Question

Which of the following options represents correct dimensions of ${ϵ}_o$?

• A. $\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$
• B. $\left[M^{-1}{L}^{-3}{T}^{3}A\right]$
• C. $\left[M^{-1}{L}^{-3}T{A}^2\right]$
• D. $\left[M^0{L}^{-3}{T}^3{A}^3\right]$

Answer 1

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

From Coulomb's law,

$F=\frac{k{q}_1{q}_2}{r^2}$

$\Rightarrow F=\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{r^2}$

$\Rightarrow \left[{ϵ}_0\right]=\frac{\left[q_1{q}_2\right]}{\left[4\pi F{r}^2\right]}(\because [q]=[It\left]\right)$

Now putting the dimension of each terms

$\Rightarrow \left[{ϵ}_0\right]=\frac{\left[A^2{T}^2\right]}{\left[ML{T}^{-2}\right]\left[L^2\right]}$

$\therefore \left[{ϵ}_0\right]=\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$

Therefore, option $\left(a\right)$ is correct.