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As a new electrical engineer for the local power company, you are assigned the project of designing a generator of sinusoidal ac voltage with a maximum voltage of 120 {\rm V}. Besides plenty of wire, you have two strong magnets that can produce a constant uniform magnetic field of 1.1{\rm T} over a square area with a length of 10.4{\rm cm} on a side when the magnets are separated by a distance of 11.6{\rm cm} . The basic design should consist of a square coil turning in the uniform magnetic field. To have an acceptable coil resistance, the coil can have at most 350 loops.What is the minimum rotation rate of the coil so it will produce the required voltage?Express your answer using two significant figures.

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Answer:

[tex]2.8\times 10^2\ rpm[/tex]

Explanation:

B = Magnetic field = 1.1 T

L = Length of square = 10.4 cm

A = Area of square = [tex]L^2[/tex]

t = Time taken

V = Voltage = 120 V

N = Number of turns = 350

[tex]\omega[/tex] = Angular frequency

Voltage in the generator is given by

[tex]V=NAB\omega sin\omega t[/tex]

Voltage is maximum when [tex]sin\omega t=1[/tex]

[tex]V=NAB\omega\\\Rightarrow \omega=\frac{V}{NAB}\\\Rightarrow \omega=\frac{120}{350\times 0.104^2\times 1.1}\\\Rightarrow \omega=28.81733\ rad/s=\frac{28.81733}{2\pi}\times 60=275.18\ rpm[/tex]

The minimum rotation rate of the coil so it will produce the required voltage is [tex]2.8\times 10^2\ rpm[/tex]