Question

Dimensional formula of permeability is.

• A. \( [ MLT^{-2}A^{-2} ] \)
• B. \( [ MLT^2 A^{-2} ] \)
• C. \( [ MLT^2 A^2 ] \)
• D. \( [ MLT^{-2} A ] \)

Hint:

The permeability constant \( \mu_0 \) is used in electromagnetism and has the dimensional formula \( [MLT^{-2}A^{-2}] \).

Answer 1

The Correct Option is A

Step 1: Understanding permeability.
Permeability (\(\mu\)) is a physical constant that measures the ability of a material to support the formation of a magnetic field within itself. The dimensional formula for permeability is derived from the relationship between the magnetic field, the electric field, and the electric current.
Step 2: Derivation.
The permeability in the MKS system is represented as: \[ \mu = \frac{{\text{Force}}}{{\text{Current}^2 \cdot \text{Length}}} \] Since force is measured in newtons (\( [MLT^{-2}] \)), current in amperes (\( [A] \)), and length in meters (\( [L] \)), the dimensional formula for permeability is: \[ \mu = [MLT^{-2}A^{-2}] \] Conclusion: The dimensional formula of permeability is \( [MLT^{-2}A^{-2}] \).