The correct M-H curve for a paramagnetic material at a constant temperature (T) is represented by

Options

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B.
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D.

Explanation

To determine the correct M-H curve for a paramagnetic material at a constant temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Variables**:
- M represents the magnetization of the material.
- H represents the magnetic intensity.

2. **Applying Curie's Law**:
- According to Curie's Law, the magnetization (M) of a paramagnetic material is directly proportional to the magnetic field (B) and inversely proportional to the temperature (T).
- Mathematically, this can be expressed as:
\[ M \propto \frac{B}{T} \]

3. **Introducing the Curie Constant**:
- We can introduce a constant (C), known as the Curie constant, to express the relationship:
\[ M = \frac{C \cdot B}{T} \]

4. **Relating B to H**:
- The magnetic field B is related to the magnetic intensity H by the equation:
\[ B = \mu_0 \cdot H \]
- Here, \(\mu_0\) is the permeability of free space, which is a constant.

5. **Substituting B in the Magnetization Equation**:
- We can substitute the expression for B into the magnetization equation:
\[ M = \frac{C \cdot (\mu_0 \cdot H)}{T} \]

6. **Simplifying the Equation**:
- This can be rearranged to:
\[ M = \left(\frac{C \cdot \mu_0}{T}\right) \cdot H \]
- Let \(k = \frac{C \cdot \mu_0}{T}\), where k is a constant since C, \(\mu_0\), and T are constants at constant temperature.

7. **Final Relationship**:
- Thus, we have:
\[ M = k \cdot H \]
- This indicates that M is directly proportional to H, suggesting a linear relationship.

8. **Graphical Representation**:
- The M-H curve will be a straight line passing through the origin, indicating that as the magnetic intensity (H) increases, the magnetization (M) also increases linearly.

9. **Conclusion**:
- Therefore, the correct M-H curve for a paramagnetic material at a constant temperature is represented by a straight line graph.