What is the maximum Emf induced in a 647 turn coil square co

What is the maximum Emf induced in a 647 turn coil square coil with sides of length 0.33 meters rotating at 466 rpm in a magnetic field of 0.267 Tesla?

Solution

a) emf = N B A w sin(wt)

w = 466 r p m = 466 x 2pi rad / 60 sec = 48.8 rad/s

Maximum emf = N B A w

    = (647) ( 0.267) (0.33^2) ( 48.8)

= 918.03 volt

b) Id = e0 d(flux)/dt

0.0023 = (8.854 x 10^-12) d(EA)/dt

A dE/dt = 2.60 x 10^8

(pi 0.071^2) dE/dt = 2.60 x 10^8

dE/dt = 1.64 x 10^10 V/m-s