Question

The magnetic field B and the magnetic intensity H in a material are found to be 1.6 T and 1000 A m−1, respectively. Calculate the relative permeability µr and the susceptibility χ of the material.

Answer 1

Explanation:

Step 1:

Intensity of Magnetic field, $B=1.6 T$

Intensity to magnetise in a substance, $\mathrm{H}=1000 \mathrm{A} / \mathrm{m}$

The relationship between the magnetic field and the field of magnetisation ,

$\mu=\frac{B}{H}$

$\mu=\frac{1.6}{1000}$

$\mu=1.6 \times 10^{-3}$

Step 2:

Relative permeability in a medium to vacuum is known as the ratio of permeability.

$\mu_{r}=\frac{\mu}{\mu_{0}}=1.6 \times \frac{10^{-3}}{\left(4 \pi \times 10^{-7}\right)}$

$\mu_{r}=0.127 \times 10^{4}$

$\mu_{r}=1.3 \times 103$

Step 3:

The relative permeability μr is calculated by,

$\mu_{r}=(1+\chi)$

$x=1.3 \times 10^{3}-1$

$x=1300-1$

$x=1299=1.299 \times 10^{3}$

$\chi \approx 1.3 \times 10^{3}$