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.