Question

Which of the following is the unit for Permeability?

• A. Henry × Meter\textsuperscript{2}
• B. Henry / Meter
• C. Henry / Meter\textsuperscript{2}
• D. Henry × Meter

Hint:

Permeability unit is derived from \( \mu = B/H \). Remember, Tesla = Weber/m\textsuperscript{2} and Weber = Henry·Ampere.

Answer 1

The Correct Option is B

Permeability is a fundamental property of a material that defines how it responds to a magnetic field. Step 1: Define permeability
Permeability (\( \mu \)) is defined as: \[ \mu = \frac{B}{H} \] Where:
- \( B \) is magnetic flux density (Tesla)
- \( H \) is magnetic field strength (A/m)
Step 2: Express Tesla in SI units
\[ 1\ \text{Tesla} = 1\ \text{Weber/m}^2 = \frac{\text{Volt}\cdot\text{second}}{\text{meter}^2} \] Also, \[ \text{Volt} = \text{Ampere} \cdot \text{Ohm} = \text{A} \cdot \Omega \] Step 3: Determine SI unit of \( \mu \)
From dimensional analysis, the unit of permeability turns out to be: \[ \mu \Rightarrow \frac{\text{Tesla}}{\text{A/m}} = \frac{\text{Weber/m}^2}{\text{A/m}} = \frac{\text{Weber}}{\text{A} \cdot \text{m}} = \frac{\text{Henry}}{\text{m}} \] So the correct unit is: \[ \boxed{\text{Henry/m}} \]