The relationship between the magnetic susceptibility $(\chi)$ and the magnetic permeability $(\mu)$ is given…

The relationship between the magnetic susceptibility $(\chi)$ and the magnetic permeability $(\mu)$ is given by :
($\mu_0$ is the permeability of free space and $\mu_{\mathrm{r}}$ is relative permeability)
  1. $\chi=\frac{\mu}{\mu_0}-1$
  2. $\chi=\frac{\mu_{\mathrm{r}}}{\mu_0}+1$
  3. $\chi=\mu_{\mathrm{r}}+1$
  4. $\chi=1-\frac{\mu}{\mu_0}$

Solution

We have
$\begin{aligned} & \mu_{\mathrm{r}}=(1+\chi) \Rightarrow \chi=\left(\mu_{\mathrm{r}}-1\right) \\ & \mu=\mu_0 \mu_{\mathrm{r}} \Rightarrow \mu_{\mathrm{r}}=\frac{\mu}{\mu_0} \\ & \therefore \chi=\left(\frac{\mu}{\mu_0}-1\right)\end{aligned}$

Asked in: JEE Main 2025 (02 Apr Shift 1)

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