Multipole expansion of the magnetic potential

In Coulomb gauge, the magnetic potential due to current around a closed loop has the multipole expansion

where is the magnetic dipole moment and is the angle between and so that . This may be combined with the principle of superposition.

Derivation

By applying the Multipole expansion of to the magnetostatic potential on a closed loop , and noting that the term vanishes since there are no magnetic monopoles we get the above expression.

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