Magnetic field due to a straight conductor

r,dl plane
Magnetic field dB due to a current carrying element dL is given by

Iluustration shows the magnetic induction vector due to a small element dL (green color) of a long straight wire oriented along the z axis (orange color) in its neighbourhood. The wire carries current in the poitive z direction. The green vector is the dL element, the red vector is the dB vector, the blue vector the radius vector r of the point relative to the element.
Grey rectangle is in the xy plane (at right angles to the wire.)
The black dotted circle is the collection of points with same magniude of magnetic field. The check box by the side of distance of element label allows a choice between finding field at a given point due to various elements or finding field at different points due to a given element.
Dragging in vertical/horizontal directions changes orientation.