Answer
The distance to the element making the greatest contribution to field $B$ is $~~s = 0$
Work Step by Step
We can write the expression for the magnetic field produced by a current in a straight wire:
$B = \frac{\mu_0~i}{2~\pi~R}$
We can see that the magnitude of $B$ is greater when the distance $R$ is decreases. Thus the current that is the closest to the point $P$ will contribute the most.
Therefore, the distance to the element making the greatest contribution to field $B$ is $~~s = 0$
