A coil with N turns and fixed area A is rotated with a constant angular speed ω about an axis perpendicular to a uniform magnetic field of magnitude B. At t=0 the normal to the coil makes an angle 0 with the field.
(i) Derive an expression for the instantaneous emf induced in the coil as a function of time.
(ii) Show that the root-mean-square (r.m.s.) value of the emf over one complete revolution is εrms=2NBAω.
(iii) The coil described above has N=500 turns and A=4.0×10−3m2. It is connected to a 20Ω resistor and rotates in a magnetic field of 0.20T at ω=120rads−1. Calculate the average electrical power dissipated in the resistor.