Space-discrete modeling of magnetic interactions is far more problematic then the modeling of interactions of electrical nature. Whereas in countless practical applications it is quite reasonable to assume that electrical currents are fully constrained to propagating along metallic conductors only, it is not the case of magnetic conductors, even those made of the best ferromagnetic materials. However, the approach of space-discrete modeling can be very often applied to closed magnetic circuits formed of ferromagnetic materials with narrow air gaps quite successfully.
Magnetic field can be represented by lines
of magnetic flux. Where these flux lines bypass the required path through
the circuit, they are termed flux leakage. Magnetic flux
fringing is somewhat similar to leakage and is a term used to describe
the spreading of flux lines in an air gap of a magnetic circuit thus
increasing its effective area. The toroidal coil in Fig. 59a
with windings of evenly distributed turns forms a completely closed
homogenous magnetic circuit without any leakage flux. This is true even if
the core is made from a nonmagnetic material. If the core of such a coil
is made from a material with large permeability, there will be no
considerable leakage fluxes even if the coil winding is concentrated into
one place on the toroid, as indicated by the dashed line in Fig. 59a.
If the core is disrupted by an air gap, as in Fig. 59b, the flux lines indicate that large leakage and fringing fluxes result and the flux within the core varies with the distance from the coil. Still, such a coil can be modeled as a magnetic circuit if the largest part of the flux lines is concentrated into the core which determines their geometric shape. In the contrary, the short cylindrical coil shown in Fig. 59c cannot be modeled as a magnetic circuit. Except for the short part of the flux lines within the core, most of their length is situated in the air.
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