The relationship between the magnetic susceptibility $(x)$ and the magnetic permeability $(\mu)$ is given by :

( $\mu_0$ is the permeability of free space and $\mu_T$ is relative permeability)

<p>The relationship between magnetic susceptibility $(\chi)$ and magnetic permeability $(\mu)$ is expressed as follows:</p> <p><p><strong>Relative Permeability ($\mu_r$)</strong>: This is defined as the ratio of the permeability of a material ($\mu$) to the permeability of free space ($\mu_0$).</p> <p>$ \mu = \mu_0 \mu_r \Rightarrow \mu_r = \frac{\mu}{\mu_0} $</p></p> <p><p><strong>Magnetic Susceptibility ($\chi$)</strong>: This relates to relative permeability as follows:</p> <p>$ \mu_r = 1 + \chi \Rightarrow \chi = \mu_r - 1 $</p> <p>Substituting the expression for $\mu_r$ from above:</p> <p>$ \chi = \left(\frac{\mu}{\mu_0} - 1\right) $</p></p> <p>Thus, the equation shows how magnetic susceptibility is derived from the magnetic permeability relative to free space.</p>