(a) Define self inductance. Write its S.I. units
(b) Derive and expression for self inductance of a long solenoid of length l cross-sectional area A having N number of turns.

Explanation

The self inductance of a coil is equal to the induced `emf` set up in the coil, when the current passing through it change at the unit rate
The `SI` unit of self inductance is henry.
Self inductance of a long solenoid:
Consider a long solenoid of length `l` number of turns `N` and radius.Suppose current `I` flows though it.Magnetic field set up in the coil is `B=(mu_(0)NI)/l`
Flux through each turn=`BA=(mu_(0)NI)/l`
But `phi=Li`
`phi=(Nxxmu_(0)NI)/l =(mu_(0)N^(2)IA)/l`
`therefore` Self inductance `L=phi/I=(mu_(0)N^(2)A)/l`