A rectangular coil of N turns and of length a and width b is rotated at frequency f in a uniform magnetic field 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
This is the principle of the commercial alternating-current generator. (b) What value of Nab gives an emf with E0=150V when the loop is rotated at 60.0 rev/s in a uniform magnetic field of 0.500 T?