magneticdipole

A magnetic dipole is the simplest magnetic source in classical physics, described by a magnetic dipole moment vector m that encapsulates the strength and orientation of the source. In the magnetostatic regime, the magnetic field produced by a localized current distribution or magnetized body at distances large compared with its size has the characteristic 1/r^3 falloff of a dipole.

The dipole moment for a small current loop is m = I A n, where I is the current, A is the loop area, and n is the unit normal to the loop. More generally, a magnetization distribution M within a body yields m = ∫ M dV. Magnetic dipole moments also arise from intrinsic properties: electrons have a magnetic moment due to spin and orbital motion, and nuclei have moments arising from nucleon spins.

In the far field, the magnetic field of a dipole is B(r) = μ0/(4π r^3) [3 (m·r̂) r̂ − m], where r̂ is the unit vector along r. The corresponding magnetic scalar potential outside current-free regions is Φm = μ0/(4π) (m·r̂)/r^2. The field satisfies ∇·B = 0 and, in vacuum, ∇×H = 0 outside sources.

The interaction of a dipole with an external magnetic field is described by a torque τ = m × B and a potential energy U = − m·B. This leads to preferred alignment with the external field.

Applications range from spectroscopy techniques such as NMR and electron spin resonance to characterizing magnetic materials. The dipole approximation is valid when the observation distance greatly exceeds the source size; closer, higher-order moments become important. The dipole moment has units of A·m^2 (or J/T).