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Concept
Magnetic dipole
Summary
In electromagnetism, a magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the size of the source is reduced to zero while keeping the magnetic moment constant. It is a magnetic analogue of the electric dipole, but the analogy is not perfect. In particular, a true magnetic monopole, the magnetic analogue of an electric charge, has never been observed in nature. However, magnetic monopole quasiparticles have been observed as emergent properties of certain condensed matter systems. Moreover, one form of magnetic dipole moment is associated with a fundamental quantum property—the spin of elementary particles.
Because magnetic monopoles do not exist, the magnetic field at a large distance from any static magnetic source looks like the field of a dipole with the same dipole moment. For higher-order sources (e.g. quadrupoles) with no dipole moment, their field decays towards zero with distance faster than a dipole field does.
In classical physics, the magnetic field of a dipole is calculated as the limit of either a current loop or a pair of charges as the source shrinks to a point while keeping the magnetic moment m constant. For the current loop, this limit is most easily derived from the vector potential:
where μ0 is the vacuum permeability constant and 4π r2 is the surface of a sphere of radius r.
The magnetic flux density (strength of the B-field) is then
Alternatively one can obtain the scalar potential first from the magnetic pole limit,
and hence the magnetic field strength (or strength of the H-field) is
The magnetic field strength is symmetric under rotations about the axis of the magnetic moment.
In spherical coordinates, with , and with the magnetic moment aligned with the z-axis, then the field strength can more simply be expressed as
Magnetic moment#Magnetic pole definition
The two models for a dipole (current loop and magnetic poles), give the same predictions for the magnetic field far from the source. However, inside the source region they give different predictions.
Official source
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