Let’s start by considering a length element dsS
located a distance
r from P. The direction of the magnetic field at point P due to
the current in this element is out of the page because dsS
3 r^ is out of
the page. In fact, because all the current elements I dsS
lie in the plane
of the page, they all produce a magnetic field directed out of the page
at point P. Therefore, the direction of the magnetic field at point P is
out of the page and we need only find the magnitude of the field. We
place the origin at O and let point P be along the positive y axis,