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 substances exhibit weak repulsion from a magnetic field. They possess a negative magnetic susceptibility ($\chi$) and a relative permeability ($\mu_r$) marginally below 1.

2. Permeability Relationships: The magnetic permeability of a material is denoted by $\mu$, the permeability of free space by $\mu_0$, and the relative permeability by $\mu_r$. The relationship is:
$\mu_r = \frac{\mu}{\mu_0}$

3. Relative Permeability and Susceptibility: Relative permeability ($\mu_r$) and magnetic susceptibility ($\chi$) are connected via:
$\mu_r = 1 + \chi$

4. Option Analysis:

• (1) $\mu<\mu_0$: This inequality simplifies to $\frac{\mu}{\mu_0} = \mu_r<1$, which is characteristic of diamagnetic materials.
• (2) $0 \le \mu_r<1$: This condition is satisfied by diamagnetic materials, where relative permeability is slightly less than 1.
• (3) $-1 \le \chi<0$: This is also accurate, as diamagnetic materials have a small negative susceptibility. Given that $\mu_r>0$, it follows that $\chi>-1$.
• (4) $1<\mu_r<1 + \epsilon$: This statement is erroneous. For diamagnetic materials, $\mu_r$ is less than 1. A relative permeability greater than 1 indicates a positive susceptibility, which is a feature of paramagnetic materials.

5. Conclusion: Statement (4) represents the incorrect relation.