The relationship between the magnetic susceptibility (chi)$(\chi)$ and the magnetic permeability (mu)$(\mu)$ is given by: (mu_0$\mu_0$ is the permeability of free space and mu_mathrmr$\mu_{\mathrm{r}}$ is relative permeability)

### Related Formula mu_mathrmr = 1 + chi$$\mu_{\mathrm{r}} = 1 + \chi$$ mu = mu_0 mu_mathrmr$$\mu = \mu_0 \mu_{\mathrm{r}}$$ ### Core Logic The relative magnetic permeability mu_mathrmr$\mu_{\mathrm{r}}$ of a magnetic material is related to its susceptibility chi$\chi$ by the basic relation: mu_mathrmr = 1 + chi implies chi = mu_mathrmr - 1$$\mu_{\mathrm{r}} = 1 + \chi \implies \chi = \mu_{\mathrm{r}} - 1$$ Since relative permeability mu_mathrmr$\mu_{\mathrm{r}}$ is the ratio of absolute permeability mu$\mu$ to the permeability of free space mu_0$\mu_0$: mu_mathrmr = fracmumu_0$$\mu_{\mathrm{r}} = \frac{\mu}{\mu_0}$$ Substituting this into the susceptibility relation yields: chi = fracmumu_0 - 1$$\chi = \frac{\mu}{\mu_0} - 1$$ ### Step 1: Final Conclusion The correct option is chi = fracmumu_0 - 1$\chi = \frac{\mu}{\mu_0} - 1$. ### Pattern Recognition Relative permeability mu_r$\mu_r$ represents total magnetic response (vacuum background + material response), while susceptibility chi$\chi$ represents the material's specific response alone. Hence they always differ by exactly 1: mu_r = 1 + chi$\mu_r = 1 + \chi$. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Magnetic Properties of Matter