Draw a labelled diagram of an ac generator. Obtain the expression for the emf induced in the rotating coil of N turns each of cross-sectional area A, in the presence of a magnetic field B.

Let say at the instant t=0, the plane of the coil is perpendicular to the direction of magnetic field i.e. area vector of coil points in same direction as that of magnetic field. So maximum flux passes through the coil. Flux passing through the coil at t=0, Φmax=NBA The coil rotates about an axis with constant angular velocity ω as shown in the figure. Angle rotated by coil in time t is ωt. Flux passing through the coil at that instant, Φ=NBAcosωt Rate of change of flux dΦ/dt=NBA d/dt(cosωt) ∴dΦ/dt=NBA × (−ωsinωt) We get dΦ/dt=−NBAωsinωt Induced emf in the coil E=−dΦ/dt ⇒E=NBAωsinωt