Mohlala oa Lipotso tsa Matla a Tšimo ea Motlakase
Matla a tšimo ea motlakase ke khopolo-taba ea motheo fisiks e hlalosang matla a tšimo ea motlakase sebakeng se itseng sebakeng. Masimo a motlakase a hlahisoa ke litefiso tsa motlakase 'me a ka susumetsa litefiso tse ling ka har'a tšimo eo. Ho utloisisa khopolo-taba ena hamolemo, ha re shebeng mehlala e meng ea mathata a amanang le matla a tšimo ea motlakase le mokhoa oa ho a rarolla.
Metheo ea Masimo a Motlakase
Pele re kena mathateng a mohlala, ha re hlahlobeng hanyane ka mohopolo oa motheo oa masimo a motlakase. Matla a tšimo ea motlakase (\(E\)) ntlheng e itseng sebakeng a hlalosoa e le matla (\(F\)) ka tefiso ea yuniti (\(q\)) a fumanoang ke tefiso e nyane ea teko ntlheng eo:
\[ E = \frac{F}{q} \]
Moo:
– \(E\) ke matla a tšimo ea motlakase (N/C kapa V/m),
– \(F\) ke matla a motlakase a fumanwang ke tjhaja (N),
– \(q\) ke boholo ba tefiso ea teko (C).
Haeba mohlodi wa tshimo ya motlakase e le tjhaja ya ntlha \(Q\), jwale matla a tshimo ya motlakase a hole \(r\) ho tloha tjhaja a fanwa ke equation:
\[ E = \frac{k \cdot |Q|}{r^2} \]
Moo:
– \(k\) ke constant ya Coulomb (\(8.99 \times 10^9 \, \text{N m}^2/\text{C}^2\)),
– \(Q\) ke tefiso ea mohloli (C),
– \(r\) ke sebaka se tlohang ho tjhaja ya mohlodi ho ya sebakeng sa ho shebella (m).
Mohlala oa Potso ea 1: Tšimo ea Motlakase ka Tefiso ea Ntlha
Potso: Tefiso \(Q\) ya \(5 \makgetlo a 10^{-6} \, \text{C}\) e bewa qalong (0,0). Bala matla a tshimo ya motlakase bohole ba dimithara tse 2 ho tloha tefisong.
Tharollo:
Ho tloha ho equation ea tšimo ea motlakase ka tjhaja ea ntlha, re ka bala matla a tšimo ea motlakase ka tsela e latelang:
\[ E = \frac{k \cdot |Q|}{r^2} \]
Kenya boleng ba \(k\), \(Q\), le \(r\):
\[ E = \frac{8.99 \makgetlo a 10^9 \makgetlo a 5 \makgetlo a 10^{-6}}{2^2} \]
\[ E = \frac{8.99 \makgetlo a 10^9 \makgetlo a 5 \makgetlo a 10^{-6}}{4} \]
\[ E = \frac{44.95 \makgetlo a 10^3}{4} \]
\[ E = 11.2375 \makgetlo a 10^3 \]
\[ E = 11,237.5 \, \mongolo{N/C} \]
Kahoo, matla a tšimo ea motlakase bohōle ba limithara tse 2 ho tloha tjhajeng ke \(11,237.5 \, \text{N/C}\).
Mohlala oa 2: Ho Fetoha ha Masimo a Motlakase
Potso: Litefiso tse peli, \(Q_1 = 4 \times 10^{-6} \, \text{C}\) le \(Q_2 = -3 \times 10^{-6} \, \text{C}\) li behiloe sebakeng sa limithara tse 3 ho tloha ho e mong. Bala matla a tšimo ea motlakase bohareng ba litefiso tse peli.
Tharollo:
Taba ea pele, re bala tšimo ea motlakase e hlahisoang ke tjhaja e 'ngoe le e 'ngoe bohareng ba motlakase.
