Imibuzo Yezibonelo Ekhuluma Ngokusebenza Kwamandla Ekushajeni Kokuhamba
I-Pendahuluan
I-physics iwucwaningo lwezimo zemvelo, okuhlanganisa namandla asebenza ezintweni. Isihloko esisodwa esithakazelisayo okuxoxwa ngaso njalo ngamandla asebenza ngamashaja ahambayo, ikakhulukazi kumongo wamasimu kagesi namagnetic. Amandla asebenza ngeshaja ehambisayo ensimini kagesi noma yamagnetic aziwa ngokuthi amandla kaLorentz. Lesi sihloko sizoxoxa ngezinkinga eziningana zezibonelo kanye nengxoxo yazo mayelana namandla asebenza ngamashaja ahambayo.
Amandla kaLorentz
Amandla e-Lorentz ayinhlanganisela yamandla kagesi kanye namandla kazibuthe asebenza ekushajweni okuhambayo ensimini kagesi kanye nensimu kazibuthe. Ngokwezibalo, amandla e-Lorentz (F) angavezwa yi-equation:
\[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \izikhathi \mathbf{B}) \]
Di mana:
– \( \mathbf{F} \) ingamandla e-Lorentz
– \( q \) yindleko
– \( \mathbf{E} \) yinsimu kagesi
– \( \mathbf{v} \) ijubane lokushaja
– \( \mathbf{B} \) yinsimu yamagnetic
Ngalesi sibalo, singahlaziya amandla asebenza ekushajweni okuhambayo ensimini kagesi kanye nensimu yamagnetic.
Imibuzo Eyisibonelo Nengxoxo
Umbuzo 1: Amandla Ekushajweni Ensimini Kagesi
Umbuzo:
Ishaja elungile \( q = 2 \times 10^{-6} \, C \) isensimini kagesi efanayo \( E = 5 \times 10^4 \, N/C \) iqondiswe kwesokudla. Bala amandla asebenza eshaja.
Ingxoxo:
Uma kushajwa ensimini kagesi ngaphandle kokuba khona kwensimu yamagnetic, amandla eLorentz aqukethe kuphela ingxenye yamandla kagesi:
\[ \mathbf{F} = q \mathbf{E} \]
Nge-\( q = 2 \times 10^{-6} \, C \) kanye ne-\( \mathbf{E} = 5 \times 10^4 \, N/C \):
\[ \mathbf{F} = (2 \times 10^{-6} \, C) \times (5 \times 10^4 \, N/C) \]
\[ \mathbf{F} = 0.1 \, N \]
Isiqondiso samandla \( \mathbf{F} \) sisehlangothini olufanayo nensimu kagesi ngoba ishaja ilungile. Ngakho-ke, amandla asebenza ekushajeni angu-0.1 N ngakwesokudla.
Umbuzo 2: Amandla Ekushajweni Ensimini KaMazibuthe
Umbuzo:
Ishaja engemihle \( q = -3 \times 10^{-6} \, C \) ihamba ngejubane \( \mathbf{v} = 2 \times 10^3 \, m/s \) eceleni kwe-x-axis ensimini yamagnetic efanayo \( \mathbf{B} = 0.5 \, T \) eqondiswe eceleni kwe-z-axis. Bala amandla asebenza kushaja.
Ingxoxo:
Uma ishaja ihamba ensimini yamagnetic ngaphandle kokuba khona kwensimu kagesi, amandla eLorentz aqukethe kuphela izingxenye zamandla kazibuthe:
\[ \mathbf{F} = q (\mathbf{v} \izikhathi \mathbf{B}) \]
Njengoba \( q = -3 \times 10^{-6} \, C \), \( \mathbf{v} = 2 \times 10^3 \, m/s \) ohlangothini lwe-x, kanye \( \mathbf{B} = 0.5 \, T \) ohlangothini lwe-z:
Ukubala \( \mathbf{v} \times \mathbf{B} \):
\[ \mathbf{v} = 2 \izikhathi 10^3 \, m/s \, \hat{i} \]
\[ \mathbf{B} = 0.5 \, T \, \hat{k} \]
\[ \mathbf{v} \times \mathbf{B} = (2 \times 10^3 \, m/s \, \hat{i}) \times (0.5 \, T \, \hat{k}) \]
\[ \mathbf{v} \izikhathi \mathbf{B} = 2 \izikhathi 10^3 \, m/s \izikhathi 0.5 \, T \, \hat{i} \izikhathi \hat{k} \]
\[ \hat{i} \times \hat{k} = -\hat{j} \]
\[ \mathbf{v} \times \mathbf{B} = – (1 \times 10^3 \, T \cdot m/s) \, \hat{j} \]
Ngakho-ke, amandla kazibuthe:
\[ \mathbf{F} = q \mathbf{v} \izikhathi \mathbf{B} \]
\[ \mathbf{F} = (-3 \times 10^{-6} C) \times ( -10^3 \, T \cdot m/s \, \hat{j}) \]
\[ \mathbf{F} = 3 \izikhathi 10^{-3} \, N \, \hat{j} \]
\[ \mathbf{F} = 0.003 \, N \, \hat{j} \]
Isiqondiso samandla \( \mathbf{F} \) sibheke ku-y-axis enhle. Ngakho-ke, amandla asebenza ekushajweni angama-N angu-0.003 phezulu (esiqondisweni se-y-axis enhle).
