Faraday's law allows us to find the magnetic field that produces the emf in the rotating system is:
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The magnetic field is: B = 0.424 T
Faraday's law of induction states that when the magnetic flux changes in time, an induced electromotive force is produced.
fem = [tex]- \frac{d \Phi_B }{dt}[/tex]
where fem is the induced electromotive force and Ф the flux,
The magnetic flux is the scalar product of the field and the area.
[tex]\Phi_B = B . A = B A \ cos \theta[/tex]
In this case we have several turns, so the expression remains.
fem = [tex]- N B A \ \frac{d cos \theta}{dt}[/tex]
Indicate that the turns rotate at a constant frequency, therefore we can use the uniform rotational motion ratio.
θ = w t
We substitute
[tex]fem = - N B A \ \frac{d \ cos \ wt}{dt}\\fem = N B A w sin \ wt[/tex]
the maximum induced electromotive force occurs when the sine function is ±1
fem = N B A w
They indicate that the fem = 24 V, the number of the turn is N = 20, the area is A = 75 cm² = 75 10⁻⁴ m² and the frequency f = 60 Hz
Frequency and angular velocity are related.
w = 2π f
We substitute.
fem = N B A 2π f
[tex]B = \frac{fem }{2 \pi \ NA \ f}[/tex]
Let's calculate.
[tex]B= \frac{24 }{2\pi \ 20 \ 75 \ 10^{-4} 60}[/tex]B = 24 / 2pi 20 75 10-4 60
B = 0.424 T
In conclusion, using Faraday's law we can find the magnetic field that produces the emf in the rotating system is:
-
The magnetic field is; B = 0.424 T
Learn more about Faraday's law here: brainly.com/question/24617581
