A rectangular coil of N turns and of length a and width b is rotated at frequenc

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 epsilon = 2 Pi fNabB sin (2 Pi ft) = epsilon_0 sin (2 Pi ft). This is the principle of the commercial alternating-current generator. What value of Nab gives an emf with epsilon_0 = 105 V when the loop is rotated at 70.3 rev/s in a uniform magnetic field of 0.570 T?

Explanation / Answer

Eo = 2*pi*f*N*a*b*B

given Eo = 105 V

w = 70.3 rev/s = 70.3*2*pi rad/s

w = 2*pi*f

Eo = 2*pi*f*N*a*b*B

Eo = w*N*a*b*B

105 = 70.3*2*pi*N*a*b*0.57

N*a*b = 0.41704

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