Consider the limit of large distances, where a finite charged rod is observed at a distance that is very large when compared to the length of the rod.
In this situation, the electric field best resembled that of a ...
point charge ... it goes like r^-2
infinite line ... it goes like r^-1
electric dipole ... it goes like r^-3
infinite plane ... it is constant
none of the above ... it is zero
I think it makes sense for it to be like a point charge..am I right?
E = k*Q/(r*sqrt(r^2+(L/2)^2)
now L/r<1
then L^2/r^2 is approximately 0
therefore take out r
E= k*Q/[r*r(sqrt(1+L/2r)^2)]
sqrt(1+L/2r)^2)= sqrt(1)
E = k*Q/r^2
therefore the answer is
point charge ... it goes like r^-2