A: Peramability of a ferromagnetic material is independent of the magnetising field.
R: Permeability is given by the area under a hysteresis loop.

Options

A. If both Assertion & Reason are the true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reson is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To determine the correctness of the assertion and reason provided in the question, let's analyze each statement step by step.

### Step 1: Analyze the Assertion
**Assertion (A): Permeability of a ferromagnetic material is independent of the magnetising field.**

- The permeability (µ) of a material is defined as the ratio of the magnetic flux density (B) to the magnetic field strength (H), given by the formula:

\[ \mu = \frac{B}{H} \]

- In ferromagnetic materials, the permeability is not constant and depends on the magnetizing field (H). As the magnetizing field increases, the permeability typically changes due to the material's response to the magnetic field.

**Conclusion for Assertion:**
- The assertion is **false** because permeability is dependent on the magnetizing field.

### Step 2: Analyze the Reason
**Reason (R): Permeability is given by the area under a hysteresis loop.**

- The area under the hysteresis loop represents the energy loss (hysteresis loss) during the magnetization and demagnetization cycles of a ferromagnetic material. It does not define permeability.

- Hysteresis loss is the energy dissipated as heat due to the lag between the magnetization of the material and the applied magnetic field.

**Conclusion for Reason:**
- The reason is also **false** because the area under the hysteresis loop does not represent permeability but rather the energy loss.

### Final Conclusion
Since both the assertion and the reason are false, the correct answer to the question is that both statements are incorrect.

### Summary of the Solution
1. **Assertion Analysis**: The permeability of ferromagnetic materials is dependent on the magnetizing field, thus the assertion is false.
2. **Reason Analysis**: The area under the hysteresis loop represents hysteresis loss, not permeability, thus the reason is also false.
3. **Final Answer**: Both Assertion (A) and Reason (R) are false.

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