The Ampère’s Law node adds Ampère’s law for the magnetic field and provides an interface for defining the constitutive relation and its associated properties as well as electric properties.

The Material type setting decides how materials behave and how material properties are interpreted when the mesh is deformed. Select Solid for materials whose properties change as functions of material strain, material orientation, and other variables evaluated in a material reference configuration (material frame). Select Non-solid for materials whose properties are defined only as functions of the current local state at each point in the spatial frame, and for which no unique material reference configuration can be defined. Select From material to pick up the corresponding setting from the domain material on each domain.

This section is described for the Current Conservation feature.

The options Porous media and Archie’s law require additional subnodes. If Porous media is selected, a Porous Media subnode is available from the context menu (right-click the parent node) as well as from the Physics toolbar, Attributes menu. If Archie’s law is selected, add an Archie’s Law subnode in the same way. These subnodes contain additional settings to specify how the material properties are computed. Porous media models a mixture of materials whose properties are computed by averaging the properties of the components. Archie’s law models a conductive liquid in a nonconductive matrix.

The default Relative permittivity εr (dimensionless) for the media is used From material and defined on the shell domain. For User defined, select Isotropic, Diagonal, Symmetric, or Anisotropic based on the characteristics of the permittivity and then enter values or expressions in the field or matrix. If Porous media is selected, a Porous Media subnode is available from the context menu (right-click the parent node) as well as from the Physics toolbar, Attributes menu, which can specify the relative permittivity of the mixture.

Specify the constitutive relation that describes the macroscopic properties of the medium (relating the magnetic flux density B and the magnetic field H) and the applicable material properties, such as the relative permeability.

The equation for the selected constitutive relation displays under the list. For all options, the default uses values From material, or select User defined to enter a different value or expression.

Select a Constitutive relation — Relative permeability (the default), HB curve, Magnetic losses, Remanent flux density, Magnetization, Effective HB curve, or Hysteresis Jiles-Atherton model.

Select Relative permeability μr (dimensionless) to use the constitutive relation B = μ0μrH. For User defined select Isotropic, Diagonal, Symmetric, or Anisotropic and enter values or expressions in the field or matrix. If Porous media is selected, a Porous Media subnode is available from the context menu (right-click the parent node) as well as from the Physics toolbar, Attributes menu, which can specify the relative permeability of the mixture.

Select HB curve |H| (SI unit: A/m) to use a curve that relates magnetic flux density B and the magnetic field H as |H| = f(|B|).

The Magnetic field norm setting can take the values From material, External, or User defined.

When External is selected, specify the External material to use (from the Materials node under Global Definitions). This setting allows using material models or constitutive relations defined in an external library. See Working with External Materials for more information.

When User defined is selected, specify an expression for the magnetic field norm. The direction of the magnetic field is taken to be the same as the direction of the magnetic flux density at each point.

This option introduces a complex relative permeability and it is intended for time-harmonic (frequency domain) studies. Therefore, it is not available for The Magnetic Fields, No Currents Interface.

Select Magnetic losses μ′ and μ″ (dimensionless) to describe the relative permeability as a complex-valued quantity: μr = μ′ + iμ″, where μ′ and μ″ are the real and imaginary parts, respectively.

Select Remanent flux density Br (SI unit: T) to use the constitutive relation B = μ0 μr H + Br, where Br is the remanent flux density (the flux density when no magnetic field is present).

Select Magnetization M (SI unit: A/m) to use the constitutive relation B = μ0H + μ0M. Enter x and y components. For 3D components, enter x, y, and z components.

Select Effective HB curve |H|eff (SI unit: A/m) to use an effective curve that provides the local linearized relation between the magnetic flux density B and the magnetic field H in time-harmonic problems.

Select the Hysteresis Jiles-Atherton model to use in the constitutive relation B = μ0H + μ0M with the magnetization M (SI unit: A/m) computed from the solution of the 5 parameters Jiles-Atherton model. Specify the five parameters Ms, a, k, c, and α either from the material (default) or as user defined. The example material Jiles-Atherton Isotropic Hysteretic Material is available in the AC/DC material library. The parameters may be tensor quantities resulting in the modeling of an anisotropic hysteretic material as shown in the application library entry:.

An entry Initial Magnetization is present to set the initial values of Jiles‑Atherton variables.

The Discretization section that is used to chose the discretization order of Jiles-Atherton variables becomes visible when “show discretization” is enabled in the model builder.