MagnetostaticPDEComponent

yields a current-free magnetostatic PDE term with variables vars and pars.

Details

MagnetostaticPDEComponent is typically used to generate a magnetostatic equation for permanent magnets with model variables vars and model parameters pars.
MagnetostaticPDEComponent returns a sum of differential operators to be used as a part of partial differential equations:

MagnetostaticPDEComponent models static magnetic fields produced by permanent magnets and other current-free magnetic sources.
MagnetostaticPDEComponent models magnetostatic phenomena with the dependent variable and the magnetic scalar potential. is in units of amperes [], independent variables in units of [].
Stationary variables vars are vars={V_m[x₁,…,x_n],{x₁,…,x_n}}.
MagnetostaticPDEComponent generally does not produces a time-dependent PDE.
To model permanent magnets, the MagnetostaticPDEComponent equation is given as:

is the vacuum permeability in units of [] and the magnetization vector in units of [].
The magnetization vector specifies the magnetic dipole moment per unit volume within a material, indicating the strength and direction of its magnetic properties.
An alternative to the magnetization vector , is the remanent magnetic flux density vector in units of [ $TemplateBox[{InterpretationBox[, 1], {"Wb", , "/", , {"m", ^, 2}}, webers per meter squared, {{(, "Webers", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]$ ]. The MagnetostaticPDEComponent equation is given as:

is the unitless recoil permeability.
For linear materials, like iron, the MagnetostaticPDEComponent equation simplifies to:

is the unitless relative permeability.
can be isotropic, orthotropic or anisotropic.
can be a function of the magnetic field and describe nonlinear materials.
The implicit default boundary condition for the magnetostatic model is a 0 MagneticFluxDensityValue.
The units of the magnetostatic model terms are in [ $TemplateBox[{InterpretationBox[, 1], {"Wb", , "/", , {"m", ^, 3}}, webers per meter cubed, {{(, "Webers", )}, /, {(, {"Meters", ^, 3}, )}}}, QuantityTF]$ ].
The following parameters pars can be given:

parameter	default	symbol
"Magnetization"	{0,…}	, magnetization vector in []
"RegionSymmetry"	None
"RelativePermeability"		, unitless relative permeability
"RemanentMagneticFluxDensity"	{0,…}	, remanent magnetic flux density in [ $TemplateBox[{InterpretationBox[, 1], {"Wb", , "/", , {"m", ^, 2}}, webers per meter squared, {{(, "Webers", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]$ ]
"Thickness"	1	, thickness in []
"VacuumPermeability"		, vacuum permeability in []

All parameters may depend on the spatial variable and dependent variable .
The number of independent variables determines the dimensions of or and the length of vectors , and .
The models are available in a 2D, a 2D axisymmetric and a 3D form.
A possible choice for the parameter "RegionSymmetry" is "Axisymmetric".
"Axisymmetric" region symmetry represents a truncated cylindrical coordinate system where the cylindrical coordinates are reduced by removing the angle variable as follows:
dimension reduction equation

2D
In 2D, when a "Thickness" is specified, the MagnetostaticPDEComponent equation is given as:

The input specification for the parameters is exactly the same as for their corresponding operator terms.
If no parameters are specified, the default magnetostatic PDE is:

If the MagnetostaticPDEComponent depends on parameters that are specified in the association pars as …,keyp_i…,p_iv_i,…], the parameters are replaced with .