Current Conservation
The Current Conservation node adds the continuity equation for the electric potential and provides an interface for defining the electric conductivity as well as the constitutive relation and the relative permittivity for the displacement current. There are two types of Current Conservation available; Current Conservation in Solids and Current Conservation in Fluids. This distinction decides how materials behave and how material properties are interpreted when the mesh is deformed.
Current Conservation in Solids applies to materials whose properties change as functions of material strain, material orientation, and other variables evaluated in a material reference configuration (material frame).
Current Conservation in Fluids applies to 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.
In COMSOL versions 6.3 and earlier, this Solids/Fluids distinction was controlled within the Current Conservation node by specifying Solid/Nonsolid in the Material type setting.
Constitutive Relation Jc-E
By default, the Electric conductivity σ (SI unit: S/m) for the media is defined From material. Or select User defined or Linearized resistivity.
User Defined
For User defined select Isotropic, Diagonal, Symmetric, or Full depending on the characteristics of the electric conductivity, and then enter values or expressions for the electric 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.
Linearized Resistivity
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:
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1 Ω⋅m for the Reference resistivity
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273.15 K for the Reference temperature, and
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0 1/K for the Resistivity temperature coefficient
Constitutive Relation D-E
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.
Note that the Current Conservation in Fluids feature only supports the Relative permittivity and Polarization dielectric constitutive relations.
For a description of the constitutive relations Relative permittivity, Polarization, and Remanent electric displacement, see Constitutive Relation D-E as described for the Charge Conservation node for the Electrostatics interface. The constitutive relations specific to Electric Currents are:
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Dielectric losses: uses the constitutive relation D = ε0(ε' − jε")E. Specify that the Relative permittivity (real part) ε' (dimensionless) and the Relative permittivity (imaginary part) ε" (dimensionless) must be taken From material or be User defined. For User defined, select Isotropic, Diagonal, Symmetric, or Full and enter values or expressions in the field or matrix. The default is 1. Note that the material parameters Relative permittivity (real part) ε' and the Relative permittivity (imaginary part) ε" form the complex relative permittivity εr = ε' – jε''. The time-harmonic Sign Convention requires a lossy material to have a positive material parameter ε''.
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Loss tangent, loss angle: uses the constitutive relation D = ε0ε'(1 − jtanδ)E. Specify the Relative permittivity (real part) ε' (dimensionless) and Loss angle δ (SI unit: rad).
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Loss tangent, dissipation factor: uses the constitutive relation D = ε0ε'(1 − jtanδ)E. Specify the Relative permittivity (real part) ε' (dimensionless) and the Dissipation factor tanδ (dimensionless).
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Dispersion to use the constitutive relation D = ε0E + P(E, εrS), where the polarization vector is calculated from the electric field using the dielectric dispersion model. You enter the Relative permittivity εrS (dimensionless) values From material.  For User defined, select Isotropic, Diagonal, or Symmetric and enter values or expressions in the field or matrix. This value of electric permittivity will be used in stationary study, for which the polarization vector is calculated as P = ε0(εrS − Ι)E.
Once this option is selected, a subnode Dispersion becomes available under the Current Conservation node. At that subnode, you can select the dispersion model, enter the corresponding parameters, and choose how the relative permittivity input on the parent node will be interpreted in Eigenfrequency, Frequency Domain, and Time Dependent studies.
In COMSOL versions 6.3 and earlier, the Dispersion option is available only when the Material type is set to Solid.