N fundamental charges each of charge ‘q’ are to be distributed as two point charges separated by a fixed distance, then the maximum to minimum force bears a ratio (N is even and greater than $2$ )

Given data: two-point charges separated by a set distance are to be dispersed among N basic charges, each of charge “q”.  

Concept used: coulomb’s law

Detailed solution:

We have N fundamental charges. Let nq be placed at one point 

So, (N-n) q planced at point

let fixed distance between both set of charges r

$F=\frac{k{q}_1{q}_2}{r^2}=\frac{k{q}^2}{r^2}n(N-n)$ 

$\left[n\right(N-n){]}_{\max }={\left(\frac{N}{2}\right)}^2$ 

$\left[n\right(N-n){]}_{min}=\left(N-1\right).1=\left(N-1\right)$

 $\Rightarrow \frac{F_{\max }}{F_{\min }}=\frac{N^2}{4(N-1)}$