JEE Main 2025 — Magnetic Properties Of Matter Question with Solution

The relationship between magnetic susceptibility $(\chi )$ and magnetic permeability $(\mu )$ is expressed as follows:

Relative Permeability (${\mu }_r$): This is defined as the ratio of the permeability of a material ($\mu$) to the permeability of free space (${\mu }_0$).

$\mu ={\mu }_0{\mu }_r\Rightarrow {\mu }_r=\frac{\mu }{{\mu }_0}$

Magnetic Susceptibility ($\chi$): This relates to relative permeability as follows:

${\mu }_r=1+\chi \Rightarrow \chi ={\mu }_r-1$

Substituting the expression for ${\mu }_r$ from above:

$\chi =\left(\frac{\mu }{{\mu }_0}-1\right)$

Thus, the equation shows how magnetic susceptibility is derived from the magnetic permeability relative to free space.