Physics - Unit & Dimension Question with Solution | TestHub

From Coulomb's law, the force of attraction/repulsion between two point charges$q$and$q$separated by distance$r$is

$F=\frac{1}{4\mathrm{\pi }{\mathrm{\epsilon }}_0}\frac{q^2}{r^2}$

$\Rightarrow {\mathrm{\epsilon }}_0=\frac{1}{4\pi } .\frac{q^2}{F{r}^2}$

Where${\mathrm{\epsilon }}_0$is electric permittivity.

Dimensions of${\mathrm{\epsilon }}_0=\frac{{\left[\mathrm{A}\mathrm{T}\right]}^2}{\left[\mathrm{M}\mathrm{L}{\mathrm{T}}^{-2}\right]\left[{\mathrm{L}}^2\right] }$

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