Suppose that you are assigned the project of designing a generator of sinusoidal

Question

Suppose that you are assigned the project of designing a generator of sinusoidal AC voltage with a maximum voltage of 120 V. You are given a wire, two strong magnets that can produce a uniform magnetic field of 1.5 T over a square area of 10.0 cm on a side when the magnets are 12.0 cm apart. The basic design should consist of a square coil turning, in a uniform magnetic field. To have an acceptable coil resistance, the coil can have at most 400 loops. What is the minimum rotation rate (in rpm) of the coil so it will produced the required voltage?

Explanation / Answer

E(t) = BANw sin(wt)

Epeak = BANw

B = field strength
A = coil area
N = No.of turns on coil
w = angular speed, rad/s .. (w = 2*pi*f)
t = time, s .. (measured from a time when the plane of the coil is perp. to field - for a linear field)

now given ,Epeak = 120 V , B = 1.5 T , A = 0.10*0.12 = 0.012 m^2 , N = 400 , w = ?

so 120 = (1.5)(0.012)(400)w

w = 16.67 rad/s = (16.67*60)/(2pi) ppm

w = 159.155 ppm

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