Question

Using mass $\left(M\right)$, length $\left(L\right)$, time $\left(T\right)$ and current $\left(A\right)$ as fundamental quantities, the dimension of permeability is

• A. $\left[M^{-1}L{T}^{-2}A\right]$
• B. $\left[M{L}^{-2}{T}^{-2}{A}^{-1}\right]$
• C. $\left[ML{T}^{-2}{A}^{-2}\right]$
• D. $\left[ML{T}^{-1}{A}^{-1}\right]$

Answer 1

The correct option is C $\left[ML{T}^{-2}{A}^{-2}\right]$

Magnetic permeability is a constant of proportionality that exists between magnetic induction and magnetic field intensity.

In SI units, permeability is measured in henries per meter $H/m$ or $H{m}^{-1}$.

Henry has the dimensions of $\left[M{L}^2{T}^{-2}{A}^{-2}\right]$.

Dimensions for magnetic permeability will be $\left[M{L}^2{T}^{-2}{A}^{-2}\right]/\left[L\right]=$$\left[ML{T}^{-2}{A}^{-2}\right]$