Magnet (vector): linear approximation
Presentation
These models ( Linear magnet described by the Cartesian / cylindrical / spherical vector B_{r} ) define a B(H) dependence of linear demagnetization in Flux (not available in material manager).
Main characteristics:
- the mathematical model and the direction of magnetization are associated
- same number of materials and/or coordinate systems than regions
Mathematical model
In the direction of magnetization the model is a straight line.
The corresponding mathematical formula is written as follows:
Β(Η)=μ_{0}μ_{r}Η+ B_{r}
where:
- μ_{0} is the permeability of vacuum, μ_{0} = 4 π 10^{-7} H/m
- μ_{r} is the relative permeability (recoil line slope)
- B_{r} is the remanent flux density T
The shape of the B(H) dependence is given in the opposite figure:
Direction of magnetization
The direction of magnetization is “associated” with the model. Three models are provided: Cartesian, cylindrical or spherical vector.
Cartesian magnetization
The mathematical model is the linear model previously described.
The B(H) dependence is defined by the following relationship in a Cartesian coordinate system:
where:
- is the remanent flux density defined by three components following the three axes of the Cartesian coordinate system: ( B_{rx}, B_{ry}, B_{rz})
- μ_{r} is the tensor of relative permeability; the three numerical values ( μ_{rx}, μ_{ry}, μ_{rz}) correspond to the three axes of the Cartesian coordinate system
Cylindrical magnetization
The mathematical model is the linear model previously described.
The B(H) dependence is defined by the following relationship in a cylindrical coordinate system:
where:
- is the remanent flux density defined by three components following the three axes of the cylindrical coordinate system: ( B_{rr}, B_{rθ} and B_{rz})
- μ r is the relative permeability
radial (B_{rr} ) | orthoradial (B_{rθ}) | axial (B_{rz}) |
Spherical magnetization
The mathematical model is the linear model previously described.
The B(H) dependence is defined by the following relationship in a spherical coordinate system:
where:
- is the remanent flux density defined by three components following the three axes of the spherical coordinate system: ( B_{rr}, B_{rθ} et B_{rφ})
- μ r is the relative permeability
radial (B_{rr} ):