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 $(2)$ $e=-\frac{d \left(L i\right)}{dt}$ $e=-L \left(\frac{d i}{dt} \right)$ $L = \frac{e}{\ ### Mutual Induction Phenomenon and its Coefficient Mutual Induction: When two coils are placed near each other then the change in current in one coil ( Primary Coil) produces electro-motive force$\left( emf \right)$in the adjacent coil ( i.e. secondary coil). This phenomenon is called the principle of Mutual Induction. The direction of electro-motive force$\left( emf \right)$depends or can be found by "Lenz's Law" Mathematical Analysis of Coefficient of Mutual Induction: Let us consider that two coils having the number of turns are$N_{1}$and$N_{2}$. If these coils are placed near to each other and the change in current of the primary coil is$i_{1}$, then linkage flux in the secondary coil will be$N_{2}\phi_{2} \propto i_{1}N_{2}\phi_{2} = M i_{1} \qquad(1)$Where$M\rightarrow$Coefficient of Mutual Induction. According to Faraday's law of electromagnetic induction. The electro-motive force$\left( emf \right)$in the secondary coil is$e_{2}=-N_{2}\left( \frac{d \phi_
Faraday's Laws of Electromagnetic Induction: The Faraday's experiment shows the two laws which are known as Farday's laws of electromagnetic induction First Law (Neumann's Law): The rate of change of magnetic flux through a circuit is equal to the emf produced in the circuit. This is also known as " Neumann Law " $e=-\frac{\Delta \phi}{ \Delta t}$ Here negative sign shows the direction of emf. If $\Delta t \rightarrow 0$ $e=-\frac{d \phi}{ d t}$ This equation represents an independent experimental law that cannot be derived from other experimental laws. If the circuit is a tightly wound coil of $N$ turns, then the induced emf $e=-N\frac{d \phi}{ d t}$ $e=-\frac{d \left(N \phi\right)}{ dt}$ Here $N \phi$ is called the 'Linkage magnetic flux'. Note: The change in flux induces emf, not the current. Second Law (Lenz's Law): The direction of induced EMF produced in a closed circuit is such that it opposes th