Question

On what factors does the self-inductance of a coil depend?

Answer 1

1. According to Faraday's law, when the current changes with time in a circuit an emf is induced.
2. This induced emf is directly proportional to the change in magnetic flux linked with the circuit with respect to time.
   $\mathrm{e}(\mathrm{induced}\mathrm{emf})=\frac{-\mathrm{d\varphi }}{\mathrm{dt}}=\frac{\mathrm{the}\mathrm{change}\mathrm{in}\mathrm{magnetic}\mathrm{flux}}{\mathrm{time}\mathrm{interval}}$
3. The magnetic flux linked with a coil is the self-inductance of a coil when the current flows $1\mathrm{A}$through the coil.
   $\mathrm{\varphi }=\mathrm{LI}$ (where $\mathrm{\varphi }=$magnetic flux, $\mathrm{L}=$self-inductance, $\mathrm{I}=$the current through the coil)
   when,
   $$\begin{gathered} \mathrm{I}=1\mathrm{A}, \\ \mathrm{\varphi }=\mathrm{L} \end{gathered}$$
4. Self-inductance coefficient is given by- $L=\frac{\mu n^{2}A}{l}$where, $\mu$ is permeability, $l$ is length of solenoid, $n$ is no of turns per unit length

Thus, self-inductance depends on the cross-sectional area of the coil$\left(L\alpha A\right)$, the number of turns per unit length of the coil$\left(L\alpha n^2\right)$, length of solenoid$\left(L\alpha \frac{1}{l}\right)$, and permeability of the core material$\left(L\alpha \mu \right)$ that is on size, shape, and material of the coil, and also on medium.