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A current I flows in a conductor placed ...

A current I flows in a conductor placed perpendicular to the plate of the paper. Indicate the direction of the magnetic field due to a small element `dvecl` at point P situated at a distance `vecr` from the element as shown in the figure.

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Here current element `Idvecl` is along z-direction and position vector `vecr` is along y-direction. So `Idvecl=Idlhatk` and `vecr=rhatj`
According to Biot Savart's law, the magnetic field at point P due to current element is
`dvecB=(mu_0)/(4pi)(Idvecrxxvecr)/(r^3)=(mu_0I)/(4pi)([dlhatkxxrhatj])/(r^3)`
`(mu_0I)/(4pi)(dl)/(r^2)(-hati)`
Hence, magnetic field at point P is directed along negative x-direction.
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