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 µ_{r} and the susceptibility χ of the material.

#### Solution

Here,

Magnetic field strength, B = 1.6 T

Magnetising intensity in a material, H = 1000 A/m

The relation between magnetic field and magnetising field is given by

\[\mu = \frac{B}{H}\]

\[ \Rightarrow \mu = \frac{1 . 6}{1000}\]

\[ \Rightarrow \mu = 1 . 6 \times {10}^{- 3}\]

Relative permeability is defined as theratio of permeability in a medium to that in vacuum.

\[\text{So, }\mu_r = \frac{\mu}{\mu_0} = \frac{1 . 6 \times {10}^{- 3}}{4\pi \times {10}^{- 7}}\]

\[ \Rightarrow \mu_r = 0 . 127 \times {10}^4 \]

\[ \Rightarrow \mu_r = 1 . 3 \times {10}^3 \]

Relative permeability `(mu_r)` is given by,

\[ \mu_r = (1 + \chi)\]

\[ \Rightarrow \chi = 1 . 3 \times {10}^3 - 1\]

\[ \Rightarrow \chi = 1300 - 1\]

\[ \Rightarrow \chi = 1299 = 1 . 299 \times {10}^3 \]

\[ \Rightarrow \chi \approx 1 . 3 \times {10}^3\]