Magnetic Properties of Matter

JEE Main level, single correct, medium

6 of 57

Question 6 of 57

The relationship between the magnetic susceptibility (χ)(\chi) and the magnetic permeability (μ)(\mu) is given by :
(μ0\mu_0 is the permeability of free space and μr\mu_{\mathrm{r}} is relative permeability)

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Answer: (A) χ=μμ0−1\chi=\frac{\mu}{\mu_0}-1

We have
μr=(1+χ)⇒χ=(μr−1)μ=μ0μr⇒μr=μμ0∴χ=(μμ0−1)\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}

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