Self-inductance of a solenoid 

Self-inductance is a process of induction of emf or voltage in a winding. A coil induces emf when the magnetic flux of the coil or current in the coil changes. When the currents start to flow in the coil at any instant, magnetic flux is directly proportional to the current passing through the coil. A magnetic field is created by changing the current in the winding and this winding itself induces a voltage. the solenoid is a long coil of metallic wire. It is an electromagnet  When an electric current is passed through the solenoid, a magnetic field is produced around the turns of the coil. 

The self-inductance of a solenoid depends upon the number of turns per unit length of the solenoid, the permeability of the material, and the cross-sectional area of turns. 

 Self-inductance formula, 

            L=N flux/current.   L is the self-inductance, N is the number of turns.

Self-inductance of the solenoid can be defined as that magnetic flux linked to the solenoid when current is passed so, the amount of current is the same in each turn or loop.  Emf in the coil as, e = -LdI/dt 

The direction of induced emf is such that it opposes the cause by which it is produced, that is to oppose the change in the current. 

As the inductance of the solenoid depends upon the number of turns and cross-sectional area of the solenoid. For increasing the self-inductance of the solenoid, we can either increase the number of turns or by increasing the diameter of the turns of the solenoid. 

Self induction in a solenoid