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Question:

A coil of cross-sectional area A having N turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity ω, the maximum e.m.f. induced in the coil will be

12nBAω

nBAω

3nBAω

32nBAω

Solution:

Given, a coil of N turns an area A, rotated with angular speed ω in a uniform magnetic field B.
The flux linking to the coil, Φ=NBA sin(ωt)
Therefore,Induced EMF, E=d(NBA sin(ωt))/dt
E= NBAω cos(ωt)
Emax= NBAω