# Isotropic soft magnetic material: Rayleigh parabola curve + straight line

## Presentation

In cases of low magnetic fields, this model defines a B(H) dependence for an isotropic material, taking the Raleigh zone into consideration.

## Mathematical model

This model is comprised of a parabola and a straight line.

The corresponding mathematical formula is written as follows:

B(H)=μ0μriH + (μrf - μri)H2/2Hj → if H < Hj

Β(Η)=μ0μrfΗ-μ0rf - μrij/2 → if H > Hj

where:

• μ0 is the permeability of vacuum, μ0 = 4 π 10-7 H/m
• μri is the initial relative permeability (at the origin)
• μrf is the final relative permeability (at the junction point of the parabola and the straight line)
• Hj is the magnetic field at the junction point of the parabola and the straight line

The shape of this B(H) dependence is given in the figure below.