The Bar Magnet: Poles, Magnetic Axis and Dipole Moment

Poles cannot be isolated. Every bar magnet has two ends, conventionally called its north (N) pole and south (S) pole, at which the magnetic effect appears strongest. Unlike an electric dipole, whose two charges CAN in principle be physically separated and studied alone, a magnetic pole has never been observed in isolation: breaking a bar magnet in half does not produce a lone N pole and a lone S pole, but two SHORTER complete magnets, each with its own N and S pole. This experimental fact -- that magnetic poles always occur in equal and opposite pairs -- is why a bar magnet is correctly described as a magnetic DIPOLE from the very outset, never as a pair of independent charges.

Magnetic axis and magnetic length. The straight line joining the two poles is the magnet's magnetic axis. The distance between the two poles is the magnetic length, denoted $2l$ (so each pole sits a distance $l$ from the magnet's centre $O$); it is slightly SHORTER than the magnet's full geometric length, because the poles behave as though concentrated slightly inside the physical ends (a correction ignored in the idealised "short bar magnet" treatment used throughout this sub-topic, exactly as a point charge is an idealisation of a small charged body).

Pole strength and dipole moment. Each pole is assigned a pole strength $q_m$ (SI unit $\text{A}\cdot\text{m}$), in rough analogy with electric charge, with the N pole carrying $+q_m$ and the S pole carrying $-q_m$. The magnet's magnetic dipole moment is then defined, exactly as for the current loop of Section 1.2, as

$\vec{m} = q_m(2l)\,\hat{m}$ …