The value of the intensity of the magnetic field at a point due to a current-carrying conductor depends on the? 

The Biot Savart law is used for computing the resultant magnetic field  B at distance r generated by a steady current I. 
$B=\frac{{\mu }_{0}I}{4\pi }\int \frac{I\overrightarrow{dl}\times \overrightarrow{r}}{r^3}$.
 So magnetic field at a distance r due to the current carrying conductor depends on the:
i)  the value of current.
ii) a small part of the length of the conductor.
iii) and, the angle between the line joining the given point to the midpoint of a small length and the distance between the small length of the point.