Su'aalo Tusaale ah oo Ka Hadlaya Kharashka Xoojinta
Pendahuluan
Fiisigis waa daraasadda dhacdooyinka dabiiciga ah, oo ay ku jiraan xoogagga ku shaqeeya walxaha. Mawduuc xiiso leh oo inta badan laga hadlo waa xoogga ku shaqeeya dallacaadaha dhaqdhaqaaqa, gaar ahaan marka la eego goobaha korontada iyo birlabta. Xoogga ku shaqeeya dallacaadaha dhaqdhaqaaqa ee ku jira goobta korontada ama birlabta waxaa loo yaqaan xoogga Lorentz. Maqaalkani wuxuu ka hadli doonaa dhowr dhibaato oo tusaale ah iyo dooddooda ku saabsan xoogga ku shaqeeya dallacaadaha dhaqdhaqaaqa.
Ciidanka Lorentz
Xoogga Lorentz waa isku-darka xoogga korantada iyo xoogga birlabta ee ka shaqeeya dallac ku socda goob koronto iyo goob birlab ah. Xisaab ahaan, xoogga Lorentz (F) waxaa lagu muujin karaa isla'egta:
\[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}) \]
Halkee:
- \ ( \mathbf {F} \) waa xoogga Lorentz
– \( q \) waa kharashka
– \( \mathbf{E} \) waa goobta korantada
– \( \mathbf{v} \) waa xawaaraha dallacaadda
– \( \mathbf{B} \) waa goobta birlabta
Isla'egtan, waxaan ku falanqeyn karnaa awoodaha ku shaqeeya dallac ku socda goob koronto iyo goob birlab ah.
Su'aalo iyo Doodo Tusaale ah
Su'aal 1aad: Xoog lagu soo rogo goob koronto
Su'aal:
Dalac togan \( q = 2 \jeer 10^{-6} \, C \) wuxuu ku jiraa goob koronto oo isku mid ah \( E = 5 \jeer 10^4 \, N/C \) oo loo jiheeyay dhanka midig. Xisaabi xoogga ku shaqeeya dalacaadda.
Dood:
Kharash ku jira goob koronto oo aan lahayn goob birlab ah, xoogga Lorentz wuxuu ka kooban yahay oo keliya qaybta xoogga korontada:
\[ \mathbf{F} = q \mathbf{E} \]
Iyadoo \( q = 2 \jeer 10^{-6} \, C \) iyo \( \mathbf{E} = 5 \jeer 10^4 \, N/C \):
\[ \mathbf{F} = (2 \jeer 10^{-6} \, C) \jeer (5 \jeer 10^4 \, N/C) \]
\[ \mathbf{F} = 0.1 \, N \]
Jihada xoogga \( \mathbf{F} \) waxay ku socotaa jihada la mid ah goobta korantada sababtoo ah dallacaaddu waa togan tahay. Markaa, xoogga ku shaqeeya dallacaaddu waa 0.1 N dhanka midig.
Su'aal 2: Xoog lagu soo rogo goob birlab ah
Su'aal:
Dalac taban \( q = -3 \times 10^{-6} \, C \) wuxuu ku socdaa xawaare \( \mathbf{v} = 2 \times 10^3 \, m/s \) oo ku teedsan dhidibka x ee goob birlab ah oo isku mid ah \( \mathbf{B} = 0.5 \, T \) oo ku teedsan dhidibka z. Xisaabi xoogga ka shaqeynaya kharashka.
Dood:
Kharash ku socda goob birlabeed iyada oo aan lahayn goob koronto, xoogga Lorentz wuxuu ka kooban yahay oo keliya qaybaha xoogga birlabka:
\[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \]
Iyadoo \( q = -3 \times 10^{-6} \, C \), \( \mathbf{v} = 2 \times 10^3 \, m/s \) jihada x, iyo \( \mathbf{B} = 0.5 \, T \) jihada z:
Xisaabinta \( \mathbf{v} \times \mathbf{B} \):
\[ \mathbf{v} = 2 \jeer 10^3 \, m/s \, \hat{i} \]
\[ \mathbf{B} = 0.5 \, T \, \hat{k} \]
\[ \mathbf{v} \times \mathbf{B} = (2 \jeer 10^3 \, m/s \, \hat{i}) \jeer (0.5 \, T \, \hat{k}) \]
\[ \mathbf{v} \times \mathbf{B} = 2 \jeer 10^3 \, m/s \jeer 0.5 \, T \, \hat{i} \times \hat{k} \]
\[ \hat{i} \times \hat{k} = -\hat{j} \]
\[ \mathbf{v} \times \mathbf{B} = – (1 \jeer 10^3 \, T \cdot m/s) \, \hat{j} \]
Markaa, xoogga magnetka:
\[ \mathbf{F} = q \mathbf{v} \times \mathbf{B} \]
\[ \mathbf{F} = (-3 \jeer 10^{-6} C) \jeer ( -10^3 \, T \cdot m/s \, \hat{j}) \]
\[ \mathbf{F} = 3 \jeer 10^{-3} \, N \, \hat{j} \]
\[ \mathbf{F} = 0.003 \, N \, \koo{j} \]
Jihada xoogga \( \mathbf{F} \) waxay u socotaa dhidibka y-ga togan. Markaa, xoogga ku shaqeeya dallacaadda waa 0.003 N kor (jihada dhidibka y-ga togan).
