Question

Find the dimensions and units of ${\epsilon }_0$ ?

Answer 1

Force= $F=\frac{1}{4\pi ϵ}\frac{q^2}{r^2}\Rightarrow ϵ=\frac{1}{4\pi F}\frac{q^2}{r^2}$
$\left[ϵ\right]=\left(ML{T}^{-2}{)}^{-1}\right(AT{)}^2{L}^{-1}=M^{-1}{L}^{-3}{T}^4{A}^2$

Electric field , $E=\frac{1}{4\pi ϵ}\frac{q}{r^2}\Rightarrow ϵ=\frac{1}{4\pi E}\frac{q}{r^2}$

Unit $\left[E\right]=Unit\left[\frac{1}{4\pi E}\frac{q}{r^2}\right]=\frac{C}{\frac{V}{m}{m}^2}=\frac{C}{Vm}$