The phase difference between induced emf and magnetic flux linked with a coil rotating in a uniform magnetic field is:

A rectangular coil of N turns and of length a and width b is rotated at frequency $f$ in a uniform magnetic field $\overrightarrow{B}$, as indicated in Figure . The coil is connected to co-rotating cylinders, against which metal brushes slide to make contact. (a) Show that the
emf induced in the coil is given (as a function of time t) by

$\mathcal{E}=2\pi fNab\sin 2\pi ft={\mathcal{E}}_0\sin 2\pi ft.$
This is the principle of the commercial alternating-current generator. (b) What value of Nab gives an emf with ${\mathcal{E}}_0=150V$ when the loop is rotated at 60.0 rev/s in a uniform magnetic field of 0.500 T?