# a rectangular coil of n turns area a is held in a uniform magnetic field b.if the coil is rotated with steady angular speed w,duduce an expression for induced emf in the coil at any instant of time.

Here in this case the rectangular coil of n turns , area 'a' is held in an uniform magnetic field b .

Now the coil is rotated with angular speed $\omega $ .

Now , we know that , electric flux , $\varphi =nba\mathrm{cos}\theta =nba\mathrm{cos}\omega t\left[\because \theta =\omega t\right]$

Now the induced emf at time instant 't' = $E=-\frac{d\varphi}{dt}=\frac{d\left(nba\mathrm{cos}\omega t\right)}{dt}=nab\omega \mathrm{sin}\omega t\phantom{\rule{0ex}{0ex}}\Rightarrow E={E}_{0}\mathrm{sin}\omega t\phantom{\rule{0ex}{0ex}}Where,{E}_{0}=nab\omega $

Regards

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