elactric charge

Force between 2 point charges = kq1q2/r^2

 

Since, the distance is fixed. So, the maximum and minimum force will depend on q1 and q2. 

 

Now, lets assume that x fundamental charges are kept together to form 1 point charge. Then (N-x) will form the second point charge. 

 

Hence, q1*q2 = x(N-x)

 

This will have minimum at x = 2 or N-2 and maximum at x  = N/2. 

 

Hence, Fmax/Fmin = (N/2 *N/2 )/ (2*(N-2) = N^2/8(N-2)