Question

Dimensions of $\frac{1}{{\mu }_0{\epsilon }_0}$ , where symbols have their usual meaning, are :

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

Answer 1

Answer: (C)

$\left[L^2{T}^{-2}\right]$

Vaccum permittivity:

$F_c=\frac{1}{4\pi {\epsilon }_0}\times \frac{q_1{q}_2}{r^2}$

Where ${\epsilon }_0$ is permttivity of vaccum.

Dimension will be $\left[M^{-1}{L}^{-3}{T}^4{I}^2\right]$

vaccum permeability:

${\mu }_0=4\pi \times {10}^{-7}N/A^2$

Dimensions will be $\left[ML{T}^{-2}{I}^{-2}\right]$

Dimensions for $\frac{1}{{\mu }_0{\epsilon }_0}$ will be $\frac{1}{\left[M^{-1}{L}^{-3}{T}^4{I}^2\right]\times \left[M^1{L}^1{T}^{-2}{I}^{-2}\right]}=\left[L^2{T}^{-2}\right]$