The armature of a small generator consists of a flat square

The armature of a small generator consists of a flat, square coil with 130 turns and sides with a length of 2.00 cm. The coil rotates in a magnetic field of 7.70times 10^ -2 T. What is the angular speed of the coil if the maximum emf produced is 2.90times10^ -2 V ?

Solution

flux = phi = BA cos wt

A = area of crossection = 0.02*0.02 m^2

w = angular speed, t =time

instantaneous emf = e(t) = - N d(phi)/dt = - w (BA) [- sin wt]

e (max) = 2.9×102 V, when sin wt = 1 or angle wt = 90 degree

eo = BANw

w = e0/BAN = 2.9*10^-2)/(7.70*10^-2*0.02*0.02*130)

w = 7.24 rad/sec