Question

(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.

Answer 1

(a) Self Inductance (or co-efficient of self induction) : Self inductance of a coil is numerically equal to the amount of magnetic flux linked with the coil when unit current flows through the coil.
Its S.I. units is Henry (H)
(b) Self Inductance of a Long solenoid. Consider a long solenoid of length l, number of turns N and radius r. Suppose current I flows through it. Magnetic field set up in the coil is
`B = (mu_(0)NI)/(l)`
Flux through each turn `= BA = (mu_(0)NIA)/(l)`
Total flux through N turns,
`phi = N xx (mu_(0)NIA)/(l) = (mu_(0)N^(2)IA)/(l) " But " phi = LI`
`:.` Self inductance, `L = (phi)/(I) = (mu_(0)N^(2)A)/(l)`