Question

In $SI$ units, the dimensions of $\sqrt{\frac{{ϵ}_0}{{\mu }_0}}$ is

• A. $A^{-1}TM{L}^3$
• B. $A^2{T}^3{M}^{-1}{L}^{-2}$
• C. $A{T}^2{M}^{-1}{L}^{-1}$
• D. $A{T}^{-3}M{L}^{3/2}$

Answer 1

The correct option is B $A^2{T}^3{M}^{-1}{L}^{-2}$

Dimension of $\sqrt{\frac{{ϵ}_0}{{\mu }_0}}$
$\left[{ϵ}_0\right]=\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$
$\left[{\mu }_0\right]=\left[ML{T}^{-2}{A}^{-2}\right]$
Dimension of $\sqrt{\frac{{ϵ}_0}{{\mu }_0}}={\left[\frac{M^{-1}{L}^{-3}{T}^4{A}^2}{ML{T}^{-2}{A}^{-2}}\right]}^{\frac{1}{2}}$
$=[M^{-2}{L}^{-4}{T}^6{A}^4{]}^{1/2}$
$=\left[M^{-1}{L}^{-2}{T}^3{A}^2\right]$.