Misali na tambayar tattaunawa game da girman EMF da aka haifar
Pendahuluan
Ƙarfin lantarki mai haifar da wutar lantarki (EMF) wani abu ne na zahiri da Michael Faraday ya gano a shekarar 1831. Faraday ya gano cewa canjin filin maganadisu a cikin madauki ko na'urar jagora na iya haifar da wutar lantarki. Wannan lamari ana kiransa da wutar lantarki kuma shine tushen fasahohin zamani da yawa, kamar janareto, transformers, da injunan lantarki. Wannan labarin zai bayyana misalai da yawa na matsaloli kuma ya tattauna girman EMF da aka haifar, wanda zai zama da amfani sosai musamman ga ɗaliban da ke nazarin kimiyyar lantarki da maganadisu.
Asalin Ma'anar EMF da aka haifar
Kafin mu shiga cikin matsalar misali, yana da kyau mu sake duba manufar asali ta emf da aka haifar. Dokar Faraday ta bayyana cewa emf da aka haifar a cikin madauki mai gudanarwa yana daidai gwargwado kai tsaye da ƙimar canjin kwararar maganadisu ta cikin madauki. A lissafi, ana iya tsara dokar Faraday kamar haka:
\[ \mathcal {E} = - \frac{d\Phi}{dt} \]
Ina:
– \( \mathcal{E} \) shine EMF da aka haifar (volts)
– \( \Phi \) shine kwararar maganadisu (Weber, Wb)
– \( t \) lokaci ne (na biyu, s)
Alamar da ba ta dace ba a cikin lissafin tana nuna Dokar Lenz wadda ta bayyana cewa alkiblar wutar lantarki da aka haifar za ta haifar da filin maganadisu wanda ke adawa da canjin kwararar maganadisu da ya haifar da shi.
Tambayoyi da Tattaunawa Samfura
Tambaya ta 1: Naɗa ɗaya
Tambaya: An sanya na'ura guda ɗaya mai faɗin saman 0.02 m² a cikin filin maganadisu iri ɗaya mai girman 0.5 T, a tsaye a saman na'urar. Ba zato ba tsammani za a rage filin maganadisu cikin daƙiƙa 0.1. A ƙididdige girman EMF da aka haifar da ke tashi a cikin na'urar.
Tattaunawa:
An sani:
– Faɗin saman na'urar \( A = 0.02 \, \text{m}^2 \)
– Girman filin maganadisu \( B = 0.5 \, \text{T} \)
– Lokacin canjin filin \( \Delta t = 0.1 \, \text{s} \)
Canje-canje a cikin kwararar maganadisu:
\[ \Delta \Phi = B \sau A \]
\[ \Delta \Phi = 0.5 \, \text{T} \times 0.02 \, \text{m}^2 \]
\[ \Delta \Phi = 0.01 \, \text{Wb} \]
Girman EMF da aka haifar:
\[ \mathcal{E} = – \frac{\Delta \Phi}{\Delta t} \]
\[ \mathcal{E} = – \frac{0.01 \, \text{Wb}}{0.1 \, \text{s}} \]
\[ \mathcal {E} = -0.1 \, \ rubutu {V} \]
Domin abin da ake tambaya shi ne girman EMF (ba tare da kula da alamar ba):
\[ |\mathcal{E}| = 0.1 \, \rubutu {V} \]
Tambaya ta 2: Na'urar Juyawa ta N
Tambaya: Na'urar tana da juyi 100 kuma faɗin samanta shine 0.03 m². Wannan na'urar tana cikin filin maganadisu iri ɗaya na 0.4 T daidai da na'urar. Idan filin maganadisu ya ƙaru zuwa 1.2 T cikin daƙiƙa 0.4, ƙididdige matsakaicin emf da aka haifar da na'urar.
Tattaunawa:
An sani:
– Adadin juyawa \( N = 100 \)
– Faɗin saman na'urar \( A = 0.03 \, \text{m}^2 \)
– Canji a filin maganadisu \( \Delta B = 1.2 \, \text{T} – 0.4 \, \text{T} \)
– Lokacin canjin filin \( \Delta t = 0.4 \, \text{s} \)
Canjin kwararar maganadisu a kowane juyi:
\[ \Delta \Phi = A \times \Delta B \]
\[ \Delta \Phi = 0.03 \, \text{m}^2 \times (1.2 \, \text{T} – 0.4 \, \text{T}) \]
\[ \Delta \Phi = 0.03 \, \text{m}^2 \times 0.8 \, \text{T} \]
\[ \Delta \Phi = 0.024 \, \text{Wb} \]
Jimlar canjin kwararar ruwa don juyawar N:
\[ \Delta \Phi_{\text{total}} = N \times \Delta \Phi \]
\[ \Delta \Phi_{\text{total}} = 100 \times 0.024 \, \text{Wb} \]
\[ \Delta \Phi_{\text{total}} = 2.4 \, \text{Wb} \]
Girman EMF da aka haifar:
\[ \mathcal {E} = – \frac{\Delta \Phi_{\text{total}}} {Delta t} \]
\[ \mathcal{E} = – \frac{2.4 \, \text{Wb}}{0.4 \, \text{s}} \]
\[ \mathcal {E} = -6 \, \ rubutu {V} \]
Domin abin da ake tambaya shi ne girman EMF (ba tare da kula da alamar ba):
\[ |\mathcal{E}| = 6 \, \rubutu {V} \]
Tambaya ta 3: Matsar da na'urar a cikin filin maganadisu
Tambaya: Ana sanya na'urar jujjuyawa mai juyi 50, tsawon santimita 4, da faɗin santimita 2, a cikin filin maganadisu iri ɗaya na 0.3 T a layi ɗaya da tsawon na'urar. Idan na'urar ta motsa daga filin maganadisu a gudun da ya dace na santimita 5/s, menene EMF da aka haifar a cikin na'urar?
Tattaunawa:
An sani:
– Adadin juyawa \( N = 50 \)
– Tsawon \( l = 0.04 \, \rubutu{m} \)
– Faɗin \( w = 0.02 \, \rubutu{m} \)
– Girman filin maganadisu \( B = 0.3 \, \text{T} \)
– Saurin fita na filin maganadisu \( v = 0.05 \, \text{m/s} \)
Ana bayar da ƙarfin lantarki a kan na'urar da ke motsawa a cikin filin maganadisu ta hanyar:
\[ \mathcal{E} = B lv \]
Tunda na'urar tana da juyawar N, jimlar EMF da aka haifar shine:
\[ \mathcal{E}_{\text{jimlar}} = NB lv \]
\[ \mathcal{E}_{\text{total}} = 50 \times 0.3 \, \text{T} \times 0.04 \, \text{m} \times 0.05 \, \text{m/s} \]
\[ \mathcal{E}_{\text{total}} = 50 \times 0.0006 \, \text{V} \]
\[ \mathcal {E}_{\text{total}} = 0.03 \, \ rubutu {V} \]
Kammalawa
Tattaunawar misalan matsalolin da ke sama ta nuna yadda za a iya ƙididdige emf da aka haifar daga canje-canje a cikin kwararar maganadisu ko kuma daga motsin na'urar maganadisu a cikin filin maganadisu. Wannan ra'ayi yana da mahimmanci ga electromagnetism kuma yana da aikace-aikace da yawa a cikin fasaha. Fahimtar yadda ake ƙididdige emf da aka haifar daidai ta hanyar matsaloli na aiki zai taimaka wa ɗalibai sosai wajen ƙware wannan kayan da kuma amfani da shi a fannoni daban-daban.
