Magnetic field on the axis of a circular coil

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

Animation shows the magnetic induction vector due to a differential element of a circular wire on the axis of the circle. The red vector is the dl element, the green vector the radius vector r of the point on the axis relative to the element and the black vector dB is the magnetic induction vector due to the element. The components parallel and perpendicular to the axis are shown in blue and red colors.Dragging in vertical/horizontal directions changes orientation of the coil.