Respuesta :
Answer:
The solenoid has 237 turns.
Explanation:
Given that, the current in a solenoid is changing at a rate [tex]\frac{di}{dt}=0.0290 \ A/s[/tex]
The magnitude of induced emf is [tex]\varepsilon[/tex] = 12.3 mV=[tex]12.3 \times 10^{-3}[/tex] v when the current flows i=1.40 A.
[tex]\phi_B[/tex]= 0.00251 is the magnitude of magnetic flux through each turns.
We need to find out the number of turns (N).
The induced emf of a solenoid is
[tex]\varepsilon =L|\frac{di}{dt}|[/tex]
[tex]\Rightarrow L=\frac{\varepsilon}{\frac{di}{dt}}[/tex] ....(1)
The self inductance of solenoid is
[tex]L=\frac{N\phi_B}{i}[/tex] ......(2)
From (1) and (2) we get
[tex]\frac{N\phi_B}{i}=\frac{\varepsilon}{\frac{di}{dt}}[/tex]
[tex]\Rightarrow \frac{N\times 0.00251}{1.40}=\frac{12.3\times 10^{-3}}{0.0290}[/tex]
[tex]\Rightarrow N=\frac{12.3\times 10^{-3}\times 1.40}{0.0290\times 0.00251}[/tex]
[tex]\Rightarrow N\approx 237[/tex]
The solenoid has 237 turns.
