magnetic moment

magnetic moment. In classical electromagnetism, the magnetic moment is a vector quantity that represents the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Fundamentally, it arises from the motion of electric charges, such as electric current in a loop or the intrinsic spin of elementary particles. The concept is central to understanding phenomena from the behavior of atomic nuclei in NMR machines to the alignment of Earth's own geomagnetic field.

Definition and basic formula

The magnetic moment is defined for a planar closed loop of electric current; its magnitude is the product of the current and the area of the loop, and its direction is perpendicular to the plane of the loop as given by the right-hand rule. For a current loop, the moment μ = IA, where I is the current and A is the area vector. This definition extends to magnetic materials, where the total moment is the vector sum of all constituent microscopic moments. The interaction energy U of a magnetic moment with an external magnetic field B is given by U = −μ·B, a relationship pivotal in technologies like magnetic resonance imaging. The torque τ experienced is τ = μ × B, causing alignment, a principle utilized in compass needles and electric motor designs.

Classical and quantum mechanical origins

Classically, magnetic moments originate from circulating charges, analogous to the Ampèrian loop model. In quantum mechanics, two primary sources exist: orbital angular momentum and intrinsic spin. The orbital magnetic moment for an electron in an atom is quantized and proportional to its orbital angular momentum quantum number, derived from solutions to the Schrödinger equation for systems like the hydrogen atom. The spin magnetic moment is an intrinsic property of particles like the electron, proton, and neutron, not arising from physical rotation but from relativistic quantum field theory described by the Dirac equation. The Landé g-factor adjusts the proportionality between magnetic moment and angular momentum, differing for orbital and spin contributions and being precisely measured for the electron in experiments like the Penning trap.

Magnetic moment of elementary particles

The electron possesses both a spin magnetic moment and, when bound, an orbital magnetic moment. Its spin moment is approximately −9.284764×10⁻²⁴ J/T, often expressed in units of the Bohr magneton, a constant derived from Max Planck's constant and the electron mass. The proton and neutron, composite particles made of quarks, have anomalous magnetic moments that deviate significantly from predictions for point particles, providing critical tests for quantum chromodynamics and the Standard Model. The muon, a heavier lepton, has been the subject of precision experiments at Fermilab and Brookhaven National Laboratory, where a measured discrepancy from theory may hint at physics beyond the Standard Model. The magnetic moment of the photon is zero, while the neutrino's possible non-zero moment is a topic of research in experiments like IceCube.

Magnetic moment in atoms and molecules

In multi-electron atoms, the total magnetic moment is the vector sum of orbital and spin moments from all electrons, calculated using Hund's rules and Russell–Saunders coupling. Diamagnetism, a weak repulsion from a magnetic field, occurs in atoms with no permanent moment, like noble gases, and is described by Lenz's law. Paramagnetism, as seen in oxygen or aluminum, arises from unpaired electron spins aligning with an external field. In transition metal ions, strong exchange interactions between moments can lead to ferromagnetism (as in iron), antiferromagnetism, or ferrimagnetism, foundational to materials used in hard disk drives and MRI contrast agents. Molecular magnetism studies systems like single-molecule magnets, with research centers including the University of Manchester and the Max Planck Institute.

Measurement and applications

Magnetic moments are measured using techniques like the Stern–Gerlach experiment, which first demonstrated spatial quantization of silver atoms, and vibrating-sample magnetometry. For nuclear moments, NMR and MRI exploit the resonant flipping of spins from nuclei like hydrogen-1 in powerful fields generated by superconducting magnets. In geophysics, measurements of the Earth's magnetic field by satellites like Swarm inform models of the geodynamo. Applications are vast: electric motors and generators rely on torque on current loops; magnetic storage media use ferromagnetic domains; and particle accelerators like the Large Hadron Collider use magnetic moments for beam steering. Medical applications extend to magnetoencephalography and targeted magnetic nanoparticle therapies.

Category:Physical quantities Category:Electromagnetism