How to formulate the magnetic dipol moment and field in a line geometry instead of a point

In classical physics, the magnetic field of a dipole is calculated as the limit of a current loop as the source shrinks to a point while keeping the magnetic moment $m$ constant. Because I come from a cable perspective, I want to shrink the current loop to a line, instead. Imagine two infitisimal thin, infinitly long line currents moving closer together, while keeping their magnetic moment constant.

What is the resulting magnetic field of this line dipol?