A rectangular coil of N turns, length a, width b is rotated at a frequency f in

Question

A rectangular coil of N turns, length a, width b is rotated at a frequency f in a uniform magnetic field, B. The ends of the coil are connected to sliding rings that keep the same end of the wire coil connected to the probes of a voltage measuring device. (a) Determine the expression for the voltage from the system as a function of time. (b) What is the magnitude of the voltage maximum? (c) If the following values are given determine the area of the coils if the maximum voltage is 60 V. N = 500, f = 60 rev/s, B = 0.200 T

Explanation / Answer

The flux through the rectangular loop is defined as the Product of magnetic field and Area

i .e phi = B.A = BA cos theta

theta is the angle made by the axis of the loop with the field direction

As the rectangular loop is rotating steadily,

the angular displacement of the loop is given by theta = Wt

where W is the angular frequency of the rotation

t is the time

so magnetic flux phi = BAcos (wt)

induced emf is defiend as the rate of change of magnetic flux

in mathematical form,

induced emf e = NAdB/dt or NABW

where W is angular velocity

where A = area

N = no. of tunrs

dB/dt = rate of change of magnetic field

If there are N loops,

emf e = -N d/dt

emf e = _ N B A W sin wt

or emf e = NB A * 2pi f * sin (2pifT)

-------------------------------------

for maximum Volatge sin Wt = sin 90 = 1

so

Emf max = N A B * 2pif
--------------------------------

emf max = 500 * A * 0.2 * 2*3.14 * 60

A = 60/(500 * 0.2* 2*3.14 * 60)

A = 1.59 e-3 m^2

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