Su'aal 3: Xoog ku baxaya goobaha Korontada iyo Birlabta
Su'aal:
Dalac togan \( q = 1.5 \jeer 10^{-6} \, C \) wuxuu ku socdaa xawaare \( \mathbf{v} = 4 \jeer 10^3 \, m/s \) jihada y ee goobta korantada \( \mathbf{E} = 3 \jeer 10^4 \, N/C \) jihada x, iyo goob birlab ah \( \mathbf{B} = 0.2 \, T \) jihada z. Xisaabi xoogga saafiga ah ee ka shaqeynaya kharashka.
Dood:
Wadarta xoogga Lorentz:
\[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}) \]
Marka hore, xisaabi \( \mathbf{v} \times \mathbf{B} \):
\[ \mathbf{v} = 4 \jeer 10^3 \, m/s \, \hat{j} \]
\[ \mathbf{B} = 0.2 \, T \, \hat{k} \]
\[ \mathbf{v} \times \mathbf{B} = (4 \jeer 10^3 \, m/s \, \hat{j}) \jeer (0.2 \, T \, \hat{k}) \]
\[ \mathbf{v} \times \mathbf{B} = 4 \jeer 10^3 \, m/s \jeer 0.2 \, T \, \hat{j} \jeer \hat{k} \]
\[ \hat{j} \times \hat{k} = \hat{i} \]
\[ \mathbf{v} \times \mathbf{B} = (0.8 \times 10^3 \, T \cdot m/s) \, \hat{i} \]
\[ \mathbf{v} \times \mathbf{B} = 800 \, T \cdot m/s \, \hat{i} \]
Kadib, xoogga korontada:
\[ q \mathbf{E} = (1.5 \jeer 10^{-6} \, C) \jeer (3 \jeer 10^4 \, N/C \, \hat{i}) \]
\[q \mathbf{E} = 0.045 \, N \, \hat{i} \]
Xoogga birlabta:
\[ q (\mathbf{v} \times \mathbf{B}) = (1.5 \jeer 10^{-6} \, C) \jeer (800 \, T \cdot m/s \, \hat{i}) \]
\[q (\mathbf{v} \times \mathbf{B}) = 0.0012 \, N \, \hat{i} \]
Qaabka guud:
\[ \mathbf{F} = q \mathbf{E} +q (\mathbf{v} \times \mathbf{B}) \]
\[ \mathbf{F} = 0.045 \, N \, \hat{i} + 0.0012 \, N \, \ koo{i} \]
\[ \mathbf{F} = 0.0462 \, N \, \koo{i} \]
Markaa, wadarta guud ee xoogga ku shaqeeya dalacaadda waa 0.0462 N dhanka midig (dhidibka x-togan).
Gabagabo
Xoogga ku baxa dallacaadaha ku socda goobaha korontada iyo birlabta waxay aad ugu xiran tahay jihada iyo baaxadda goob kasta iyo sidoo kale xawaaraha iyo nooca dallacaadda. Iyada oo loo marayo su'aalaha tusaalaha ah iyo doodda kor ku xusan, waxaa la rajeynayaa in akhristayaashu ay si fiican u fahmi karaan sida loo dabaqo mabda'a xoogga Lorentz xaalado kala duwan. Fahamkan ma aha oo kaliya muhiim aragti ahaan laakiin sidoo kale waa muhiim codsiyada wax ku oolka ah ee goobaha tignoolajiyada iyo sayniska sida naqshadeynta matoorada korontada, fahamka ifafaalaha aurora, iyo shaqada walxaha ku jira dardar-gelinta walxaha.
