 Solution

Let $\theta =\omega t+{\theta }_0$ be the angle between the coil's area normal and the uniform magnetic flux density. The linked magnetic flux is ${\Phi }_N=NBA\cos \theta$. Faraday's law givesThe sign uses the winding direction associated with the chosen normal; reversing the terminal convention changes it. The magnitude is largest when $\cos \theta =0$: the coil's normal is perpendicular to the magnetic field, so the plane of the coil is parallel to it. At that orientation the instantaneous magnetic flux is zero but its rate of change has maximum magnitude.