Question

The armature of an ac generator is a rectangular coil 2.00 cm by 6.00 cm with 80 turns. It is immersed in a uniform magnetic field of magnitude 0.250 T. If the amplitude of the emf in the coil is 22.0 V, at what angular speed is the armature rotating?

Answer 1

flux through the coil is given by

$\phi = NBA cos(\theta)$

induced emf can be calculated as

$\epsilon =- \frac{d\phi}{dt}$

de € = N B Asin(0) dt

since $\frac{d\theta}{dt} =\omega$

So,

N B Awsin(@

maximum emf when $\theta = 90$

$\epsilon =NBA \omega$

$22 =(80)(0.25)(0.02\times 0.06) \omega$

$\omega = 1833.33 rad/s$