magnetmoment

A magnetic moment, or magnet moment, is a vector quantity that describes the strength and orientation of a magnet's interaction with a magnetic field. It characterizes both intrinsic properties of particles, such as spin, and the geometry of current distributions, such as loops of electric current.

For a simple current loop, the magnetic moment is μ = I A n, where I is the current, A is the loop area, and n is a unit vector normal to the loop. For a point particle with angular momentum J, the magnetic moment is μ ≈ γ J, with γ the gyromagnetic ratio. In quantum mechanics, the electron has orbital and spin contributions. The orbital moment is μ_L = -μ_B m_l, where μ_B is the Bohr magneton, and the spin moment is μ_S = -g_s μ_B S/ħ, with g_s ≈ 2.0023.

Units and typical magnitudes: the magnetic moment is measured in joules per tesla (J/T) or in ampere-square meters (A·m^2). The Bohr magneton μ_B ≈ 9.274 × 10^-24 J/T, while the nuclear magneton μ_N ≈ 5.051 × 10^-27 J/T. Nuclear and particle moments include values such as the proton μ_p ≈ 1.41 × 10^-26 J/T and the neutron μ_n ≈ -1.91 × 10^-26 J/T.

Interactions with magnetic fields follow E = -μ·B and τ = μ × B, determining energy shifts and torques on magnets and spins. In bulk matter, the net moment per volume is the magnetization M, and materials exhibit phenomena such as diamagnetism, paramagnetism, or ferromagnetism depending on how moments align with fields.

Measurement and applications: magnetic moments are probed by magnetometry, SQUID devices, and spectroscopic techniques like NMR and ESR. They play key roles in chemistry, condensed matter physics, imaging, and emerging technologies such as spintronics.