What is the SI unit of permeability

Options

A. `Am^(-1)`
B. A-m
C. `"Henry m^(-1)`
D. No unit, it is a dimensionless number

Answer

To find the SI unit of permeability, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Permeability**:
Permeability (denoted as μ) is a measure of how easily a magnetic field can penetrate a material. It is related to the inductance of a coil.

2. **Recall the Formula for Inductance**:
The inductance \( L \) of a coil can be expressed in terms of permeability:
\[ L = \frac{\mu n_1 n_2 A}{l} \]
where:
- \( L \) is the inductance,
- \( n_1 \) and \( n_2 \) are the number of turns,
- \( A \) is the cross-sectional area,
- \( l \) is the length of the coil.

3. **Rearranging the Formula**:
To isolate permeability \( \mu \), rearrange the formula:
\[ \mu = \frac{L \cdot l}{n_1 n_2 A} \]

4. **Identify the Units**:
- The unit of inductance \( L \) is Henry (H).
- The unit of length \( l \) is meter (m).
- The number of turns \( n_1 \) and \( n_2 \) are dimensionless (they have no units).
- The unit of area \( A \) is square meter (m²).

5. **Substituting the Units**:
Substitute the units into the rearranged formula:
\[ \text{Units of } \mu = \frac{\text{Henry} \cdot \text{meter}}{\text{meter}^2} \]

6. **Simplifying the Units**:
Simplify the expression:
\[ \text{Units of } \mu = \frac{\text{H} \cdot \text{m}}{\text{m}^2} = \frac{\text{H}}{\text{m}} \]

7. **Conclusion**:
Therefore, the SI unit of permeability is:
\[ \text{Henry per meter (H/m)} \]

### Final Answer:
The SI unit of permeability is **Henry per meter (H/m)**.

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