Distinguish between self-induction and mutual induction. Calculate self-inductance of a long solenoid of length $l$, number of turns $N$ and radius $r$.

A coil is mechanically rotated with angular speed $\omega$ in a uniform magnetic field which is perpendicular to the axis of rotation of the coil. The plane of the coil is initially perpendicular to the field. Plot a graph showing variation of

(i) magnetic flux $\varphi$ and (ii) the induced emf in the coil as a function of $\omega t$.

Sketch the change in flux, emf and force when a conducting rod $PQ$ of resistance $R$ and length $l$ moves freely to and fro between $A$ and $C$ with speed $v$ on a rectangular conductor placed in uniform magnetic field as shown in the figure.