Question

In $SI$ units, the dimension of $\sqrt{\frac{{\epsilon }_0}{{\mu }_0}}$ 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

Answer: (B)

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