Question

The relation connecting magnetic susceptibility $\chi_{m}$ and relative permeability $\mu _{r}$ is

• A. $\chi _{m}=\mu_{r}+1$
• B. $\chi _{m}=\mu _{r}-1$
• C. $\chi _{m}=\frac{1}{\mu _{r}}$
• D. $\chi _{m}=3(1+\mu _{r})$

Answer 1

Answer: (B)

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

Answer 2

Total magnetic flux density $B$ in a material is the sum of magnetic flux density in vacuum $B_{0}$ produced by magnetising force and magnetic flux density due to magnetisation of material $B_{m}$ ie, $B=B_{0}+B_{m}$ $\Rightarrow$ $B=\mu _{0}H+\mu_{0}I=\mu _{0}(H+I)$ $=\mu _{0}H(1+\chi _{m})$ Also $\mu _{r}=(1+\chi _{m})$