Inductance of a solenoid
Now we will prove “Inductance of a solenoid derivation”.
Consider a solenoid having n turns per unit length. When current passes through the solenoid, the magnetic field is produced inside the solenoid which is directed along the axis of the solenoid. The magnetic field in space outside the solenoid is so weak that it is considered zero. The inductance of solenoid: A tightly wound cylindrical coil of wire is called a solenoid.
The relation for the inductance of solenoid: Consider a solenoid of length l, area of cross-section A having number of turns N .The magnetic field B inside a solenoid carrying a current i is given as:
B=μi ni —————(1)
Where n is the number of turns per unit length. 
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