The Current Conservation node adds the continuity equation for the electrical potential and provides an interface for defining the electric conductivity as well as the constitutive relation and the relative permittivity for the displacement current.

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 Nonsolid 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.

By default, the Electrical conductivity σ (SI unit: S/m) for the media is defined From material. Or select User defined, Effective medium, Archie’s Law, Hall effect, or Linearized resistivity. When Effective medium is selected, either right-click Current Conservation or in the Physics toolbar, Attributes menu click to add an Effective Medium subnode. When Archie’s law is selected, do the same to add an Archie’s Law subnode.

For User defined select Isotropic, Diagonal, Symmetric, or Full depending on the characteristics of the electrical conductivity, and then enter values or expressions for the electrical conductivity σ in the field or matrix. The default is 0 S/m. If type of temperature dependence is used other than a linear temperature relation, enter any expression for the conductivity as a function of temperature.

Select Linearized resistivity for a temperature-dependent conductivity (this occurs in, for example, Joule heating, and is also called resistive heating). The equation describing the conductivity:

where ρ0 is the resistivity at the reference temperature Tref, and α is the temperature coefficient of resistance, which describes how the resistivity varies with temperature.

The default Reference resistivity ρ0 (SI unit: Ω⋅m), Reference temperature Tref (SI unit: K), and Resistivity temperature coefficient α (SI unit: 1/K) are taken From material, which means that the values are taken from the domain (or boundary) material. T is the current temperature, which can be a value that is specified as a model input or the temperature from a heat transfer interface. The definition of the temperature field is in the Model Inputs section.

To specify other values for any of these properties, select User defined from the list and then enter a value or expression for each. The default values are:

Select Hall Effect to incorporate the effect of a magnetic field on the constitutive relation. A Hall current term σRHJc × B is added to the total conduction current Jc, where RH is the Hall coefficient, and B is the magnetic flux density. This current component is incorporated using an anisotropic modified electrical conductivity tensor.

The specified Electrical conductivity is isotropic and can be defined From material or User defined. The Hall coefficient RH (SI unit: m3/(s·A)) is defined macroscopically as the inverse of the carrier charge density RH = 1/(nq), with n the carrier density, and q the carrier charge, with the value set by user input. The default magnetic flux density is User defined, but can also be defined from Common model input or from an appropriate magnetic fields interface.

Not that the Hall Effect model is based on the assumption that changes in the magnetic field are relatively small and do not produce significant induced currents. Therefore it is only suitable for stationary studies. In cases where the induced electric field is negligible, the stationary formulation can be used in time-dependent studies by setting the Equation form to Stationary, instead of the default Study controlled.

Select a Dielectric model to describe the macroscopic properties of the medium (relating the electric displacement D with the electric field E) and the applicable material properties, such as the relative permittivity. For a description of the constitutive relations Relative permittivity, Polarization, Remanent electric displacement and Dielectric losses, see Constitutive Relation D-E as described for the Charge Conservation node for the Electrostatics interface. The constitutive relations specific to Electric Currents are: