Chapter 30, Problem 11P

A rectangular coil of N turns and of length a and width b is rotated at frequency f in a uniform magnetic field $\stackrel{\to }{B}$, as indicated in Fig. 30-40. 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

ℰ =2πf NabB sin(2πft) = ℰ₀ sin(2πft).

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

Figure 30-40 Problem 11.