makgetlo a 10^9 \, \frac{(3 \makgetlo a 10^{-6})(4 \makgetlo a 10^{-6})}{(0.5)^2}
\]
3. Bala Liphetho:
\[
F = 8.99 \ka makhetlo a 10^9 \, \frac{12 \ka makhetlo a 10^{-12}}{0.25}
\]
\[
F = 8.99 \makgetlo a 10^9 \makgetlo a 48 \makgetlo a 10^{-12}
\]
\[
F = 431.52 \makgetlo a 10^{-3} \, N
\]
\[
F \hoo e ka bang 0.432 \, N
\]
Kahoo, matla a motlakase a sebetsang pakeng tsa litefiso tse peli ke hoo e ka bang 0.432 Newtons.
Potso ea 2: Tefiso ka Litefiso tse 'maloa
Litefiso tse tharo tsa lintlha, \( q_1 = 2 \, \mu C \), \( q_2 = 3 \, \mu C \), le \( q_3 = -1 \, \mu C \) li behiloe moleng o otlolohileng moo sebaka se pakeng tsa \( q_1 \) le \( q_2 \) e leng limithara tse 0.6 le pakeng tsa \( q_2 \) le \( q_3 \) e leng limithara tse 0.4. Bala matla a hlahang ho \( q_2 \).
Puisano:
1. Tlhaloso ea Mojaro le Sebaka:
– \( q_1 = 2 \, \mu C = 2 \makgetlo a 10^{-6} \, C \)
– \( q_2 = 3 \, \mu C = 3 \makgetlo a 10^{-6} \, C \)
– \( q_3 = -1 \, \mu C = -1 \makgetlo a 10^{-6} \, C \)
– Sebaka se pakeng tsa (q_1 \) le (q_2 \) ke 0.6 m
– Sebaka se pakeng tsa (q_2 \) le (q_3 \) ke 0.4 m
2. Qobella \(q_1 \) khahlanong le \(q_2 \):
\[
F_{12} = k_e \frac{|q_1 q_2|}{r_{12}^2}
\]
\[
F_{12} = 8.99 \makgetlo a 10^9 \, \frac{(2 \makgetlo a 10^{-6})(3 \makgetlo a 10^{-6})}{(0.6)^2}
\]
\[
F_{12} = 8.99 \makgetlo a 10^9 \, \frac{6 \makgetlo a 10^{-12}}{0.36}
\]
\[
F_{12} = 8.99 \makgetlo a 10^9 \makgetlo a 16.67 \makgetlo a 10^{-12}
\]
\[
F_{12} \hoo e ka bang 0.15 \, N
\]
Tsela eo matla a tswelang ka yona e hole le (q_1) (ka letsohong le letona).
3. Qobella \(q_3 \) khahlanong le \(q_2 \):
\[
F_{32} = k_e \frac{|q_3 q_2|}{r_{32}^2}
\]
\[
F_{32} = 8.99 \makgetlo a 10^9 \, \frac{(1 \makgetlo a 10^{-6})(3 \makgetlo a 10^{-6})}{(0.4)^2}
\]
\[
F_{32} = 8.99 \makgetlo a 10^9 \, \frac{3 \makgetlo a 10^{-12}}{0.16}
\]
\[
F_{32} = 8.99 \makgetlo a 10^9 \makgetlo a 18.75 \makgetlo a 10^{-12}
\]
\[
F_{32} \hoo e ka bang 0.17 \, N
\]
Tsela eo matla a tswelang ka yona e hulela ho (q_3) (ka letsohong le letshehadi).
4. Matla a Phello:
Kaha \( F_{12} \) e ka letsohong le letona mme \( F_{32} \) e ka letsohong le letšehali, matla a hlahang \( F_{res} = F_{32} – F_{12} \):
\[
F_{res} = 0.17 \,N – 0.15 \,N
\]
\[
F_{res} = 0.02 \, N (ka letsohong le letshehadi)
\]
Kahoo, matla a hlahang ho \(q_2 \) ke 0.02 Newton ka letsohong le letshehadi.
Potso ea 3: Sistimi ea ho Jara ka Khutlotharo
Litefiso tse tharo tsa lintlha \( q_1 = 5 \, \mu C \), \( q_2 = -3 \, \mu C \), le \( q_3 = 4 \, \mu C \) li behiloe likhutlong tse tharo tsa khutlotharo e lekanang ka bolelele ba lehlakore ba limithara tse 0.2. Bala matla ohle a motlakase a sebetsang ho tefo \( q_1 \).
Puisano:
1. Qobella \(q_2 \) khahlanong le \(q_1 \):
\[
F_{12} = k_e \frac{|q_1 q_2|}{r^2}
\]
\[
F_{12} = 8.99 \makgetlo a 10^9 \, \frac{(5 \makgetlo a 10^{-6})(3 \makgetlo a 10^{-6})}{(0.2)^2}
\]
\[
F_{12} = 8.99 \makgetlo a 10^9 \, \frac{15 \makgetlo a 10^{-12}}{0.04}
\]
\[
F_{12} = 8.99 \makgetlo a 10^9 \makgetlo a 375 \makgetlo a 10^{-12}
\]
\[
F_{12} \hoo e ka bang 3.37 \, N
\]
Tsela eo matla a tswelang ka yona \( F_{12} \) e kgahla ka tsela eo \( q_2 \).
2. Qobella \(q_3 \) khahlanong le \(q_1 \):
\[
F_{13} = k_e \frac{|q_1 q_3|}{r^2}
\]
\[
F_{13} = 8.99 \makgetlo a 10^9 \, \frac{(5 \makgetlo a 10^{-6})(4 \makgetlo a 10^{-6})}{(0.2)^2}
\]
\[
F_{13} = 8.99 \makgetlo a 10^9 \, \frac{20 \makgetlo a 10^{-12}}{0.04}
\]
\[
F_{13} = 8.99 \makgetlo a 10^9 \makgetlo a 500 \makgetlo a 10^{-12}
\]
\[
F_{13} \hoo e ka bang 4.50 \, N
\]
Tsela eo matla a tswelang ka yona \( F_{13} \) e nyonyehang ho tloha ho \( q_3 \).
3. Matla a Phello:
Re hloka ho sebedisa mokgwa wa vektara ho fumana sephetho sa \( F_{12} \) le \( F_{13} \), hobane sekhutlo se pakeng tsa matla ke di-degree tse 60 (khutlotharo e lekanang).
Re sebelisa likarolo tsa x le y, re ka fumana matla a felletseng. Leha ho le joalo, bakeng sa ho nolofatsa, re tla sebelisa mekhoa ea litšoantšo kapa lipalo tsa lipalo ho fumana hore matla a felletseng a feta 4.50 N 'me a lutse kae-kae pakeng tsa mola o hokahanyang \( q_2 \) le \( q_3 \) ho \( q_1 \).
Qetello
Ka mohlala oa bothata le puisano e kaholimo, re ka utloisisa mokhoa oa ho bala matla a motlakase re sebelisa Molao oa Coulomb. Ka ho arola bothata ka mehato e bonolo le ho sebelisa lintlha tsa vector, re ka fumana matla a felletseng ho tjhaja e 'ngoe le e 'ngoe tsamaisong. Matla a motlakase, leha a le bonolo ka mokhoa oa 'ona oa lipalo, a ka ba le litlamorao tse kholo le tse rarahaneng lits'ebetsong tsa lefats'e la nnete.
