Question

The incorrect relation for a diamagnetic material (all the symbols carry their usual meaning and ε is a small positive number) is:

• A. \(\mu < \mu_0\)
• B. \(0 \leq \mu_r < 1\)
• C. \(-1 \leq \chi < 0\)
• D. \(1 < \mu_r < 1 + \epsilon\)

Answer 1

The Correct Option is B

1.Diamagnetic Materials: Diamagnetic materials are weakly repelled by a magnetic field. They have a negative magnetic susceptibility ($\chi$) and a relative permeability ($\mu_r$) slightly less than 1.

2.Relationship between $\mu$, $\mu_0$, and $\mu_r$: $\mu$ is the magnetic permeability of the material, $\mu_0$ is the permeability of free space, and $\mu_r$ is the relative permeability. They are related by:
$\mu_r = \frac{\mu}{\mu_0}$

3.Relationship between $\mu_r$ and $\chi$: The relative permeability and magnetic susceptibility are related by: 
$\mu_r = 1 + \chi$

4.Analyze the Options:

• (1) $\mu < \mu_0$: This is equivalent to $\frac{\mu}{\mu_0} = \mu_r < 1$, which is true for diamagnetic materials.
• (2) $0 \le \mu_r < 1$: This is true for diamagnetic materials. The relative permeability is slightly less than 1.
• (3) $-1 \le \chi < 0$: This is also true. Diamagnetic materials have a small negative susceptibility. Since $\mu_r > 0$, $\chi > -1$.
• (4) $1 < \mu_r < 1 + \epsilon$: This is incorrect. For diamagnetic materials, $\mu_r$ is less than 1, not greater. This would imply a positive susceptibility, which is characteristic of paramagnetic materials.

5.Conclusion: The incorrect relation is (4).