Misali na Tambayoyin Tattaunawa na Solenoid
Solenoids muhimman abubuwa ne a aikace-aikacen lantarki da lantarki da yawa, tun daga na'urorin likitanci zuwa na'urorin masana'antu. Kafin mu shiga cikin tambayoyi da tattaunawa, bari mu fara fahimtar menene solenoid da kuma yadda yake aiki.
Fahimtar Solenoids
Solenoid wani nau'in waya ne da aka yi da waya, wanda yawanci yake kama da dogon silinda. Lokacin da wutar lantarki ke ratsawa ta cikin solenoid, yana ƙirƙirar filin maganadisu a cikinsa. Ana iya amfani da wannan filin maganadisu don dalilai daban-daban, kamar motsa piston a cikin solenoid na lantarki, ko don samar da filin maganadisu iri ɗaya a wasu bincike da aikace-aikacen fasaha.
Wani muhimmin siffa na solenoid shine filin maganadisu da yake samarwa. Filin maganadisu da ke cikin doguwar solenoid mai cike da ƙarfi kusan iri ɗaya ne. Daidaito da ke bayyana filin maganadisu na B a cikin solenoid mai kyau shine:
\[ B = \mu_0 \cdot n \cdot I \]
Ina:
– \( B \) shine filin maganadisu,
– \( \mu_0 \) shine ikon shiga cikin injin (\( 4\pi \times 10^{-7} \) T m/A),
– \( n \) shine adadin juyawa a kowane tsawon raka'a (juyawa/m),
– \( I \) shine wutar lantarki da ke gudana ta cikin solenoid.
Wannan filin maganadisu yana daidai gwargwado kai tsaye da kwararar wutar lantarki da adadin juyawa a kowane tsawon raka'a, kuma yana tasiri ne ta hanyar halayen matsakaiciyar da ke cikin solenoid, a wannan yanayin iska ko injin tsotsa.
Tambaya ta 1: Lissafin Filin Magnetic da ke Cikin Solenoid
Tambaya:
Solenoid yana da juyawa 1000 kuma tsawonsa mita 0,5 ne. Idan wutar da ke gudana ta cikin solenoid ɗin amperes 2 ne, ƙididdige filin maganadisu da ke cikin solenoid ɗin.
Tattaunawa:
Da farko, muna buƙatar ƙididdige adadin juyawa a kowane tsawon raka'a (n):
\[ n = \frac{N}{L} = \frac{1000}{0,5} = 2000 \, \text{juyawa/m} \]
Sannan, yi amfani da dabarar filin maganadisu na solenoid:
\[ B = \mu_0 \cdot n \cdot I \]
\[
B = (4\pi \sau 10^{-7}) \cdot 2000 \cdot 2
= 8\pi \sau 10^{-4} \, \text{T}
\]
\[
B \kimanin 2,51 \sau 10^{-3} \, \text{T}
\]
Don haka, filin maganadisu da ke cikin solenoid yana kusan \( 2,51 \sau 10^{-3} \, \text{T} \) ko 2,51 mT (milliTesla).
Tambaya ta 2: Lissafin Ƙarfin Lorentz akan Waya a cikin Filin Magnetic na Solenoid
Tambaya:
A cikin wani solenoid wanda ke samar da filin maganadisu na \( 2,51 \sau 10^{-3} \, \text{T} \), akwai waya madaidaiciya mai tsawon mita 0,2 tana ɗauke da kwararar amperes 3 a tsaye zuwa filin maganadisu. Lissafa ƙarfin Lorentz da ke aiki akan wayar.
Tattaunawa:
Ana iya ƙididdige ƙarfin Lorentz da ke aiki akan waya a cikin filin maganadisu ta amfani da dabarar:
\[ F = I \cdot L \cdot B \]
Ina:
– \( F \) shine ƙarfin Lorentz,
– \(I \) shine wutar lantarki,
– \( L \) shine tsawon wayar,
– \( B \) shine filin maganadisu.
Muna maye gurbin ƙimar da aka bayar:
\[ F = 3 \cdot 0,2 \cdot 2,51 \sau 10^{-3} \]
\[ F = 1,506 \sau 10^{-3} \, \text{N} \]
Don haka, ƙarfin Lorentz da ke aiki akan wayar shine \( 1,506 \times 10^{-3} \, \text{N} \).
Tambaya ta 3: Makamashin Magnetic a cikin Solenoid
Tambaya:
Nawa ne makamashin maganadisu da aka adana a cikin na'urar solenoid mai tsawon mita 1 tare da radius na mita 0,05, tana da juyawa 1000, kuma tana ɗauke da wutar lantarki ta amperes 2?
Tattaunawa:
Ana iya ƙididdige makamashin maganadisu a cikin solenoid ta amfani da dabarar:
\[ U = \frac{1}{2} \cdot L \cdot I^2 \]
inda \( L \) shine inductance na solenoid. Ana iya ƙididdige inductance na solenoid (\( L \)) ta amfani da dabarar:
\[ L = \mu_0 \cdot \frac{N^2 \cdot A}{l} \]
tare da:
– \( N \) shine adadin juyawa,
– \(A \) yanki ne na giciye na solenoid,
– \( l \) shine tsawon solenoid.
Yankin giciye \( A \):
\[ A = \pi r^2 \]
\[ A = \pi (0,05)^2 = 7,85 \sau 10^{-3} \, \text{m}^2 \]
Inductance \( L \):
\[
L = (4\pi \sau 10^{-7}) \cdot \frac{1000^2 \cdot 7,85 \sau 10^{-3}}{1}
\]
\[
L \kimanin 9,87 \sau 10^{-3} \, \text{H}
\]
Makamashin maganadisu \( U \):
\[
U = \frac{1}{2} \cdot 9,87 \sau 10^{-3} \cdot (2)^2
\]
\[
U = 1,97 \sau 10^{-2} \, \text{J}
\]
Don haka, ƙarfin maganadisu da aka adana a cikin solenoid shine ( 1,97 sau 10^{-2} \, \text{J} \) ko 19,7 mJ (milliJoules).
