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. 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

e = 2pfNabB sin (2pft) = e0 sin (2pft).

This is the principle of the commercial alternating-current generator. What value of Nab (in square meters) gives an emf with e0 = 189 V when the loop is rotated at 62.8 rev/s in a uniform magnetic field of 0.388 T?

Explanation / Answer

Given that induced e.m.f in the circuit is (in fuction of timt 't') = 2fNabB sin (2ft) = 0 sin (2ft).....................(1) 0=189 V angular frequency =62.8 rev/s =62.8*2 rad/s     since 1 rev =2 rad                                                  =394.58 rad/s uniform magnetic field is B =0.388T we also written as =2f ...................(2) from equation (1) and (2) NabB sin (t) = 0 sin (t) NabB =0 Nab = 0 /(B)         =189/(394.58 *0.388)         =1.234 m^2

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