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Question

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.

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Solution

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 w as shown in the figure.
Angle rotated by coil in time t is wt.
Flux passing through the coil at that instant, ϕ=NBAcoswt
Rate of change of flux dϕdt=NBAddt(coswt)
dϕdt=NBA×(wsinwt)
We get dϕdt=NBAwsinwt
Induced emf in the coil E=dϕdt
E=NBAwsinwt

657580_623204_ans_504ddfec1f784d49a6e9d99bbd2e3bd3.png

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