A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B . When it is rotated…

Magnetic flux through a coil of area $A$ of $n$ turns at an angle $\theta$ to the magnetic field of magnitude $B$ is, $\phi =nBA cos\theta =nBAcos\omega t$. The induced emf,

$\epsilon =\left|\frac{d\varphi }{dt}\right|=nBA\omega \sin \omega t$. Since, the maximum value of the sine function is $1$,

${\epsilon }_{max}=nBA\omega$