Electrostatics (es)

Electric field and potential in dielectrics. Elmer StatElecSolver.

Category

AC/DC › Electric Fields and Currents

Name (tag)

es

Space dimensions

3D, 2D, 2D axisymmetric

Studies

Stationary, Time Dependent

Dependent variables

V Electric potential (V)

Default features

Charge Conservation, Initial Values, Zero Charge

\(-\nabla\cdot(\varepsilon_0\varepsilon_r\nabla V) = \rho_V\)

Material properties used: Relative permittivity (εᵣ).

Interface settings

Setting Symbol Unit Default Choices / type

Discretization

Element order

Quadratic

Linear, Quadratic

Elmer Solver

Additional Elmer solver keywords
Lines appended verbatim to this interface’s Solver section in the .sif file

Text (multi-line)

Domain features

Charge Conservation

Selection: Domains (all by default) · Physics ribbon › Domains, or right-click the interface in the Model Builder

\(\nabla\cdot\mathbf{D} = \rho_V,\quad \mathbf{E}=-\nabla V,\quad \mathbf{D}=\varepsilon_0\varepsilon_r\mathbf{E}\)

Setting Symbol Unit Default Choices / type

Constitutive Relation D-E

Relative permittivity

εᵣ

From material

From material, User defined

epsr

εᵣ

1

0

Expression

Space Charge Density

Selection: Domains · Physics ribbon › Domains, or right-click the interface in the Model Builder

\(\nabla\cdot\mathbf{D} = \rho_V\)

Setting Symbol Unit Default Choices / type

Space Charge Density

Space charge density

ρ_V

C/m^3

0

Expression

Initial Values

Selection: Domains (all by default) · Physics ribbon › Domains, or right-click the interface in the Model Builder

Setting Symbol Unit Default Choices / type

Initial Values

Electric potential

V

V

0

Expression

Boundary features

Ground

Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder

\(V = 0\)

No settings.

Electric Potential

Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder

\(V = V_0\)

Setting Symbol Unit Default Choices / type

Electric Potential

Electric potential

V₀

V

1[V]

Expression

Surface Charge Density

Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder

\(-\mathbf{n}\cdot(\mathbf{D}_1-\mathbf{D}_2) = \rho_s\)

Setting Symbol Unit Default Choices / type

Surface Charge Density

Surface charge density

ρₛ

C/m^2

0

Expression

Zero Charge

Selection: Boundaries (all by default) · Physics ribbon › Boundaries, or right-click the interface in the Model Builder

\(\mathbf{n}\cdot\mathbf{D} = 0\)

No settings.

Result variables

Name Description Unit

V

Electric potential

V

es.E

Electric field

V/m

es.normE

Electric field norm

V/m

es.Ex

Electric field, x component

V/m

es.Ey

Electric field, y component

V/m

es.Ez

Electric field, z component

V/m

es.normD

Electric displacement field norm

C/m^2

es.We

Electric energy density

J/m^3