Question

(a) Define self inductance. Write its S.I. units. 

(b) Derive an expression for self inductance of a long solenoid of length l, cross-sectional area A having N number of turns.

Answer 1

(a) The self inductance is defined on the magnetic flux linked with the coil when unit current flows through it.

The self inductance is defined as the emf induced in the coil, when the rate of change of current in the coil is 1 ampere/second. The SI unit of self inductance is henry (H).

(b) Self Inductance of a long air-cored solenoid: Consider a long air solenoid having `n' number of turns per unit length. If current in solenoid is I , then magnetic field within the solenoid, B = μ₀nI  ...(1) 

where μ₀ = 4π x 10^-7 henry/metre is the permeability of free space. 

If A is cross-sectional area of solenoid, then effective flux linked with solenoid of length `l'; ϕ  = NBA where N =nl is the number of turns in length 'l' of solenoid.