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Description

For info about the math of the equation, see the Elmer models manual, section Electrostatics.

Usage

1. Add an Elmer solver.
2. Select it in the Tree view.
3. There are several ways to invoke the command:
   • Press the Electrostatic equation button.
   • Select the Solve → Electromagnetic Equations → Electrostatic equation option from the menu.
4. Change the equation's solver settings or the general solver settings if necessary.

Solver Settings

For the general solver settings, see the Elmer solver settings.

The electrostatic equation provides these special settings:

• DatiCalculate Capacitance Matrix: Calculates the capacitance matrix. The matrix contains the point charges of the mesh knots.
• DatiCalculate Electric Energy: Calculates the electric potential energy.
• DatiCalculate Electric Field: Calculates the electric field.
• DatiCalculate Electric Flux: Calculates the electric flux.
• DatiCalculate Surface Charge: Calculates the surface charge.
• DatiCapacitance Matrix Filename: File in which the capacitance matrix is being saved. It is only used if DatiCalculate Capacitance Matrix is set to true.
• DatiConstant Weights: If constant weighting for results is used.
• DatiPotential Difference: Potential difference in Volt for which the capacitance is calculated. It is only used if DatiCalculate Capacitance Matrix is set to false. Therefore in fact this setting specifies the voltage between the electrodes of a simple capacitor. Note that the given voltage has to be consistent with the potentials defined in the boundary conditions.

Analysis Feature Information

The electrostatic equation takes the following analysis features into account if they are set:

• Electrostatic potential boundary condition
• Electric charge density - introduced in 1.1
• Constant vacuum permittivity

Note

Except for calculations in 2D, for electrostatic potential boundary conditions it is important that they act on a face or body. Boundary conditions in 3D set to lines or vertices are not recognized by the Elmer solver.

Results

The available results depend on the solver settings. If none of the DatiCalculate * settings was set to true, only the electric force density and the electric potential are calculated. Otherwise also the corresponding results will be available.

The possible results are:

• Electric energy density in ${\displaystyle {\rm {J/m^{3}}}}$
• Electric field in ${\displaystyle {\rm {V/m}}}$
• Electric flux in ${\displaystyle {\rm {A\cdot s/m^{2}}}}$
• Electric force density in ${\displaystyle {\rm {N/m^{2}}}}$
• Potential in ${\displaystyle {\rm {V}}}$
• Potential loads in ${\displaystyle {\rm {C}}}$