Question

Among the following, the unit of permeability is NOT represented by

• A. \( \text{henry/metre} \)
• B. \( \text{weber/ampere} \)
• C. \( \text{ohm-second/metre} \)
• D. \( \text{volt-second/metre} \)

Hint:

When dealing with units of permeability, remember that permeability is related to magnetic flux and is typically represented in terms of \( \text{henry/meter} \), \( \text{weber/ampere} \), or \( \text{ohm-second/meter} \).

Answer 1

The Correct Option is D

The unit of permeability, \( \mu \), in a magnetic context is given by \( \mu = \frac{\text{weber}}{\text{ampere} \cdot \text{meter}} \), which is equivalent to \( \mu = \frac{\text{henry}}{\text{meter}} \). - Option (1), \( \text{henry/metre} \), is a correct unit of permeability. - Option (2), \( \text{weber/ampere} \), is also a correct unit of permeability. - Option (3), \( \text{ohm-second/metre} \), is another valid representation of permeability. However, option (4), \( \text{volt-second/metre} \), does not represent permeability as it is related to electric fields, not magnetic permeability. Thus, the correct answer is option (4). % Final Answer The correct answer is \( \text{volt-second/metre} \).

Answer 2

Step 1: Understand permeability and its units
Permeability (\( \mu \)) is a measure of how much a material supports the formation of a magnetic field within itself.
It is defined as the ratio of magnetic flux density (\( B \)) to magnetic field strength (\( H \)):
\[ \mu = \frac{B}{H} \]

Step 2: Units of magnetic quantities
- Magnetic flux density \( B \) is measured in tesla (T).
- Magnetic field strength \( H \) is measured in ampere per meter (A/m).
- Therefore, permeability unit is tesla per ampere per meter:
\[ [\mu] = \frac{T}{A/m} = T \cdot \frac{m}{A} \]

Step 3: Express tesla in base units
1 tesla (T) = 1 weber per square meter (Wb/m\(^2\))
And 1 weber (Wb) = 1 volt-second (V·s)
So, \[ T = \frac{V \cdot s}{m^2} \]
Thus, \[ [\mu] = \frac{V \cdot s}{m^2} \times \frac{m}{A} = \frac{V \cdot s}{A \cdot m} \]

Step 4: Analyze the given option
Given unit: volt-second per metre (\( \frac{V \cdot s}{m} \))
This unit misses the ampere (\( A \)) in the denominator, so it does not correctly represent permeability.

Conclusion: Among the given options, \( \text{volt-second/metre} \) is NOT a correct unit of permeability.