Relative Permeability And Susceptibility

The magnetic behaviour of a material links its susceptibility $\chi$ and its relative permeability ${\mu }_r$ through ${\mu }_r=1+\chi$. This follows because the total field inside a medium is the sum of the applied field and the field due to induced magnetization, and combining $B={\mu }_0(H+M)$ with $M=\chi H$ gives $B={\mu }_0(1+\chi )H={\mu }_0{\mu }_{r}H$. Substituting $\chi =0.0004$, we get ${\mu }_r=1+0.0004=1.0004$. The small positive value, just above unity, is exactly what is expected for a paramagnetic substance, which is feebly attracted into a field. The option $0.0004$ mistakenly reports $\chi$ itself rather than ${\mu }_r$. The option $0.9996$ uses $1-\chi$, which would describe a diamagnet with negative susceptibility. The option $1.4000$ misplaces the decimal point of $\chi$. This relation is established in the NCERT magnetism chapter alongside the definitions of magnetic intensity and magnetization. A plausibility check confirms that paramagnets have ${\mu }_r$ slightly greater than one, diamagnets slightly less, and ferromagnets very much greater. These distinctions matter when selecting core materials: paramagnets and diamagnets barely alter the field and are treated as essentially non-magnetic in most circuits, whereas ferromagnets with relative permeabilities in the hundreds or thousands are chosen for transformer and electromagnet cores precisely because they multiply the field enormously. The simple linear relation used here holds for dia- and paramagnets but breaks down for ferromagnets, whose permeability depends on the field itself.