Question

The dimensional formula for permittivity of free space $\left({ϵ}_0\right)$ in the equation $F=\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{r^2}$ where, symbols have their usual meaning is

• A. $\left[M^1{L}^3{A}^{-2}{T}^{-4}\right]$
• B. $\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$
• C. $\left[M^{-1}{L}^{-3}{A}^{-2}{T}^{-4}\right]$
• D. $\left[M^1{L}^3{A}^2{T}^{-4}\right]$

Answer 1

The correct option is B $\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$

Permittivity of free space ${ϵ}_o=\frac{q_1{q}_2}{4\pi F{r}^2}$

Dimensions of $\left[F\right]=\left[ML{T}^{-2}\right]$

Dimensions of $\left[q\right]=\left[AT\right]$

Dimensions of $\left[r\right]=\left[L\right]$

Thus dimensional formula of $\left[{ϵ}_o\right]=\frac{\left[AT\right]\left[AT\right]}{\left[ML{T}^{-2}\right]\left[L^2\right]}$

$⟹$ $\left[{ϵ}_o\right]=\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$