Lipotso tsa Mehlala le Puisano ea Masimo a Motlakase
Tšimo ea motlakase ke khopolo ea motheo fisiks e hlalosang phello ea ntho e tjhajwang ka motlakase sebakeng se potolohileng. Tšimo ea motlakase ke matla a sebelisoang sebakeng se seng le se seng ka boteng ba tjhaja eo. Ho utloisisa khopolo ena ka botebo, hangata ho hlokahala boikoetliso bo matla. Ka tlase ke mathata a mohlala le lipuisano tse qaqileng mabapi le masimo a motlakase.
Mohlala oa Potso ea 1: Ho Bala Boholo ba Tšimo ea Motlakase Ntlheng e 'Ngoe
Potso:
Litefiso tse peli tsa lintlha \( q_1 = +4 \mu C \) le \( q_2 = -8 \mu C \) li behiloe ho li-coordinates (0, 0) le (0, 2) metres. Bala boholo le tataiso ea tšimo ea motlakase ntlheng ea A e leng ho (0, 1) metres.
Puisano:
1. Fumana sebaka se pakeng tsa ntlha A le litefiso tse peli:
– Sebaka ho tloha ho (q_1 \) ho ya ntlheng ya A ke mithara e le 1.
– Sebaka ho tloha ho (q_2 \) ho ya ntlheng ya A ke mithara e le 1.
2. Bala tšimo ea motlakase e bakoang ke tefiso ka 'ngoe ntlheng ea A:
Tšimo ea motlakase e bakoang ke tjhaja ea ntlha \( q \) hole \( r \) ke:
\[ E = \frac{k \cdot |q|}{r^2} \]
bakeng sa \( q_1 \) le \( q_2 \):
\[ E_1 = \frac{9 \times 10^9 \cdot 4 \times 10^{-6}}{1^2} = 36 \times 10^3 \, \text{N/C} \]
\[ E_2 = \frac{9 \times 10^9 \cdot 8 \times 10^{-6}}{1^2} = 72 \times 10^3 \, \text{N/C} \]
3. Fumana tsela eo tšimo ea motlakase e tsamaeang ka eona:
Kaha \(q_1 \) ke tjhaja e ntle, sebaka sa yona sa motlakase se supa hole le tjhaja, kahoo \(E_1 \) se ka lehlakoreng le letle la y (hodimo).
Kaha \(q_2 \) ke tjhaja e mpe, tshimo ya motlakase e lebile tjhaja, kahoo \(E_2 \) e ka lehlakoreng le mpe la y (tlase).
4. Bala tšimo ea motlakase e hlahang:
Kaha \( E_1 \) le \( E_2 \) li moleng o otlolohileng o tšoanang, re ka tlosa masimo a motlakase:
\[ E_{\ mongolo{kakaretso}} = E_2 – E_1 \]
\[ E_{\text{total}} = 72 \makgetlo a 10^3 – 36 \makgetlo a 10^3 \]
\[ E_{\text{total}} = 36 \makgetlo a 10^3 \, \text{N/C} \]
Tsela eo tšimo ea motlakase e tsamaeang ka eona e lebile ho negative y-axis (tlase).
Mohlala oa Potso ea 2: Ho Bala Bokhoni ba Motlakase Ntlheng e 'Ngoe
Potso:
Litefiso tse peli tsa lintlha \( q_1 = +2 \mu C \) le \( q_2 = +3 \mu C \) li behiloe ho li-coordinates (0, 0) le (4, 0) metres. Bala matla a motlakase ntlheng ea B e leng ho (2, 0) metres.
Puisano:
1. Fumana sebaka se pakeng tsa ntlha ea B le litefiso tse peli:
– Sebaka ho tloha ho (q_1 \) ho ya ntlheng ya B ke dimithara tse 2.
– Sebaka ho tloha ho (q_2 \) ho ya ntlheng ya B ke dimithara tse 2.
2. Bala matla a motlakase a bakoang ke tjhaja e 'ngoe le e 'ngoe ntlheng ea B:
Bokgoni ba motlakase bo bakwang ke tjhaja ya ntlha \( q \) hole \( r \) ke:
\[ V = \frac{k \cdot q}{r} \]
bakeng sa \( q_1 \) le \( q_2 \):
\[ V_1 = \frac{9 \times 10^9 \cdot 2 \times 10^{-6}}{2} = 9 \times 10^3 \, \text{V} \]
\[ V_2 = \frac{9 \times 10^9 \cdot 3 \times 10^{-6}}{2} = 13.5 \times 10^3 \, \text{V} \]
3. Bala kakaretso ea matla a motlakase ntlheng ea B:
Bokgoni ba motlakase ke bongata ba scalar, kahoo bokgoni bohle ke kakaretso ya algebraic ya bokgoni bona:
\[ V_{\text{total}} = V_1 + V_2 \]
\[ V_{\text{total}} = 9 \makgetlo a 10^3 + 13.5 \makgetlo a 10^3 \]
\[ V_{\text{total}} = 22.5 \makgetlo a 10^3 \, \text{V} \]
Mohlala oa 3: Tšimo ea Motlakase ka har'a thepa ea Dielectric
Potso:
Haeba tjhaja \( q = 5 \mu C \) e bewa bohareng ba didikadikwe tse se nang letho tse nang le radius ya dimithara tse 3 e tletseng ka dielectric e nang le dielectric constant \( \kappa = 2 \). Bala tshimo ya motlakase bohole ba dimithara tse 2 ho tloha bohareng ba didikadikwe.
Puisano:
1. Foromo ea tšimo ea motlakase thepa ea dielectric:
Tšimo ea motlakase \(E \) e hole \(r \) ka har'a thepa ea dielectric ke:
\[ E = \frac{q}{4 \pi \epsilon_0 \kappa r^2} \]
moo \( \epsilon_0 = 8.85 \makgetlo a 10^{-12} \) F/m.
2. Kenya boleng bo fanoeng:
\[ E = \frac{5 \times 10^{-6}}{4 \pi \cdot 8.85 \times 10^{-12} \cdot 2 \cdot (2)^2} \]
\[ E = \frac{5 \times 10^{-6}}{4 \pi \cdot 8.85 \times 10^{-12} \cdot 8} \]
\[ E = \frac{5 \times 10^{-6}}{8 \cdot 3.54 \times 10^{-10}} \]
\[ E = \frac{5 \times 10^{-6}}{28.32 \times 10^{-10}} \]
\[ E = 1.77 \makgetlo a 10^4 \, \mongolo{N/C} \]
Qetello
Ka mehlala e kaholimo, re ka fumana kutloisiso e hlakileng haholoanyane ea mohopolo oa masimo a motlakase. Sena se kenyelletsa boholo ba tšimo ea motlakase ntlheng e itseng ka lebaka la litefiso tse ngata, palo ea matla a motlakase, le tšimo ea motlakase linthong tsa dielectric. Kutloisiso e tiileng ea mohopolo ona e bohlokoa hobane liketsahalo tse ngata tsa 'mele li ka hlalosoa ke masimo a motlakase, hammoho le ts'ebeliso ea ona theknolojing ea sejoale-joale. Tsoela pele ho ikoetlisa ka mathata a fapaneng ho tseba mohopolo ona ka botebo.
