Magnetic Dipole - Dipolar Fields From Finite Sources

Dipolar Fields From Finite Sources

See also: Near and far field

The magnetic scalar potential ψ produced by a finite source, but external to it, can be represented by a multipole expansion. Each term in the expansion is associated with a characteristic moment and a potential having a characteristic rate of decrease with distance r from the source. Monopole moments have a 1/r rate of decrease, dipole moments have a 1/r2 rate, quadrupole moments have a 1/r3 rate, and so on. The higher the order, the faster the potential drops off. Since the lowest-order term observed in magnetic sources is the dipolar term, it dominates at large distances. Therefore, at large distances any magnetic source looks like a dipole with the same magnetic moment.

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