Question

An AC generator consists of 20 circular loops of wire with an area of 75 cm2. It has a maximum induced voltage of 24 V. If its armature rotates at a frequency of 60 Hz, what is the magnitude of the magnetic field, assuming it is uniform?
Pls help

Answer 1

Faraday's law allows us to find the magnetic field that produces the emf in the rotating system is:

• 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 = $- \frac{d \Phi_B }{dt}$  

where fem is the induced electromotive force and Ф the flux,

The magnetic flux is the scalar product of the field and the area.

           $\Phi_B = B . A = B A \ cos \theta$  

In this case we have several turns, so the expression remains.

           fem = $- N B A \ \frac{d cos \theta}{dt}$  

Indicate that the turns rotate at a constant frequency, therefore we can use the uniform rotational motion ratio.

           

           θ = w t

We substitute

 

         $fem = - N B A \ \frac{d \ cos \ wt}{dt}\\fem = N B A w sin \ wt$

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

           $B = \frac{fem }{2 \pi \ NA \ f}$  

Let's calculate.

         $B= \frac{24 }{2\pi \ 20 \ 75 \ 10^{-4} 60}$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