physics question (slightly difficult)?

Question

The armature of a simple AC generator has 20 circular loops of wire with a radius of 10cm. It is rotated with a frequency of 60Hz in a uniform magnetic field of 800mT. What is the max value of the emf induced in the loops, and how often is this value attained?

Answer 1

I have an idea :

You know by the Faraday's law that :

E = -dp / dt

p = (magnetic field)*(area)

E = emf induced

But, lineal velocity = w*r

now : dE = Nd(B*v)

now E = integrate( N*B*w*R)

R = (10/100)

B = 800*10^-3

N = 20

w = 120*pi

20*integrate(800*10^-3*120pi*rdr)

20*800*10^-3*120pi*r^2 / 2

E = 20*800*10^-3*120pi*(10/100)^3 / 3

E = 2.01 (Volts)

E = emf induced.