The `SI` unit of magnetic permebility is

Options

A. `Wbm^-2A^-1`
B. `Wbm^-1A`
C. `Wbm^-1A^-1`
D. `WbmA^-1`

Explanation

To determine the SI unit of magnetic permeability, we can start from the relationship between magnetic field (B), magnetic permeability (μ), current (I), and the geometry of the system.

### Step-by-Step Solution:

1. **Understanding the Formula**:
We know that the magnetic field (B) can be expressed in terms of magnetic permeability (μ) and current (I). The formula is:
\[ B = \frac{\mu}{4\pi} \cdot \frac{I \cdot dl \cdot \sin \theta}{r^2} \]
where:
- \( B \) is the magnetic field,
- \( \mu \) is the magnetic permeability,
- \( I \) is the current,
- \( dl \) is a differential length element,
- \( \theta \) is the angle between the current element and the line connecting the element to the point where the field is being measured,
- \( r \) is the distance from the current element to the point where the field is measured.

2. **Identifying Units**:
We need to identify the SI units of each term in the equation:
- The SI unit of magnetic field \( B \) is Weber per square meter (Wb/m²).
- The SI unit of current \( I \) is Ampere (A).
- The unit of \( dl \) (length) is meter (m).
- The sine function is dimensionless (unitless).
- The distance \( r \) is also in meters (m).

3. **Rearranging the Equation**:
Rearranging the formula to solve for \( \mu \):
\[ \mu = B \cdot \frac{4\pi r^2}{I \cdot dl \cdot \sin \theta} \]

4. **Substituting Units**:
Substitute the units into the rearranged equation:
\[ \text{Unit of } \mu = \left( \frac{\text{Wb}}{\text{m}^2} \right) \cdot \frac{4\pi \cdot \text{m}^2}{\text{A} \cdot \text{m} \cdot \text{(unitless)}} \]

5. **Simplifying the Units**:
Simplifying the expression:
\[ \text{Unit of } \mu = \frac{\text{Wb} \cdot \text{m}^2}{\text{m}^2 \cdot \text{A}} = \frac{\text{Wb}}{\text{A} \cdot \text{m}} \]

6. **Final Answer**:
Thus, the SI unit of magnetic permeability (μ) is:
\[ \text{Wb} \cdot \text{A}^{-1} \cdot \text{m}^{-1} \]

### Summary:
The SI unit of magnetic permeability is \( \text{Wb} \cdot \text{A}^{-1} \cdot \text{m}^{-1} \).