Tambayoyi Misali Game da Ƙarfin Magnetic akan Wayar da ke ɗauke da Wuta
Ƙarfin maganadisu wani abu ne na zahiri wanda ya shafi hulɗar da ke tsakanin filin maganadisu da wutar lantarki. An bayyana wannan lamari ta hanyar dokar Ampère, wadda ta bayyana cewa wutar lantarki da ke gudana ta cikin waya na iya samar da filin maganadisu. Wannan labarin zai zana misalai kuma ya tattauna ƙarfin maganadisu a cikin wayar da ke ɗauke da wutar lantarki, wanda zai iya taimaka muku fahimtar wannan ra'ayi sosai.
Pendahuluan
An san abin da ke haifar da maganadisu tun zamanin da, amma ba a gano wani bayani na kimiyya game da hulɗar da ke tsakanin kwararar wutar lantarki da filayen maganadisu ba sai a ƙarni na 19. Hans Christian Ørsted shi ne farkon wanda ya gano cewa kwararar wutar lantarki na iya samar da filayen maganadisu. Daga baya, André-Marie Ampère ya ci gaba da wannan gano ta hanyar tsara abin da yanzu ake kira Dokar Ampère.
Ka'idoji na Asali
1. Dokar Biot-Savart
Ana iya ƙididdige filin maganadisu da ƙaramin sinadarin wutar lantarki ya samar ta amfani da dokar Biot-Savart:
\[
dB = \frac{\mu_0}{4\pi} \cdot \frac{I \cdot (d\mathbf{l} \times \mathbf{r})}{r^3}
\]
Ina:
– \(dB\) = sinadarin filin maganadisu
– \(\mu_0\) = iskar da ke shiga cikin injin \((4\pi \sau 10^{-7} \text{Tm/A})\)
– \(I\) = Wutar lantarki (A)
– \(d\mathbf{l}\) = kashi na tsawon waya (m)
– \(\mathbf{r}\) = vektor ɗin matsayi tsakanin abin da ke yanzu da wurin lura (m)
2. Ƙarfin Lorentz
Waya mai ɗauke da wutar lantarki \(I\) kuma aka sanya ta a cikin filin maganadisu \(B\) za ta fuskanci ƙarfin \(F\) da aka bayar ta:
\[
\mathbf{F} = I \cdot (\mathbf{L} \times \mathbf{B})
\]
Ina:
– \(\mathbf{F}\) = Ƙarfin maganadisu (N)
– \(I\) = Wutar lantarki (A)
– \(\mathbf{L}\) = Tsawon waya a filin maganadisu (m)
– \(\mathbf{B}\) = Filin maganadisu (T)
Tambayoyi da Tattaunawa Samfura
Tambaya ta 1:
Ana sanya waya madaidaiciya mai tsawon mita 0.5 a cikin filin maganadisu iri ɗaya na 0.2 Tesla. Idan wayar tana ɗauke da wutar lantarki ta 3 A kuma alkiblar wutar tana daidai da filin maganadisu, a ƙididdige girman ƙarfin Lorentz da ke aiki akan wayar.
Mafita:
Ta amfani da lissafin ƙarfin Lorentz, muna da:
\[
\mathbf{F} = I \cdot (\mathbf{L} \times \mathbf{B})
\]
Za mu iya ayyana alkiblar halin yanzu \(I\) a layi ɗaya da \(\mathbf{L}\) da kuma filin maganadisu \(B\) a tsaye zuwa \(\mathbf{L}\).
\[
|\mathbf{F}| = I \cdot L \cdot B \cdot \sin\theta
\]
Tunda filin yanzu da na maganadisu suna tsaye (\(\theta = 90^\circ\)), to \(\sin 90^\circ = 1\), don haka:
\[
|\mathbf{F}| = 3 \, \text{A} \cdot 0.5 \, \text{m} \cdot 0.2 \, \text{T} \cdot 1 = 0.3 \, \text{N}
\]
Tambaya ta 2:
Wayar da ke da'ira mai tsawon mita 0.1 tana ɗauke da wutar lantarki ta 2 A. Kayyade filin maganadisu a tsakiyar da'irar.
Mafita:
Amfani da dabarar filin maganadisu a tsakiyar madauri mai zagaye:
\[
B = \frac{\mu_0 I}{2R}
\]
tare da:
– \(\mu_0 = 4\pi \sau 10^{-7} \, \text{Tm/A}\)
– \(I = 2 \, \rubutu{A}\)
– \(R = 0.1 \, \rubutu{m}\)
Don haka:
\[
B = \frac{(4\pi \sau 10^{-7} \, \text{Tm/A} \sau 2 \, \text{A})}{2 \sau 0.1 \, \text{m}}
= \frac{4\pi \sau 10^{-7} \sau 2}{0.2} \, \text{T}
= 4\pi \sau 10^{-6} \, \text{T}
\kimanin 1.26 \sau 10^{-5} \, \text{T}
\]
Tambaya ta 3:
Ana sanya wayoyi biyu madaidaiciya masu layi ɗaya masu tsawon \(L\) a nesa \(d\) daga juna. Idan kowace waya tana ɗauke da wutar lantarki \(I\) a akasin alkibla, ƙayyade ƙarfin da ke aiki tsakanin wayoyi biyu.
Mafita:
Tsawon kowace naúra tsakanin wayoyi biyu masu layi ɗaya waɗanda ke ɗauke da wutar lantarki:
\[
f = \frac{\mu_0 I_1 I_2}{2\pi d}
\]
Domin kuwa igiyoyin suna daidai kuma akasin haka ne a alkibla:
\[
f = \frac{\mu_0 I^2}{2\pi d}
\]
Misali:
– \(\mu_0 = 4\pi \sau 10^{-7} \, \text{Tm/A}\)
– \(I_1 = I_2 = I\)
– \(d\) shine nisan da ke tsakanin wayoyi.
Sauya dabi'u zuwa dabarar, mun sami:
\[
f = \frac{(4\pi \sau 10^{-7}) \, I^2}{2\pi d}
= \frac{2 \sau 10^{-7} I^2}{d} \, \text{N/m}
\]
Kammalawa
Fahimtar hulɗar da ke tsakanin filayen maganadisu da kwararar wutar lantarki abu ne mai mahimmanci ga fasahohin zamani da yawa, tun daga injinan lantarki zuwa janareta. Ta hanyar fahimtar ra'ayoyin ƙarfin Lorentz, dokar Biot-Savart, da kuma amfani da dabarun filin maganadisu, za mu iya amfani da wannan ilimin ga matsaloli da yanayi iri-iri na yau da kullun. An yi nufin wannan labarin don samar da tushe mai ƙarfi don fahimtar da warware matsalolin da suka shafi ƙarfin maganadisu a cikin wayoyi masu ɗauke da halin yanzu.
