A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^2}{4\pi {\epsilon }_0}$c  is velocity of light, G is universal constant of gravitation and e is charge]

Dimensions of 

$\frac{e^2}{4\pi {\epsilon }_o}=\left[F\times d^2\right]=\left[{\mathrm{ML}}^3{ \mathrm{T}}^{-2}\right]$

$\text{ Dimensions of }G=\left[M^{-1}{L}^3{T}^{-2}\right]$

$\text{ Dimensions of }c=\left[{\mathrm{LT}}^{-1}\right]$

$l\propto {\left(\frac{e^2}{4\pi {\epsilon }_o}\right)}^p{G}^q{c}^r$

$\therefore \left[{\mathrm{L}}^1\right]={\left[{\mathrm{ML}}^3{ \mathrm{T}}^{-2}\right]}^p{\left[{\mathrm{M}}^{-1}{ \mathrm{L}}^3{ \mathrm{T}}^{-2}\right]}^q{\left[{\mathrm{LT}}^{-1}\right]}^r$

On comparing both sides and solving, we get 

$p=\frac{1}{2}, q=\frac{1}{2}\text{ and }r=-2$

$\therefore l=\frac{1}{c^2}{\left[\frac{G{e}^2}{4\pi {\epsilon }_o}\right]}^{1/2}$