Mehlala ea Lipotso Tse Buisanang ka Matla a ho Falla
Pendahuluan
Fisiks ke thuto ea liketsahalo tsa tlhaho, ho kenyeletsoa le matla a sebetsang linthong. Sehlooho se seng se khahlisang seo ho buuoang ka sona khafetsa ke matla a liqoso tse tsamaeang, haholo-holo moelelong oa masimo a motlakase le a makenete. Matla a sebetsang holim'a tjhaja e tsamaeang tšimong ea motlakase kapa ea makenete a tsejoa e le matla a Lorentz. Sehlooho sena se tla tšohla mehlala e 'maloa ea mathata le puisano ea bona mabapi le matla a sebetsang holim'a liqoso tse tsamaeang.
Lebotho la Lorentz
Matla a Lorentz ke motsoako oa matla a motlakase le matla a makenete a sebetsang holim'a tjhaja e tsamaeang tšimong ea motlakase le tšimo ea makenete. Ka lipalo, matla a Lorentz (F) a ka hlalosoa ka equation:
\[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \linako \mathbf{B}) \]
Di mana:
- \( \ mathbf{F} \) ke matla a Lorentz
– \( q \) ke tefiso
– \( \mathbf{E} \) ke tšimo ea motlakase
– \( \mathbf{v} \) ke lebelo la tjhaja
– \( \mathbf{B} \) ke matla a makenete
Ka equation ena, re ka sekaseka matla a sebetsang hodima tjhaja e tsamayang tshimong ya motlakase le tshimong ya makenete.
Lipotso tsa Mehlala le Puisano
Potso ea 1: Matla a Tefiso Tšimong ea Motlakase
Potso:
Tefiso e ntle \( q = 2 \times 10^{-6} \, C \) e lebaleng la motlakase le lekanang \( E = 5 \times 10^4 \, N/C \) e lebisitsweng ka ho le letona. Bala matla a sebetsang hodima tefiso.
Puisano:
Bakeng sa tjhaja tshimong ya motlakase ntle le boteng ba matla a makenete, matla a Lorentz a bopilwe feela ka karolo ya matla a motlakase:
\[ \mathbf{F} = q \mathbf{E} \]
Ka \( q = 2 \times 10^{-6} \, C \) le \( \mathbf{E} = 5 \times 10^4 \, N/C \):
\[ \mathbf{F} = (2 \makgetlo a 10^{-6} \, C) \makgetlo (5 \makgetlo a 10^4 \, N/C) \]
\[ \mathbf{F} = 0.1 \, N \]
Tsela eo matla a kgutlang ka yona (\mathbf{F} \) e lebile lehlakoreng le le leng le tshimo ya motlakase hobane tjhaja e ntle. Kahoo, matla a sebetsang hodima tjhaja ke 0.1 N ka ho le letona.
Potso ea 2: Matla a Tefiso Tšimong ea Magnetic
Potso:
Tefiso e mpe \( q = -3 \times 10^{-6} \, C \) e tsamaya ka lebelo \( \mathbf{v} = 2 \times 10^3 \, m/s \) ho latela x-axis ka hara matla a makenete a tshwanang \( \mathbf{B} = 0.5 \, T \) a lebisitsweng ho latela z-axis. Bala matla a sebetsang hodima tefiso.
Puisano:
Bakeng sa tjhaja e tsamayang tshimong ya makenete ntle le boteng ba tshimo ya motlakase, matla a Lorentz a bopilwe feela ka dikarolo tsa matla a makenete:
\[ \mathbf{F} = q (\mathbf{v} \linako \mathbf{B}) \]
Ka \( q = -3 \times 10^{-6} \, C \), \( \mathbf{v} = 2 \times 10^3 \, m/s \) ka lehlakoreng la x, le \( \mathbf{B} = 0.5 \, T \) ka lehlakoreng la z:
Palo \( \mathbf{v} \times \mathbf{B} \):
\[ \mathbf{v} = 2 \makgetlo a 10^3 \, m/s \, \hat{i} \]
\[ \mathbf{B} = 0.5 \, T \, \hat{k} \]
\[ \mathbf{v} \times \mathbf{B} = (2 \times 10^3 \, m/s \, \hat{i}) \times (0.5 \, T \, \hat{k}) \]
\[ \mathbf{v} \times \mathbf{B} = 2 \times 10^3 \, m/s \times 0.5 \, T \, \hat{i} \times \hat{k} \]
\[ \hat{i} \times \hat{k} = -\hat{j} \]
\[ \mathbf{v} \times \mathbf{B} = – (1 \times 10^3 \, T \cdot m/s) \, \hat{j} \]
Kahoo, matla a makenete:
\[ \mathbf{F} = q \mathbf{v} \nako \mathbf{B} \]
\[ \mathbf{F} = (-3 \makgetlo a 10^{-6} C) \makgetlo ( -10^3 \, T \cdot m/s \, \hat{j}) \]
\[ \mathbf{F} = 3 \makhetlo 10^{-3} \, N \, \hat{j} \]
\[ \mathbf{F} = 0.003 \, N \, \hat{j} \]
Tsela eo matla a tswelang pele ka yona e lebile ho positive y-axis. Kahoo, matla a sebetsang hodima tjhaja ke 0.003 N ho ya hodimo (ka tsela e positive y-axis).
