Self Induction: When a changing current flows in a coil then due to the change in magnetic flux in the coil produces an electro-motive force $\left(emf \right)$ in that coil. This phenomenon is called the principle of Self Induction. The direction of electro-motive force can be found by applying "Lenz's Law". Mathematical Analysis of Coefficient of Self Induction: Let us consider that a coil having the number of turns is $N$. If the change in current is $i$, then linkage flux in a coil will be $N \phi \propto i$ $N\phi = L i \qquad(1)$ Where $L$ $\rightarrow$ Coefficient of Self Induction. According to Faraday's law of electromagnetic induction. The electro-motive force $\left(emf \right)$ in a coil is $e=-N\left( \frac{d \phi}{dt} \right)$ $e=-\frac{d \left(N \phi \right)}{dt} \qquad(2)$ From equation $(1)$ and equation $(2)$ $e=-\frac{d \left(L i\right)}{dt} $ $e=-L \left(\frac{d i}{dt} \right) $ $L = \frac{e}{\
(The Advance Learning Institute of Physics and Technology)