Self inductance is defined as the induction of a voltage in a current-carrying wire when the current in the wire itself is changing. In the case of self - inductance , the magnetic field created by a changing current in the circuit itself induces a voltage in the same circuit. Therefore, the voltage is self - induced .
If you are student in college , follow the griffith's electrodynamics book for the proof of long solenoid and if not then search HCV , you will surely get a guidance.
We have no scope to derive this here.
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