Question

What is the effect on the self inductance of a solenoid, if a core of soft iron is placed in it?

Answer 1

Formula for self inductance is given as:
$L = \dfrac{{{\mu _0}{n^2}A}}{l}$ , where n is the number of turns, A is the cross sectional area ,l is the length and ${\mu _0}$ is the permeability of free space.
Using the above relation we will check what affects the self inductance of solenoid when a soft iron core is placed in it .

Complete step by step solution:
First let’s discuss what is solenoid and self inductance then we can easily conclude the problem .

Solenoid : Solenoid is a type of electromagnet, which is used to generate controlled magnetic fields through a coil which is wound like a helix on a conducting material like iron , other ferromagnetic materials or on hollow form.

Self inductance: Self inductance is a phenomenon by which a changing electric current produces an induced emf across the coil itself .It is the ratio of electromotive force to the change in current flowing through the coil.

After inserting an iron rod in solenoid, permeability of flux through the solenoid increases , leakage flux would be less and the electric field also increases.

From the formula we have :
$L = \dfrac{{{\mu _0}{\mu _r}{n^2}A}}{l}$, ${\mu _r}$ relative permeability of iron .
Self inductance is directly proportional to relative permeability of iron, thus self inductance of the solenoid increases on inserting soft iron core inside the solenoid.

Note:
When an iron core is inserted in the solenoid , overall impedance of the solenoid increases and thus the current carrying capacity of the solenoid decreases. Then power losses will increase in AC circuits and the saturation of the solenoid core will also take place.