Define mutual inductance. Write its SI unit. Give two factors on which the coefficient of mutual inductance between a pair of coils depends.

Define self-inductance and give its SI unit. Derive an expression for self-inductance of a long, air-cored solenoid of length $l$, radius $r$ and having $N$ number of turns.

Or

Deduce an expression for the self-inductance of a long solenoid of $N$ turns, having a core of relative permeability ${\mu }_r$.

Deduce an expression for the self-inductance of a long solenoid of $N$ turns, having a core of relative permeability ${\mu }_r$.