A circular conductor with current , radius results in a magnetic field strength at the point a length of along its "axis".1
The above situation yields a number of useful symmetries:
viz. any components of arising from one point on the wire perpendicular to the axis will be canceled out by the on the opposite side.
Therefore, along this axis is always parallel to the axis itself.
Specifically, solving the Biot-Savart Law for this setup gives
which, when , i.e. the field strength directly in the ring's centre, simplifies to
The direction of the -field at any point along the axis can be determined by a right hand rule:
curl the fingers in the direction of current and the thumb points in the direction of the -field.
Note when this gives a ,
which is analogous to an electric dipole.
See Magnetic dipole moment.
A circular conductor with current