EMF from rotating coil
One way to generate an EMF is to rotate a coil through a magnetic field. The B-field is constant and the area of the loop is constant, but the angle between the field and the loop is changing. The flux is:
If the angle is changing as , the flux and therefore the voltage changes as(after a little calculus):
Thus the voltage oscillates as the flux goes from positive to negative, with the peak voltage being 2pfNAB. The magnitude of the voltage increases with higher rotation frequency since it leads to a higher rate-change in the flux. Bigger loops, more loops and a stronger magnetic field all increase the voltage one achieves.
Electric generators work through one of two ways. They either rotate a loop in a magnetic field or the rotate a magnet inside a fixed loop.