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 E = 2 pi f Nab Bs in (2 pi ft) = e_0 sin (2 pi ft) This is the principle of the commercial alternating-current generator. What value of Nab gives an emf with E_0 = 102 V when the loop is rotated at 55.8 rev/s in a uniform magnetic field of 0.434 T?

Answer 1

Here

ε0=102V

angular frequency ω =55.8rev/s

=55.8*2π rad/s

=350.6 rad/s

Uniform magnetic field is B =0.434T

we also written as ω =2πf ...................(2)

from equation (1) and (2)

ωNabB sin (ωt) = ε0 sin (ωt)

ωNabB =ε0

Nab = ε0 /(ωB)

        =102/(350.6*0.434)

        =0.67034 m^2