Self-Induction
The phenomenon in which a changing current in a coil induces an emf in itself is called self-induction.
The electromagnetic field can be envisaged as concentric loops of magnetic flux that border the wire, as well as larger ones that join up with others from other loops of the coil allowing self-coupling within the coil.
When current passes along a wire, and especially when it passes through a coil or inductor, a magnetic field is generated. This prolongs in an outward direction from the wire or inductor and can combine with various other circuits. Nonetheless, it additionally pairs with the circuit where it is set up.
Self-Inductance:
Self-inductance is the ratio of induced electromotive force (EMF) across a coil to the rate of change of current in the same coil.
When the current in the coil changes, this triggers a voltage to be induced in the different loops of the coil – the result of self-inductance.
Derivation of Self-Inductance
Let 
be the flux passing through one loop of the coil then the total flux for N number of turns will be N . Since the flux ( = B.A) is proportional to the magnetic field which is B = µᵒ n I and the magnetic field is proportional to current
So,
Where L is the constant of proportionality known as self-inductance.
According to Faraday’s law, emf can be expressed as
If the current in the coil is increasing, the self-induced emf produced in the coil will certainly oppose the cause of the current, which means the direction of the generated emf is contrary to the applied voltage.
If the current in the coil is decreasing, the emf generated in the coil remains in such a direction as to oppose the cause of the current; this implies that the direction of the self-induced emf is the same as that of the applied voltage.
Self-inductance does not prevent the change of current, however, it delays the change of current flowing through it.
Unit of Self-Inductance
The S I unit of self-inductance is Vs A -1 which is equal to Henry.
Henry
The self-inductance of the coil is said to be one henry if current changes at the rate of one ampere per second through it which causes an induced emf of one volt in the same coil.
Self-Induced Emf as Back Emf
The negative sign shows that the self-induced emf opposes the change which produces it. That is why self-induced emf is also called back emf.
This is according to Lenz’s law. If the current is increased, the self-induced emf tries to decrease the current, and similarly when the current is decreased the induce emf tries to increase the current.