Would the inductance ‘of a solenoid be larger or smaller if the solenoid is filled with iron? Explain briefly.

Inductance is defined as the tendency of an electrical conductor to resist a change in the electrical current flowing through it.

The self-inductance $L$of a solenoid is given by the expression,

$L=\frac{{\mu }_0{N}^2}{d}\left(\pi R^2\right)$

Here, the length of the solenoid is d, its radius is R, and the number of loops it contains is N. The term ${\mu }_0$is called permeability of free space. This term comes into play when the solenoid has an air core.

If the solenoid were to be filled with iron, then the permeability $\mu$of iron is to be used in the expression instead of ${\mu }_0$.

Rewriting expression for a solenoid with iron core,

$L=\frac{\mu N^2}{d}\left(\pi R^2\right)$

The value of permeability of iron is much higher (of the order $200,00$) than the value of that for free space.

The inductance therefore increases.

Hence, the inductance of a coil filled with iron would be larger than that of a solenoid with air core.