Current Loop as a Magnetic Dipole

The claim. A flat loop of wire carrying a steady current $I$, viewed from a point far away compared to the loop's own size, produces a magnetic field with EXACTLY the same mathematical form as the field of a short bar magnet placed at the loop's centre, with its axis perpendicular to the plane of the loop. This is the magnetic parallel to the electric dipole: just as two opposite point charges a short distance apart act, from far away, like a single electric dipole, a small current loop acts, from far away, like a single magnetic dipole.

Magnetic dipole moment of a current loop. For a single-turn loop of area $A$ carrying current $I$, the magnitude of its equivalent magnetic dipole moment is defined as

and for a tightly wound coil of $N$ identical turns, each contributing the same moment, the total dipole moment is

with SI unit ampere-metre-squared ($\text{A}\cdot\text{m}^2$), exactly analogous to the electric dipole moment's unit of coulomb-metre.

Direction. The direction of $\vec{m}$ is fixed by the right-hand rule: if the fingers of the right hand are curled in the sense the current flows around the loop, the extended thumb points along $\vec{m}$ (Figure 1). This direction is also, by definition, the direction from the equivalent magnet's S pole to its N pole -- so the face of the loop from which $\vec{m}$ emerges (and the current, viewed from outside, runs anticlockwise) behaves as the N pole, and the opposite face behaves as the S pole. …