Question

In terms of basic units of mass $\left(M\right)$, length $\left(L\right)$, time $\left(T\right)$ and charge $\left(Q\right)$, the dimensions of magnetic permeability of vacuum $\left({\mu }_0\right)$ would be

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

Answer 1

Answer: (A)

$\left[ML{Q}^{-2}\right]$

Magnetic permeability of free space $=4\pi \times {10}^{-7}N{A}^{-2}$

The dimension of force is $\left[ML{T}^{-2}\right]$

The dimension of current is $\left[T^{-1}Q\right]$

Hence, the dimension of magnetic permeability of free space is$=N/A^2=$ $\left[ML{T}^{-2}\right][T^{-1}Q{]}^{-2}$

$=\left[ML{T}^{-2}\right][T^{-1}Q{]}^{-2}$

$=\left[ML{Q}^{-2}\right]$