Which of the following is not correct about relative magnetic permeability `(mu_(r))`?

Options

A. It is a dimensionless pure ratio.
B. For vacuum medium its value is one.
C. For ferromagnetic materials of `mu gt gt 1`
D. For paramagnetic materials `mu_(r) gt 1`

Explanation

To determine which statement about relative magnetic permeability (μ_r) is not correct, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Relative Magnetic Permeability (μ_r)**:
- Relative magnetic permeability (μ_r) is defined as the ratio of the permeability of a material (μ) to the permeability of free space (μ₀).
- Mathematically, it is expressed as:
\[ μ_r = \frac{μ}{μ₀} \]
- Since both μ and μ₀ have the same units (H/m or N/A²), μ_r is a dimensionless quantity.

2. **Evaluating the Options**:
- **Option 1**: "Relative magnetic permeability (μ_r) is a dimensionless pure ratio."
- This is correct because μ_r is defined as a ratio of two quantities with the same dimensions.

- **Option 2**: "For vacuum medium, its value is 1."
- This is also correct because in a vacuum, the permeability of the medium (μ) is equal to the permeability of free space (μ₀), thus:
\[ μ_r = \frac{μ₀}{μ₀} = 1 \]

- **Option 3**: "For ferromagnetic materials, μ_r is much more than 1."
- This statement is correct. Ferromagnetic materials have a relative permeability significantly greater than 1 due to their ability to be magnetized.

- **Option 4**: "For paramagnetic materials, μ_r is much more than 1."
- This statement is incorrect. For paramagnetic materials, μ_r is slightly greater than 1, but not "much more." This is a key distinction as it misrepresents the behavior of paramagnetic materials.

3. **Conclusion**:
- The statement that is not correct is **Option 4**: "For paramagnetic materials, μ_r is much more than 1."

### Final Answer:
The option that is not correct about relative magnetic permeability (μ_r) is **Option 4**.

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