draw a labelled diagram of ac generator
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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, ϕ
max
=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
dt
dϕ
=NBA
dt
d
(coswt)
∴
dt
dϕ
=NBA×(−wsinwt)
We get
dt
dϕ
=−NBAwsinwt
Induced emf in the coil E=−
dt
dϕ
⟹ E=NBAwsinwt
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