How does a current loop act like a magnetic dipole?

A current loop acts like a magnetic dipole because, at distances much greater than the loop's size, the magnetic field it produces has the same shape as the field of an electric dipole.1

The strength of this dipole is characterized by the magnetic dipole moment, denoted as $m$ (or $\mu$), which is defined by the product of the current $i$ and the area $A$ of the loop ($m=iA$). The direction of this moment is perpendicular to the plane of the loop. You can determine this direction using the right-hand rule: if you curl the fingers of your right hand in the direction of the current, your extended thumb points in the direction of the magnetic dipole moment.12

Mathematically, the magnetic field produced by a small current loop at a distance $r$ decreases rapidly as the cube of the distance, mirroring the behavior of a standard magnetic dipole. This equivalence is fundamental in physics, as it explains the magnetic properties of atoms, where circulating electrons act as tiny current loops.12