Tauira o ngā Pātai Kōrero mō te Solenoid
He mea nui ngā solenoid i roto i ngā mahi hiko me te hikohiko maha, mai i ngā taputapu hauora ki ngā mīhini ahumahi. I mua i te peke atu ki ngā pātai me ngā kōrero, me mārama tuatahi tātou he aha te solenoid me pēhea tana mahi.
Te Mārama ki ngā Solenoids
He koiri waea te solenoid, he rite te āhua ki te rango roa. Ina rere te iahiko hiko mā roto i te solenoid, ka hangaia he papa aukume i roto. Ka taea te whakamahi i tēnei papa aukume mō ngā kaupapa maha, pērā i te neke i te piston i roto i te solenoid hiko-ā-ringa, te whakaputa rānei i tētahi papa aukume ōrite i roto i ētahi tono rangahau me te hangarau.
Ko tētahi āhuatanga nui o te solenoid ko te papa aukume e whakaputaina ana e ia. He tata rite te papa aukume i roto i te solenoid roa, piri tonu. Ko te whārite e whakaahua ana i te papa aukume B i roto i te solenoid pai ko:
\[ B = \mu_0 \cdot n \cdot I \]
kāore i te mana:
– Ko te papa aukume te \( B \),
– Ko te uruhanga korehau \( \mu_0 \) (\( 4\pi \times 10^{-7} \) T m/A),
– Ko te \( n \) te maha o ngā takahuri mō ia roa (takahuri/m),
– Ko te iahiko e rere ana i roto i te solenoid ko \( I \).
He rite tonu te auau o tēnei papa aukume ki te ia e rere ana me te maha o ngā takahuri mō ia roa, ā, e pāngia ana e ngā āhuatanga o te reo kei reira te solenoid, arā, te hau, te korehau rānei.
Pātai 1: Te Tatau i te Papa Aukume i Roto i te Solenoid
Pātai:
E 1000 ngā hurihanga o te hiko solenoid, ā, e 0,5 mita te roa. Mēnā he 2 āpere te iahiko e rere ana i roto i te hiko solenoid, tatauhia te papa aukume i roto i te hiko solenoid.
Kōrero:
Tuatahi, me tatau tātou i te maha o ngā takahuri mō ia roa (n):
\[ n = \frac{N}{L} = \frac{1000}{0,5} = 2000 \, \text{huringa/m} \]
Kātahi, whakamahia te tātai o te papa aukume solenoid:
\[ B = \mu_0 \cdot n \cdot I \]
\[
B = (4\pi \times 10^{-7}) \cdot 2000 \cdot 2
= 8\pi \times 10^{-4} \, \text{T}
\]
\[
B \tata ki te 2,51 \times 10^{-3} \, \text{T}
\]
Nō reira, ko te papa aukume i roto i te solenoid he tata ki te \( 2,51 \times 10^{-3} \, \text{T} \) 2,51 mT rānei (milliTesla).
Pātai 2: Te Tātai i te Kaha Lorentz i runga i te Waea i roto i te Papa Aukume o te Solenoid
Pātai:
I roto i tētahi solenoid e whakaputa ana i tētahi papa aukume o \( 2,51 \times 10^{-3} \, \text{T} \), kei reira tētahi waea tika, 0,2 mita te roa, e kawe ana i te ia o te 3 ampere e poutū ana ki te papa aukume. Tātaihia te kaha Lorentz e pā ana ki te waea.
Kōrero:
Ka taea te tatau i te kaha Lorentz e pā ana ki tētahi waea i roto i tētahi papa aukume mā te whakamahi i te tātai:
\[ F = I \cdot L \cdot B \]
kāore i te mana:
– Ko te kaha Lorentz te \( F \),
– Ko te iahiko hiko te \( I \),
– Ko te roa o te waea ko \( L \),
– Ko te papa aukume ko \( B \).
Ka whakakapia e mātou ngā uara kua hoatu:
\[ F = 3 \cdot 0,2 \cdot 2,51 \times 10^{-3} \]
\[ F = 1,506 \times 10^{-3} \, \text{N} \]
Nō reira, ko te kaha Lorentz e pā ana ki te waea ko \( 1,506 \times 10^{-3} \, \text{N} \).
Pātai 3: Pūngao Aukume i roto i te Solenoid
Pātai:
E hia te kaha aukume e rongoa ana i roto i tētahi solenoid he 1 mita te roa, he 0,05 mita te whānui, he 1000 ngā hurihanga, ā, he 2 ampere te iahiko e mau ana?
Kōrero:
Ka taea te tatau i te kaha aukume i roto i te solenoid mā te whakamahi i te tātai:
\[ U = \frac{1}{2} \cdot L \cdot I^2 \]
ko \( L \) te inductance o te solenoid. Ka taea te tatau i te inductance o te solenoid (\( L \)) mā te whakamahi i te tātai:
\[ L = \mu_0 \cdot \frac{N^2 \cdot A}{l} \]
me:
– Ko te maha o ngā takahuri ko \( N \),
– Ko te horahanga whakawhiti-wāhanga o te solenoid te \( A \),
– Ko te \( l \) te roa o te solenoid.
Te horahanga whakawhiti-wāhanga \( A \):
\[ A = \pi r^2 \]
\[ A = \pi (0,05)^2 = 7,85 \times 10^{-3} \, \text{m}^2 \]
Te Āheinga \( L \):
\[
L = (4\pi \times 10^{-7}) \cdot \frac{1000^2 \cdot 7,85 \times 10^{-3}}{1}
\]
\[
L \tata ki te 9,87 \times 10^{-3} \, \text{H}
\]
Pūngao aukume \( U \):
\[
U = \frac{1}{2} \cdot 9,87 \times 10^{-3} \cdot (2)^2
\]
\[
U = 1,97 \times 10^{-2} \, \text{J}
\]
Nō reira, ko te pūngao aukume e rongoatia ana i roto i te solenoid ko \( 1,97 \times 10^{-2} \, \text{J} \) ko 19,7 mJ (milliJoules rānei).
