The coefficient of self induction (L) can be determined from any one of the following three relations.

Fist Method: In case the dimensions of the solenoid are given , the coefficient of self induction may be determined from the relation

 L= N²aμ_rμ_o  henrys
          l

Second Method: In case the magnitude of induced e.m.f. in a coil for a given rate of change of current in the coil is known, self inductance of the coil may be determined from the following relation

e = L  di
         dt

L =  e  
     di/dt

Third Method: In case the number of turns of the coil and flux produced per ampere of current in the coil is known, the self inductance of the coil may be determined from the following relation

 L = N∅
        i

The above relation can be derived as follows
Magnetic flux produced in a coil of N turns length l metres, area of x-section a metres2 and relative permeability μ_r when carrying a current of amperes is given by

∅ = Ni  =   Naμ_rμ_o  i
     l μ_rμ_oa     l

and self inductance of the coil L = N²aμ_rμ_o = N X Naμ_rμ_o i = N∅
                                                     l           i       l               i

From the above relation it is obvious that the self inductance of a coil or circuit is equal to weber-turns per ampere in the coil or circuit.

In the above relation if N∅ = 1 Wb-turn and  i = 1A then  L = 1H

Hence, a coil is said to have a self inductance of one henry if a current of 1 A when flowing through it produces flux linkages of 1 wb-turn in it.

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