Explain self induction and obtain equation of self induced emf in a coil.

Explanation

When magnetic flux linked with coil itself change due to change in current flowing in it then such emf is called self induced emf. This phenomena is called self induction.
In this case, flux linkage through a coil of N turns is proportional to the current through the coil and is expressed as
`Nphi_B=prop I`
`Nphi_B`=LI ...(1)
Where constant of proportionality L is called self-inductance of the coil. It is also called the coefficient of self-induction of the coil. When the current is varied, the flux linked with the coil also changes and an emf is induced in the coil.
Using equation (1), the induced emf is given by
`epsilon=-(d(Nphi_B))/(dt)=(-d(dI))/(dt)`
`therefore epsilon=-L(dI)/(dt)`...(2)
Thus, the self-induced emf always opposes any change (increase or decrease) of current in the coil.