Question

If a magnetic material has magnetic susceptibility \( \chi = -0.5 \), then its relative magnetic permeability \( \mu_r \), and the type of material is

• A. \(0,\ \text{diamagnetic} \)
• B. \(2,\ \text{ferromagnetic} \)
• C. \(1,\ \text{paramagnetic} \)
• D. \(-1,\ \text{ferromagnetic} \)
• E. \(0.5,\ \text{diamagnetic} \)

Hint:

\( \chi<0 \) $\Rightarrow$ diamagnetic, \( \chi>0 \) $\Rightarrow$ paramagnetic.

Answer 1

Answer: (E)

Step 1: Understanding Magnetic Properties:
Magnetic Susceptibility (\(\chi\)): A dimensionless quantity that indicates the degree of magnetization of a material in response to an applied magnetic field.
Relative Magnetic Permeability (\(\mu_r\)): The factor by which the magnetic field is increased or decreased inside a material compared to vacuum.
Step 2: Key Formula or Approach:
The relationship between relative magnetic permeability (\(\mu_r\)) and magnetic susceptibility (\(\chi\)) is:
\[ \mu_r = 1 + \chi \] Step 3: Detailed Explanation and Calculation:
First, we calculate \(\mu_r\) using the given value of \(\chi = -0.5\).
\[ \mu_r = 1 + (-0.5) = 0.5 \] Next, we identify the type of material based on the sign of \(\chi\).
Diamagnetic materials have a small, negative susceptibility (\(\chi<0\)). They are weakly repelled by magnetic fields. For them, \(\mu_r<1\).
Paramagnetic materials have a small, positive susceptibility (\(\chi>0\)). They are weakly attracted by magnetic fields. For them, \(\mu_r>1\).
Ferromagnetic materials have a large, positive susceptibility (\(\chi \gg 1\)). They are strongly attracted by magnetic fields. For them, \(\mu_r \gg 1\).
Since the given susceptibility \(\chi = -0.5\) is negative, the material is diamagnetic. Our calculated value \(\mu_r = 0.5\) is less than 1, which is consistent with a diamagnetic material.
Step 4: Final Answer:
The relative magnetic permeability is 0.5 and the material is diamagnetic.