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.

Dear Student ,
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 , $\varphi =nba\cos \theta =nba \cos \omega t \left[\because \theta =\omega t\right]$
Now the induced emf  at time instant 't' =  $$\begin{gathered} E=-\frac{d\varphi }{dt}=\frac{d\left(nba \cos \omega t\right)}{dt}=nab\omega \sin \omega t \\ \Rightarrow E =E_0 \sin \omega t \\ Where , E_0=nab\omega \end{gathered}$$
Regards