Table of Contents
What Is Magnetic Moment?
Magnetic moment is a fundamental quantity that characterizes the strength and direction of a magnetic source. It determines the torque the source experiences in an external field and the field it produces at distant points. The magnetic moment is a vector quantity, with units of A·m² (equivalent to J/T). It appears in contexts ranging from nuclear physics (nuclear magnetic moments) to astrophysics (stellar and planetary magnetic moments).
For a simple current loop, the magnetic moment equals the current times the enclosed area times the number of turns. This creates a magnetic dipole field that, at large distances, is identical in shape to that of a small bar magnet. The equivalence between current loops and permanent magnets is a profound result of electromagnetism.
Magnetic Moment Formulas
Where N is turns, I is current, A is area, gs is the electron g-factor (~2), μB is the Bohr magneton, and S is the spin quantum number.
Types of Magnetic Moment
| Type | Source | Typical Magnitude |
|---|---|---|
| Nuclear | Proton/neutron spin | ~10-26 J/T |
| Electron orbital | Orbital angular momentum | ~10-24 J/T |
| Electron spin | Intrinsic spin | 9.274 × 10-24 J/T |
| Macroscopic coil | Current loop | 10-3 to 103 A·m² |
Frequently Asked Questions
What is the relationship between magnetic moment and angular momentum?
For a charged particle in orbit, the magnetic moment is proportional to the angular momentum: m = -(e/2m)L for orbital motion, where e is the charge and m is the mass. For electron spin, the proportionality includes the g-factor: m = -gμB S/ℏ. This gyromagnetic ratio is fundamental to NMR and MRI physics.
How is magnetic moment measured?
For macroscopic objects, a torque magnetometer measures the torque in a known field. For atoms, the Stern-Gerlach experiment deflects atoms in a non-uniform field, with deflection proportional to the magnetic moment component. For nuclear moments, NMR spectroscopy measures the precession frequency in a magnetic field.
Can magnetic moment be negative?
The magnitude is always positive, but the vector direction can oppose the angular momentum (as it does for the electron due to its negative charge). In diamagnetic materials, the induced magnetic moment opposes the applied field, giving a negative magnetic susceptibility.