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 solve the given question, we need to evaluate the assertion and reason statements provided:

### Step 1: Analyze the Assertion
The assertion states: "The permeability of a ferromagnetic material is independent of the magnetizing field."

- **Understanding Permeability**: Permeability (μ) is defined as the ability of a material to support the formation of a magnetic field within itself. It is given by the formula:
\[ \mu = \frac{B}{H} \]
where \(B\) is the magnetic flux density and \(H\) is the magnetizing field strength.

- **Dependence on Magnetizing Field**: For ferromagnetic materials, permeability is not constant and varies with the magnetizing field. As the magnetizing field increases, the permeability can change due to the material's magnetic properties.

**Conclusion**: The assertion is **false**.

### Step 2: Analyze the Reason
The reason states: "Permeability is given by the area under a hysteresis loop."

- **Understanding Hysteresis Loop**: The hysteresis loop represents the relationship between the magnetic flux density \(B\) and the magnetic field strength \(H\) in a ferromagnetic material. The area enclosed by the hysteresis loop represents the energy loss (hysteresis loss) during a complete cycle of magnetization and demagnetization.

- **Relation to Permeability**: The area under the hysteresis loop does not represent permeability. Instead, it represents energy loss due to hysteresis. Permeability is calculated using the relationship between \(B\) and \(H\), not the area of the hysteresis loop.

**Conclusion**: The reason is also **false**.

### Step 3: Final Evaluation
Since both the assertion and reason are false, we conclude that the correct option is:

**Both assertion and reason are false.**

### Summary of Solution
- Assertion: False (permeability depends on the magnetizing field).
- Reason: False (permeability is not given by the area under the hysteresis loop).