Bakeng sa tefiso \(Q_1\):
\[r_1 = \frac{3}{2} = 1.5 \, \text{m} \]
\[ E_1 = \frac{k \cdot |Q_1|}{r_1^2} \]
\[ E_1 = \frac{8.99 \makgetlo a 10^9 \makgetlo a 4 \makgetlo a 10^{-6}}{1.5^2} \]
\[ E_1 = \frac{35.96 \makgetlo a 10^3}{2.25} \]
\[ E_1 = 15.9822 \makgetlo a 10^3 \]
\[ E_1 = 15,982.2 \, \ mongolo{N/C} \]
Bakeng sa tefiso \(Q_2\):
\[r_2 = 1.5 \, \mongolo{m} \]
\[ E_2 = \frac{k \cdot |Q_2|}{r_2^2} \]
\[ E_2 = \frac{8.99 \makgetlo a 10^9 \makgetlo a 3 \makgetlo a 10^{-6}}{1.5^2} \]
\[ E_2 = \frac{26.97 \makgetlo a 10^3}{2.25} \]
\[ E_2 = 11.9822 \makgetlo a 10^3 \]
\[ E_2 = 11,982.2 \, \ mongolo{N/C} \]
Kaha \(Q_1\) e ntle mme \(Q_2\) e mpe, masimo a bona a motlakase bohareng a tla be a ntse a kgutlela morao. Kahoo, re eketsa masimo a mabedi a motlakase:
\[ E = E_1 + E_2 \]
\[ E = 15,982.2 + 11,982.2 \]
\[ E = 27,964.4 \, \mongolo{N/C} \]
Kahoo, matla a tšimo ea motlakase bohareng ba litefiso tse peli ke \(27,964.4 \, \text{N/C}\).
Mohlala oa 3: Tšimo ea Motlakase ka Pole
Potso: Pole ea motlakase e na le litefiso tse peli \(\pm 4 \times 10^{-6} \, \text{C}\) tse arohaneng ka 1 cm. Bala matla a tšimo ea motlakase ntlheng ea mithara e le 'ngoe ho tloha bohareng ba dipole mothating oa dipole.
Tharollo:
Matla a tšimo ea motlakase ho latela mothapo oa dipole (bakeng sa libaka tse kholo ka ho lekaneng ha li bapisoa le sebaka se pakeng tsa litefiso tsa dipole) a fanoa ke:
\[ E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{2p}{r^3} \]
Moo \(p\) e leng motsotso wa dipole wa motlakase (\(p = q \cdot d\)), \(d\) ke sebaka se pakeng tsa ditefiso tsa dipole, mme \(r\) ke sebaka se tlohang bohareng ba dipole ho ya sebakeng seo ho shebellwang ho sona.
Taba ea pele, bala motsotso oa dipole:
\[ p = q \cdot d \]
\[ p = 4 \makgetlo a 10^{-6} \cdot 0.01 \]
\[ p = 4 \makgetlo a 10^{-8} \, \mongolo{C m} \]
Ebe, bala matla a tšimo ea motlakase:
\[ E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{2p}{r^3} \]
\[ E = \frac{8.99 \times 10^9}{1} \cdot \frac{2 \times 4 \times 10^{-8}}{1^3} \]
\[ E = 8.99 \makgetlo a 10^9 \cdot 8 \makgetlo a 10^{-8} \]
\[ E = 7.192 \makgetlo a 10^2 \]
\[ E = 719.2 \, \mongolo{N/C} \]
Kahoo, matla a tšimo ea motlakase ntlheng ea mithara e le 1 ho tloha bohareng ba dipole ho axis ea dipole ke \(719.2 \, \text{N/C}\).
Qetello
Ho utloisisa matla a tšimo ea motlakase ho bohlokoa fisiks le lits'ebetsong tsa eona. Mehlala ea mathata a kaholimo e bontša kamoo melao-motheo ea mantlha ea masimo a motlakase e ka sebelisoang ho bala matla a tšimo litlhophisong tse fapaneng tsa tjhaja. Mathata a mokhoa oa ho itloaetsa a kang ana a thusa haholo ho utloisiseng mohopolo le ts'ebeliso ea molao oa Coulomb le superposition ea tšimo ea motlakase. Ka ho utloisisa le ho itloaetsa mathata a mangata, re ka tebisa kutloisiso ea rona ea likamano tsa motlakase litsamaisong tse fapaneng.
