Explain the rate of change of magnetic flux due to change in the orientation of the loop

A loop having area ‘A’ is rotating about an axis with a constant angular velocity ‘ω’ as shown in the figure. Due to this rotation, the orientation of the loop is changing w.r.t. the field direction. As a result there is a rate of change of magnetic flux passing through the loop. This is inducing an alternating EMF. This is nothing but a prototype of A.C. generator (or) Alternator.

\(phi =overrightarrow{B},.,overrightarrow{A}\) \(=BAcos theta =BAcos omega t\) \(frac{dphi }{dt}=-BAomega sin omega t\) \(varepsilon =frac{-dphi }{dt}=BAomega sin omega t={{varepsilon }_{0}}sin omega t\)

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