Umbuzo 3: Amandla Ashajayo Emasimini Kagesi Namagnetic
Umbuzo:
Ishaja enhle \( q = 1.5 \times 10^{-6} \, C \) ihamba ngejubane \( \mathbf{v} = 4 \times 10^3 \, m/s \) ohlangothini lwe-y ensimini kagesi \( \mathbf{E} = 3 \times 10^4 \, N/C \) ohlangothini lwe-x, kanye nensimu yamagnetic \( \mathbf{B} = 0.2 \, T \) ohlangothini lwe-z. Bala amandla aphelele asebenza ekushajeni.
Ingxoxo:
Amandla e-Lorentz aphelele:
\[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \izikhathi \mathbf{B}) \]
Okokuqala, bala \( \mathbf{v} \times \mathbf{B} \):
\[ \mathbf{v} = 4 \izikhathi ezingu-10^3 \, m/s \, \hat{j} \]
\[ \mathbf{B} = 0.2 \, T \, \hat{k} \]
\[ \mathbf{v} \times \mathbf{B} = (4 \times 10^3 \, m/s \, \hat{j}) \times (0.2 \, T \, \hat{k}) \]
\[ \mathbf{v} \izikhathi \mathbf{B} = 4 \izikhathi 10^3 \, m/s \izikhathi 0.2 \, T \, \hat{j} \izikhathi \hat{k} \]
\[ \hat{j} \times \hat{k} = \hat{i} \]
\[ \mathbf{v} \times \mathbf{B} = (0.8 \times 10^3 \, T \cdot m/s) \, \hat{i} \]
\[ \mathbf{v} \times \mathbf{B} = 800 \, T \cdot m/s \, \hat{i} \]
Bese kuthi, amandla kagesi:
\[ q \mathbf{E} = (1.5 \izikhathi 10^{-6} \, C) \izikhathi (3 \izikhathi 10^4 \, N/C \, \hat{i}) \]
\[ q \mathbf{E} = 0.045 \, N \, \isigqoko{i} \]
Amandla kazibuthe:
\[ q (\mathbf{v} \times \mathbf{B}) = (1.5 \times 10^{-6} \, C) \times (800 \, T \cdot m/s \, \hat{i}) \]
\[ q (\mathbf{v} \izikhathi \mathbf{B}) = 0.0012 \, N \, \hat{i} \]
Isitayela esiphelele:
\[ \mathbf{F} = q \mathbf{E} + q (\mathbf{v} \izikhathi \mathbf{B}) \]
\[ \mathbf{F} = 0.045 \, N \, \isigqoko{i} + 0.0012 \, N \, \isigqoko{i} \]
\[ \mathbf{F} = 0.0462 \, N \, \isigqoko{i} \]
Ngakho-ke, amandla aphelele asebenza ekushajweni ngu-0.0462 N ngakwesokudla (i-x-axis enhle).
Isiphetho
Amandla asebenza emashajini ahambayo emasimu kagesi namagnetic ancike kakhulu ekuqondisweni nasekukhulwini kwensimu ngayinye kanye nesivinini kanye nohlobo lweshaja. Ngemibuzo eyisibonelo kanye nengxoxo engenhla, kunethemba lokuthi abafundi bangaqonda kangcono ukuthi bangayisebenzisa kanjani isimiso samandla sikaLorentz ezimweni ezahlukahlukene. Lokhu kuqonda akubalulekile nje kuphela emcabangweni kodwa futhi nasekusetshenzisweni okusebenzayo emikhakheni yezobuchwepheshe neyesayensi njengasekuklanyweni kwama-motor kagesi, ukuqonda isenzakalo se-aurora, kanye nomsebenzi wezinhlayiya kuma-accelerator ezinhlayiya.
