Magnetic dipole

A magnetic dipole is the simplest unit of magnetism. It is what you get when you shrink any closed current loop down to a point while keeping its product of current × area constant — or equivalently, the intrinsic angular-momentum spin of an elementary particle like an electron. Far from the source, the magnetic field of any localised current distribution looks like that of a magnetic dipole, the same way the electric field of any localised charge distribution looks like that of an electric dipole far away.

The dipole's strength is a vector m, the magnetic moment, with units of ampere-square-metre (A·m²). For a small flat loop of area A carrying current I, m = IA n̂, where n̂ is the unit normal to the loop in the right-hand-rule sense (curl your fingers along the current, thumb points along m). For a magnetised material, m comes from the cumulative alignment of the atomic moments — primarily electron spins — that build up the bulk magnetisation.

There are no magnetic monopoles in classical or known fundamental physics, so the dipole is the leading term in any multipole expansion of a magnetic field. This is why a bar magnet has both a north and a south pole, why cutting a magnet in half gives you two complete magnets rather than one isolated north and one isolated south, and why the field of a spinning electron, the field of a magnetised iron filing, and the field of the Earth all have the same fundamental structure. The dipole moment is the right concept for thinking about magnetic torques (τ = m × B), magnetic potential energy (U = −m·B), the way compass needles align with fields, and the way MRI machines flip nuclear spins to generate their signals.