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A coil of 150 turns, each of area 50 cm^...

A coil of 150 turns, each of area `50 cm^(2)`, is rotating in a magnetic field of 0.15 T with a constant frequency of 20 rotations per second about an axis in the plane of the coil and normal to the field. Calculate the peak emf, rms emf and the instantaneous emf induced in the coil.

Text Solution

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Data: `N=150, A=50 cm^(2) = 50 xx 10^(-4) m^(2) = 0.005 m^(2), f=20 reps, B=0.15 T`
`omega=2pif= 2pi xx 20 = 40pi` rad/s
(i) The peak emf is
`E_(0) = omega NAB = (40 xx 3.142) (150)(0.005)(0.15)`
`=14.14`V
(ii) The rms emf is
`E_(0)/sqrt(2) = 14.14/(1.414 )= 10V`
(iii) The instantaneous value fo the induced emf is
`E=E_(0)sin omegat = 14.14 sin (40 pit)V`
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