In physics, the magnetic moment of an object is a vector relating the aligning torque in a magnetic field experienced by the object to the field vector itself. The relationship is given by:

<math>\mathbf{\tau} = \mathbf{{\mu}} \times \mathbf{B}<math>

where

τ is the torque, measured in newton · metres

μ is the magnetic moment, measured in ampere · square metres

B is the magnetic field, measured in newtons per ( ampere &middot metre )

The alignment of the magnetic moment with the field creates a difference in potential energy U:

<math>U = - \mathbf{\mu}.\mathbf{B}<math>

One of the simplest examples of magnetic moments is that of the current-carrying loop, carrying current I and of area A for which the magnitude is given by:

<math>\mathbf{\mu} = I A<math>

where

μ is the magnetic moment, measured in ampere · square metres

I is the current, measured in amperes

A is the loop area, measured in square metres

Electrons and many nuclei also have intrinsic magnetic moments, an explanation of which requires a quantum mechanical treatment and relates to the intrinsic angular momentum of the particles. It is these intrinsic magnetic moments that give rise to the macroscopic effects of magnetism, and other phenomena, such as Nuclear Magnetic Resonance.

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