Magnetic flux area S is where "B" is the magnitude of the magnetic field (the magnetic flux density) having the unit of Wb/m (tesla), "S" is the area of the surface, and "θ" is the angle between the magnetic field lines and the normal (perpendicular) to S. For a varying magnetic field, we first consider the magnetic flux through an infinitesimal area element dS, where we may consider the field to be constant: A generic surface, S, can then be broken into infinitesimal elements and the total magnetic flux through the surface is then the surface integral From the definition of 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