A rectangular coil of N turns and of length a and width b is rotated at frequenc
ID: 1415093 • Letter: A
Question
A rectangular coil of N turns and of length a and width b is rotated at frequency f in a uniform magnetic field of magnitude B, as indicated in the figure. The coil is connected to co-rotating cylinders, against which metal brushes slide to make contact. The emf induced in the coil is given (as a function of time t) by = 2fNabB sin (2ft) = 0 sin (2ft). This is the principle of the commercial alternating-current generator. What value of Nab gives an emf with 0 = 182 V when the loop is rotated at 72.2 rev/s in a uniform magnetic field of 0.601 T?
Explanation / Answer
Eo = 182 Volts
B = magnetic field = 0.601 T
w = 72.2 rev/s = 72.2 x 2 x 3.14 rad/s = 453.42 rad/s
using the equation
Eo = Nab B w
182 = (Nab) (0.601) (453.42)
Nab = 0.67