When a rectangular coil is rotated in a uniform magnetic field about an axis passing through its centre and perpendicular to the field, the emf induced in the coil varies

When a rectangular coil is rotated in a uniform magnetic field about an axis passing through its centre and perpendicular to field, then magnetic flux associated with coil is given as \(\phi=B A \cos \theta=B A \cos \omega t\) ...(i) \(\therefore\) Induced emf, \(e=-\frac{d \phi}{d t}=-\frac{d}{d t} B A \cos \omega t\) [From Eq. (i)] \(=+B A \omega \sin \omega t\) \(\Rightarrow \quad e=e_0 \sin \omega t\) ...(ii) where, \(e_0\) is the peak value of induced emf. i.e. \(e_0=B A \omega\) From Eq. (ii) it is clear that, induced emf varies sinusoidally.