However, magnetic monopole quasiparticles have been observed as emergent properties of certain condensed matter systems.
[2] Moreover, one form of magnetic dipole moment is associated with a fundamental quantum property—the spin of elementary particles.
This distinction only matters if the dipole limit is used to calculate fields inside a magnetic material.
If a magnetic dipole is formed by making a current loop smaller and smaller, but keeping the product of current and area constant, the limiting field is where δ(r) is the Dirac delta function in three dimensions.
Unlike the expressions in the previous section, this limit is correct for the internal field of the dipole.
The torque can be obtained from the formula The magnetic scalar potential ψ produced by a finite source, but external to it, can be represented by a multipole expansion.