Question

A rod of magnetic material of cross-section 0.25 cm² is placed in a magnetizing field of intensity 4000 A/m^-1. The magnetic flux passing through the rod is 25 × 10^-6 Wb. Find out

(a) relative permeability

(b) magnetic susceptibility and 

(c) magnetisation of the rod.

Answer 1

Given: A = 0.25 cm² = 25 × 10^-6 m²

H = 4000 A m^-1, Φ = 25 × 10^-6 Wb

Magnetic induction is

B = ${\displaystyle \frac{\varphi }{\text{A}}}$

${\displaystyle =\frac{25\times {10}^{-6}}{25\times {10}^{-6}}}$

= 1 Wb/m²

(a) B = μ₀μ_rH

∴ The relative permeability of the material,

${\displaystyle {\mu }_{\text{r}}=\frac{\text{B}}{{\mu }_0\text{H}}}$

${\displaystyle =\frac{1}{4\times 3.142\times {10}^{-7}\times 4000}}$

${\displaystyle =\frac{10000}{50.272}}$

= 198.91 = 199

(b) ${\displaystyle {\mu }_{\text{r}}=1+{\chi }_{\text{m}}}$

∴ The magnetic susceptibility of the material,

${\displaystyle {\chi }_{\text{m}}={\mu }_{\text{r}}-1}$

= 199 - 1

= 198

(c) ${\displaystyle {\chi }_{\text{m}}=\frac{{\text{M}}_{\text{z}}}{\text{H}}}$

The magnetization of the rod,

${\displaystyle {\text{M}}_{\text{z}}={\chi }_{\text{m}}\text{H}=198\times 4000=7.92\times {10}^5}$A/m