What Exactly is Axis of A Solenoid? How does placing a soft Iron Core Along The Axis increase its Strength of Magnetic Field?

Question

I have trouble understanding what is meant by axis of solenoid.

According to textbooks placing a soft iron core "along the axis of solenoid" increases the strength of the magnetic field of the solenoid as the soft iron has a high magnetic permeability

Can someone explain how this works ^

Answer 1

The axis of a solenoid is its geometrical axis.

As a first approximation, the magnetic field in the region of space "inside" a solenoid is uniform, and equal to

$\mathbf{B} = \mu \dfrac{N}{L} i \, \mathbf{\hat{z}}$,

being:

• $\mu$ the magnetic permeability of the medium "inside" the solenoid,
• $\frac{N}{L} = \dfrac{\text{n. windings of the solenoid}}{\text{length of the solenoid}}$ the density of windings per unit length,
• and $i$ the electric current in the wire.

With the same current, if you put a ferromagnetic medium inside the solenoid, the magnitude of the magnetic field increases, since $\mu = \mu_r \mu_0 \gg \mu_0$, with $\mu_0$ the permeability of vacuum as a good approximation of permeability of air, and with relative permeability of order $\mu_r = 10^2 \div 10^5$ for ferromagnetic materials,

$B^{ferro} = \mu_r\mu_0 \dfrac{N}{L} i = \mu_r B^{air} = ( 10^2 \div 10^5 ) \cdot B^{air}$.