Magnetic dipole magnetic dipole as the distance from the source increases. 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 constant. For the current loop, this limit is most easily derived for the vector potential. Outside of the source region, this potential is (in SI units) with 4"π r" being the surface of a sphere of radius "r"; and the magnetic flux density (strength of the B-field) in teslas is In spherical coordinates with the
Magnetic helicity it (gauge transformation). However, for perfectly conducting boundaries or periodic systems without a net magnetic flux, the magnetic helicity is gauge invariant. A gauge-invariant "relative helicity" has been defined for volumes with non-zero magnetic flux on their boundary surfaces. If the magnetic field is turbulent and weakly inhomogeneous a magnetic helicity "density" and its associated flux can be defined in terms of the density of field line linkages. Magnetic helicity The helicity of a smooth vector field defined on a domain in 3D space is the standard measure of the extent to which the field lines wrap and coil around