Imibuzo Eyisibonelo Ekhuluma Ngamandla Kamagnetic Entanjeni Ethwala Amandla
Amandla kazibuthe yisenzakalo esibonakalayo esihilela ukusebenzisana phakathi kwensimu kazibuthe kanye nogesi. Lesi simo sichazwa ngumthetho ka-Ampère, othi ugesi ogeleza ngentambo ungakhiqiza insimu kazibuthe. Lesi sihloko sizochaza izibonelo futhi sixoxe ngamandla kazibuthe entanjeni ethwala ugesi, okungakusiza ukuthi uqonde lo mqondo ngokujulile.
I-Pendahuluan
Isenzakalo se-magnetism besilokhu saziwa kusukela ezikhathini zasendulo, kodwa incazelo yesayensi yokusebenzisana phakathi kwemisinga kagesi namasimu kazibuthe ayizange itholakale kwaze kwaba yikhulu le-19. UHans Christian Ørsted wayengowokuqala ukuthola ukuthi imisinga kagesi ingakhiqiza amasimu kazibuthe. Kamuva, u-André-Marie Ampère waqhubekisela phambili lokhu kutholwa ngokwakha lokho okwaziwa manje ngokuthi uMthetho ka-Ampère.
Imiqondo Eyisisekelo
1. Umthetho we-Biot-Savart
Insimu yamagnetic ekhiqizwa yisici esincane samandla kagesi ingabalwa kusetshenziswa umthetho we-Biot-Savart:
\[
dB = \frac{\mu_0}{4\pi} \cdot \frac{I \cdot (d\mathbf{l} \times \mathbf{r})}{r^3}
\]
Kuphi:
– \(dB\) = isici sensimu yamagnetic
– \(\mu_0\) = ukuvuleka kwe-vacuum \((4\pi \times 10^{-7} \text{Tm/A})\)
– \(I\) = Amandla kagesi (A)
– \(d\mathbf{l}\) = isici sobude bentambo (m)
– \(\mathbf{r}\) = ivektha yesikhundla esihlobene phakathi kwento yamanje kanye nephuzu lokubuka (m)
2. Amandla kaLorentz
Ucingo oluphethe ugesi \(I\) bese lufakwa ensimini yamagnetic \(B\) luzozwa amandla \(F\) anikezwe yi:
\[
\mathbf{F} = I \cdot (\mathbf{L} \times \mathbf{B})
\]
Kuphi:
– \(\mathbf{F}\) = Amandla kazibuthe (N)
– \(I\) = Amandla kagesi (A)
– \(\mathbf{L}\) = Ubude bentambo ensimini yamagnetic (m)
– \(\mathbf{B}\) = Insimu yamagnetic (T)
Imibuzo Eyisibonelo Nengxoxo
Umbuzo 1:
Intambo eqondile engamamitha angu-0.5 ubude ifakwa ensimini efanayo yamagnetic engu-0.2 Tesla. Uma intambo iphethe ugesi ongu-3 A futhi isiqondiso samandla kagesi siqondene nensimu yamagnetic, bala ubukhulu bamandla kaLorentz asebenza entanjeni.
Isixazululo:
Sisebenzisa i-Lorentz force equation, sinalokhu okulandelayo:
\[
\mathbf{F} = I \cdot (\mathbf{L} \times \mathbf{B})
\]
Singachaza indlela yamanje \(I\) ehambisana ne-\(\mathbf{L}\) kanye nensimu yamagnetic \(B\) eqondile ne-\(\mathbf{L}\).
\[
|\mathbf{F}| = I \cdot L \cdot B \cdot \sin\theta
\]
Njengoba insimu yamanje kanye neyamagnetic ziqondile (\(\theta = 90^\circ\)), khona-ke \(\sin 90^\circ = 1\), ngakho-ke:
\[
|\mathbf{F}| = 3 \, \text{A} \cdot 0.5 \, \text{m} \cdot 0.2 \, \text{T} \cdot 1 = 0.3 \, \text{N}
\]
Umbuzo 2:
Intambo eyindilinga enobubanzi obungamamitha angu-0.1 ithwala ugesi ongu-2 A. Thola insimu yamagnetic enkabeni yendilinga.
Isixazululo:
Ukusebenzisa ifomula yensimu yamagnetic enkabeni yeluphu eyindilinga:
\[
B = \frac{\mu_0 I}{2R}
\]
no:
– \(\mu_0 = 4\pi \izikhathi 10^{-7} \, \text{Tm/A}\)
– \(I = 2 \, \umbhalo{A}\)
– \(R = 0.1 \, \umbhalo{m}\)
Ngakho-ke:
\[
B = \frac{(4\pi \times 10^{-7} \, \text{Tm/A} \times 2 \, \text{A})}{2 \times 0.1 \, \text{m}}
= \frac{4\pi \times 10^{-7} \times 2}{0.2} \, \text{T}
= 4\pi \izikhathi 10^{-6} \, \umbhalo{T}
\cishe 1.26 \izikhathi eziyi-10^{-5} \, \umbhalo{T}
\]
Umbuzo 3:
Izintambo ezimbili eziqondile ezihambisanayo ezinobude \(L\) zibekwe kude \(d\) komunye nomunye. Uma intambo ngayinye iphethe ugesi \(I\) ohlangothini oluphambene, nquma amandla ngeyunithi ubude obusebenza phakathi kwezintambo ezimbili.
Isixazululo:
Amandla ngeyunithi ubude phakathi kwezintambo ezimbili ezihambisanayo ezithwala ugesi:
\[
f = \frac{\mu_0 I_1 I_2}{2\pi d}
\]
Ngoba imisinga iyalingana futhi iphambene ngendlela eqondile:
\[
f = \frac{\mu_0 I^2}{2\pi d}
\]
Ngokwesibonelo:
– \(\mu_0 = 4\pi \izikhathi 10^{-7} \, \text{Tm/A}\)
– \(I_1 = I_2 = I\)
– \(d\) ibanga eliphakathi kwezintambo.
Ukufaka amanani kufomula, sithola:
\[
f = \frac{(4\pi \times 10^{-7}) \, I^2}{2\pi d}
= \frac{2 \times 10^{-7} I^2}{d} \, \text{N/m}
\]
Isiphetho
Ukuqonda ukusebenzisana phakathi kwamasimu kazibuthe kanye nemisinga kagesi kubalulekile kwezobuchwepheshe eziningi zesimanje, kusukela kumamotha kagesi kuya kumajeneretha. Ngokuqonda imiqondo yamandla kaLorentz, umthetho weBiot-Savart, kanye nokusetshenziswa kwamafomula ensimu kazibuthe, singasebenzisa lolu lwazi ezinkingeni nasezimweni ezahlukahlukene zansuku zonke. Lesi sihloko sihloselwe ukunikeza isisekelo esiqinile sokuqonda nokuxazulula izinkinga ezihlobene namandla kazibuthe ezintanjeni ezithwala ugesi.
