Magnetic dipole moment

The magnetic dipole moment $⃗ 𝐦$ is defined as a pseudovector relating the aligning torque on an object from an externally applied magnetic field such that

⃗ 𝜏 = ⃗ 𝐦 \times ⃗ 𝐁

and measures the strength of a Magnet, determining the dipole term in the Multipole expansion of the magnetostatic potential. For a closed loop carrying current $𝐼$ around an Orientated surface $Σ$ , the magnetic moment is given by

⃗ 𝐦 = 𝐼 \oint Σ 𝑑 ⃗ 𝐚

It is useful to introduce the concept of magnetization, so that the magnetic dipole moment due to a volume $Ω$ is given by

⃗ 𝐦 = ∭ Ω ⃗ 𝐌 (⃗ 𝐫') 𝑑 𝜏'

Analysis of the Magnetic potential of a magnetized material motivates the surface and volume bound current densities

⃗ 𝐊 𝑏 (⃗ 𝐫') = ⃗ 𝐌 (⃗ 𝐫') \times ˆ 𝐧 ⃗ 𝐉 𝑏 (⃗ 𝐫') = ⃗ \nabla \times ⃗ 𝐌 (⃗ 𝐫')

Magnetic dipole moment

See also