Electromagnetic Induction - Self Inductance of long Solenoid

As shown in figure we have a long solenoid of length l and current i .Magnetic field for long solenoid is given below.
where n is number of turns per unit length and N is total number of turns.



As we know that magnetic flux linked with the coil is proportional to the current in coil. 


 


Hence Self inductance of long solenoid is given below




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