Chitsanzo cha Mafunso Okambirana a Solenoid
Ma Solenoid ndi zinthu zofunika kwambiri pa ntchito zambiri zamagetsi ndi zamagetsi, kuyambira pazida zamankhwala mpaka makina amafakitale. Tisanayambe kukambirana mafunso ndi zokambirana, choyamba tiyeni timvetse tanthauzo la solenoid ndi momwe imagwirira ntchito.
Kumvetsetsa Solenoids
Solenoid ndi waya wozungulira, womwe nthawi zambiri umaoneka ngati silinda yayitali. Mphamvu yamagetsi ikadutsa mu solenoid, imapanga mphamvu ya maginito mkati mwake. Mphamvu ya maginito iyi ingagwiritsidwe ntchito pazinthu zosiyanasiyana, monga kusuntha pisitoni mu solenoid yamagetsi, kapena kupanga mphamvu ya maginito yofanana mu kafukufuku wina ndi ntchito zaukadaulo.
Chinthu chimodzi chofunikira cha solenoid ndi mphamvu ya maginito yomwe imapanga. Mphamvu ya maginito mkati mwa solenoid yayitali, yolumikizidwa bwino imakhala yofanana. Equation yofotokoza mphamvu ya maginito B mkati mwa solenoid yoyenera ndi iyi:
\[ B = \mu_0 \cdot n \cdot I \]
Kumene:
– \( B \) ndi mphamvu ya maginito,
– \( \mu_0 \) ndi kulola kwa vacuum (\( 4\pi \times 10^{-7} \) T m/A),
– \( n \) ndi chiwerengero cha ma turns pa unit length (turns/m),
– \( I \) ndi mphamvu yamagetsi yomwe imayenda kudzera mu solenoid.
Mphamvu yamaginito iyi imagwirizana mwachindunji ndi kayendedwe ka mphamvu yamagetsi ndi kuchuluka kwa ma turns pa unit unit, ndipo imakhudzidwa ndi makhalidwe a medium yomwe solenoid ili, pamenepa mpweya kapena vacuum.
Funso 1: Kuwerengera Magnetic Field mkati mwa Solenoid
Funso:
Solenoid ili ndi ma turn 1000 ndipo ndi yayitali mamita 0,5. Ngati mphamvu yamagetsi yomwe ikuyenda mu solenoid ndi 2 amperes, werengani mphamvu ya maginito yomwe ili mkati mwa solenoid.
Kukambirana:
Choyamba, tifunika kuwerengera chiwerengero cha ma turns pa unit length (n):
\[ n = \frac{N}{L} = \frac{1000}{0,5} = 2000 \, \text{turns/m} \]
Kenako, gwiritsani ntchito njira ya solenoid magnetic field:
\[ B = \mu_0 \cdot n \cdot I \]
\[
B = (4\pi \nthawi 10^{-7}) \cdot 2000 \cdot 2
= 8\pi \nthawi 10^{-4} \, \malemba{T}
\]
\[
B \pafupifupi 2,51 \nthawi 10^{-3} \, \malemba{T}
\]
Kotero, mphamvu ya maginito mkati mwa solenoid ndi pafupifupi \( 2,51 \times 10^{-3} \, \text{T} \) kapena 2,51 mT (milliTesla).
Funso 2: Kuwerengera Mphamvu ya Lorentz pa Waya mu Magnetic Field ya Solenoid
Funso:
Mkati mwa solenoid yomwe imapanga mphamvu ya maginito ya \( 2,51 \times 10^{-3} \, \text{T} \), pali waya wowongoka wa mamita 0,2 kutalika kwake womwe umanyamula mphamvu ya ma ampere atatu yolunjika ku mphamvu ya maginito. Werengani mphamvu ya Lorentz yomwe imagwira ntchito pa waya.
Kukambirana:
Mphamvu ya Lorentz yomwe imagwira ntchito pa waya mu magnetic field ikhoza kuwerengedwa pogwiritsa ntchito njira iyi:
\[ F = I \cdot L \cdot B \]
Kumene:
– \( F \) ndi mphamvu ya Lorentz,
– \( I \) ndi mphamvu yamagetsi,
– \( L \) ndi kutalika kwa waya,
– \( B \) ndi mphamvu ya maginito.
Timalowetsa mfundo zomwe zaperekedwa:
\[ F = 3 \cdot 0,2 \cdot 2,51 \times 10^{-3} \]
\[ F = 1,506 \nthawi 10^{-3} \, \malemba{N} \]
Kotero, mphamvu ya Lorentz yomwe imagwira ntchito pa waya ndi \( 1,506 \times 10^{-3} \, \text{N} \).
Funso 3: Mphamvu ya Maginito mu Solenoid
Funso:
Kodi mphamvu ya maginito yochuluka bwanji imasungidwa mu solenoid ya mita imodzi kutalika ndi utali wa mamita 0,05, yokhala ndi ma turn 1000, komanso kunyamula ma current a 2 amperes?
Kukambirana:
Mphamvu ya maginito mu solenoid ikhoza kuwerengedwa pogwiritsa ntchito fomula iyi:
\[ U = \frac{1}{2} \cdot L \cdot I^2 \]
kumene \( L \) ndi inductance ya solenoid. Inductance ya solenoid (\( L \)) ikhoza kuwerengedwa pogwiritsa ntchito fomula iyi:
\[ L = \mu_0 \cdot \frac{N^2 \cdot A}{l} \]
ndi:
– \( N \) ndi chiwerengero cha ma turn,
– \( A \) ndi gawo lozungulira la solenoid,
– \( l \) ndi kutalika kwa solenoid.
Malo ozungulira \( A \):
\[ A = \pi r^2 \]
\[ A = \pi (0,05)^2 = 7,85 \nthawi 10^{-3} \, \malemba{m}^2 \]
Kutulutsa \( L \):
\[
L = (4\pi \nthawi 10^{-7}) \cdot \frac{1000^2 \cdot 7,85 \nthawi 10^{-3}}{1}
\]
\[
L \pafupifupi 9,87 \nthawi 10^{-3} \, \malemba{H}
\]
Mphamvu ya maginito \( U \):
\[
U = \frac{1}{2} \cdot 9,87 \times 10^{-3} \cdot (2)^2
\]
\[
U = 1,97 \nthawi 10^{-2} \, \malemba{J}
\]
Kotero, mphamvu ya maginito yosungidwa mu solenoid ndi \( 1,97 \times 10^{-2} \, \text{J} \) kapena 19,7 mJ (milliJoules).