Potso ea 3: Matla a Tefiso Masimong a Motlakase le a Makenete
Potso:
Tefiso e ntle \( q = 1.5 \times 10^{-6} \, C \) e tsamaya ka lebelo \( \mathbf{v} = 4 \times 10^3 \, m/s \) ka lehlakoreng la y tšimong ea motlakase \( \mathbf{E} = 3 \times 10^4 \, N/C \) ka lehlakoreng la x, le matla a makenete \( \mathbf{B} = 0.2 \, T \) ka lehlakoreng la z. Bala matla a net a sebetsang holim'a tefiso.
Puisano:
Matla ohle a Lorentz:
\[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \linako \mathbf{B}) \]
Taba ea pele, bala \( \mathbf{v} \times \mathbf{B} \):
\[ \mathbf{v} = 4 \makgetlo a 10^3 \, m/s \, \hat{j} \]
\[ \mathbf{B} = 0.2 \, T \, \hat{k} \]
\[ \mathbf{v} \times \mathbf{B} = (4 \times 10^3 \, m/s \, \hat{j}) \times (0.2 \, T \, \hat{k}) \]
\[ \mathbf{v} \times \mathbf{B} = 4 \times 10^3 \, m/s \times 0.2 \, T \, \hat{j} \times \hat{k} \]
\[ \hat{j} \times \hat{k} = \hat{i} \]
\[ \mathbf{v} \times \mathbf{B} = (0.8 \times 10^3 \, T \cdot m/s) \, \hat{i} \]
\[ \mathbf{v} \times \mathbf{B} = 800 \, T \cdot m/s \, \hat{i} \]
Ebe, matla a motlakase:
\[ q \mathbf{E} = (1.5 \makgetlo a 10^{-6} \, C) \makgetlo (3 \makgetlo a 10^4 \, N/C \, \hat{i}) \]
\[ q \mathbf{E} = 0.045 \, N \, \ katiba{i} \]
Matla a makenete:
\[ q (\mathbf{v} \times \mathbf{B}) = (1.5 \times 10^{-6} \, C) \times (800 \, T \cdot m/s \, \hat{i}) \]
\[ q (\mathbf{v} \nako \mathbf{B}) = 0.0012 \, N \, \hat{i} \]
Setaele sohle:
\[ \mathbf{F} = q \mathbf{E} + q (\mathbf{v} \linako \mathbf{B}) \]
\[ \mathbf{F} = 0.045 \, N \, \het{i} + 0.0012 \, N \, \het{i} \]
\[ \mathbf{F} = 0.0462 \, N \, \hat{i} \]
Kahoo, matla ohle a sebetsang hodima tjhaja ke 0.0462 N ka ho le letona (mokhahlelo wa x o positive).
Qetello
Matla a litjhaja tse tsamayang masimong a motlakase le a makenete a itshetlehile haholo ka tataiso le boholo ba tshimo ka nngwe hammoho le lebelo le mofuta wa tjhaja. Ka mehlala ya dipotso le puisano e ka hodimo, ho tshepuwa hore babali ba ka utlwisisa hamolemo mokhoa wa ho sebedisa molaomotheo wa matla a Lorentz maemong a fapaneng. Kutlwisiso ena ha e bohlokwa feela thutong empa hape e bohlokwa le ditshebedisong tse sebetsang masimong a theknoloji le saense jwalo ka moralo wa dienjini tsa motlakase, ho utlwisisa ketsahalo ya aurora, le mosebetsi wa dikarolwana tse potlakisang dikarolwana.
