Self inductance:

When current through a coil changes, the changing flux induces an emf that opposes the current flow.  This emf is the result of self inductance and is called 'back emf'.  The term 'self inductance' is often replaced merely by inductance.  The value of back emf is given by:

          E  =  -L x dl/dt  

Where L is the inductance in henries, and dl/dt the rate of change of current.

The minus indicates back emf.

The unit of inductance is the henry and is based on the equation.  If current changing at a rate of 1 amp a second induces an emf of 1 volt then the inductance is 1 henry. 

All circuits have inductance even a straight conductor, but if a straight piece of wire is formed into a coil the number of flux linkages increases and so does the inductance.

A further increase in inductance is achieved by increasing the flux density.  This depends on the area, the length of the coil and the permeability of material in which flux is established,

Thus,                  L    =   Henries

                   N      =  Number of Turns

                   μ_o μ_r          =  Absolute Permeability

                   A       =  Area in square metres

                   I        =  Length of coil in metres (not wire)

As  reluctance (S) =          μ_o μ_r A  =1/S       and     L  = N²/S

Also by transposition of E  =  -L  ×  dl/dt

          L  =  -E  ×  dl/dt