A coil of cross-sectional area A having n turns is placed in a...

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

$ε = \left|\dfrac{dϕ}{dt}\right| = nBA\omega sin \omegat$. Since, the maximum value of the sine function is $1$,

{ε}_\max = nBA\omega