When a ferromagnetic material goes through a hysteresis loop, the magnetic susceptibility

Options

A. has a fixed value
B. may be zero
C. may be infinity
D. may be negative

Answer

To solve the question regarding the behavior of magnetic susceptibility when a ferromagnetic material goes through a hysteresis loop, we will analyze the properties of the hysteresis loop and the definition of magnetic susceptibility step by step.

### Step-by-Step Solution:

1. **Understanding Hysteresis Loop**:
- The hysteresis loop represents the relationship between the magnetization (I) of a ferromagnetic material and the external magnetic field intensity (H). The x-axis represents the magnetic field intensity (H), while the y-axis represents the magnetization (I).

2. **Defining Magnetic Susceptibility**:
- Magnetic susceptibility (χ) is defined as the ratio of magnetization (I) to the magnetic field intensity (H):
\[ \chi = \frac{I}{H} \]

3. **Analyzing Points on the Hysteresis Loop**:
- **Point B**: At this point, the magnetization (I) is positive, and the magnetic field intensity (H) is zero.
- Since H is zero, the susceptibility (χ) tends to infinity:
\[ \chi \to \infty \quad \text{(as } H \to 0\text{)} \]

- **Point C**: Here, the magnetization (I) is positive, but the magnetic field intensity (H) is negative.
- Thus, the susceptibility (χ) will be negative:
\[ \chi < 0 \quad \text{(since } I > 0 \text{ and } H < 0\text{)} \]

- **Point D**: At this point, the magnetization (I) is zero, and the magnetic field intensity (H) is negative.
- Therefore, the susceptibility (χ) will be zero:
\[ \chi = \frac{0}{H} = 0 \quad \text{(where } H < 0\text{)} \]

4. **Conclusion**:
- From the analysis of the points on the hysteresis loop:
- At point B: χ tends to infinity.
- At point C: χ is negative.
- At point D: χ is zero.
- Thus, the magnetic susceptibility is not fixed and can take on different values throughout the hysteresis loop.

5. **Final Answer**:
- The correct options based on the analysis are:
- Magnetic susceptibility may be 0 (Option 2).
- Magnetic susceptibility may be negative (Option 4).
- Magnetic susceptibility may be infinity (Option 3).
- Therefore, the magnetic susceptibility is not a fixed value (Option 1 is incorrect).