Many uncanny comparisons can be made between the behavior of electric currents and magnetic flux ( ϕ ) within conductive materials. In the same way that some materials conduct current better than others, metallic materials differentially provide pathways through which magnetic flux can permeate. The permeability ( μ ) of any material is relative to that of a vacuum ( μo ), which is 4𝜋 x 10-7 Wb / At*m. The relative permeability of a material is expressed as follows:
μr = ( μ / μo )
Magnetic materials also differ in their ability to resist the establishment of magnetic field lines within them. The reluctance ( ℛ ) of a material, therefore, is inversely proportional to its permeability:
ℛ 1/∝ μ
Intuitively, the ability of a material to restrict being permeated by magnetic fields is directly proportional to the length of the magnetic pathway, but this restriction decreases with increases in the cross-sectional area at hand; thus, when taking all three parameters into account, the equation for reluctance takes the following form:
ℛ = ( l / μA )
If a unit analysis is done, the units cancel and leave behind a ratio of ampere-turns ( At ) per weber ( Wb ):
ℛ = ( At / Wb )
If a relatively large number of loops must be used to establish a given amount of flux within a material, that material has a higher reluctance value than ones that can establish the same quantity of flux with fewer loops present. It is also interesting that the reluctance equation has a form that is similar to that for wire resistance ( R ):
R = ( ρl / A )
Furthermore, the reciprocal of resistivity ( ρ ) is conductivity ( σ ):
ρ 1/∝ σ
And,
R = ( l / σA )
Thus, the conductivity of an electrical circuit is analogous to the permeability of a magnetic circuit, and the resistance of an electrical circuit is analogous to the reluctance of a magnetic circuit.
RENAISSANCE PHYSICS 