JEE Physics 2025 Question with Solution

Given: The relation between magnetic susceptibility $\chi$, magnetic permeability $\mu$, permeability of free space $\mu_0$, and relative permeability $\mu_r$ is to be found.

Find: The correct expression for $\chi$ in terms of $\mu$ and $\mu_0$.

Using the standard relation,

$$\mu_r = 1 + \chi$$

So,

$$\chi = \mu_r - 1$$

Also,

$$\mu = \mu_0 \mu_r$$

Hence,

$$\mu_r = \frac{\mu}{\mu_0}$$

Substituting in the expression for $\chi$,

$$\chi = \frac{\mu}{\mu_0} - 1$$

Therefore, the correct option is A.

Given: Magnetic susceptibility is defined through magnetization, and magnetic permeability is defined through magnetic flux density.

Find: The relationship between $\chi$ and $\mu$.

Start with the magnetic field relation,

$$\vec{B} = \mu_0 (\vec{H} + \vec{M})$$

Using the definition of magnetic susceptibility,

$$\vec{M} = \chi \vec{H}$$

Substitute this into the equation for $\vec{B}$,

$$\vec{B} = \mu_0 (\vec{H} + \chi \vec{H})$$

Factor out $\vec{H}$,

$$\vec{B} = \mu_0 (1 + \chi) \vec{H}$$

Now use the definition of magnetic permeability,

$$\vec{B} = \mu \vec{H}$$

Comparing the two expressions for $\vec{B}$,

$$\mu \vec{H} = \mu_0 (1 + \chi) \vec{H}$$

Cancel $\vec{H}$ from both sides,

$$\mu = \mu_0 (1 + \chi)$$

Divide by $\mu_0$,

$$\frac{\mu}{\mu_0} = 1 + \chi$$

Therefore,

$$\chi = \frac{\mu}{\mu_0} - 1$$

Equivalently, since

$$\mu_r = \frac{\mu}{\mu_0}$$

we get

$$\chi = \mu_r - 1$$

Thus, the correct relationship is $\chi = \frac{\mu}{\mu_0} - 1$, so the correct option is A.