# FEM EquationElectrostatic

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This equation perform electrostatic analyses using Gauss' law.

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

## Usage

1. After adding an Elmer solver as described here, select it in the tree view.
2. Now either use the toolbar button or the menu Solve → Electromagnetic Equations → Electrostatic equation.
3. 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:

• DataCalculate Capacitance Matrix: Calculates the capacitance matrix. The matrix contains the the point charges of the mesh knots.
• DataCalculate Electric Energy: Calculates the electric potential energy.
• DataCalculate Electric Field: Calculates the electric field.
• DataCalculate Electric Flux: Calculates the electric flux.
• DataCalculate Surface Charge: Calculates the surface charge.
• DataCapacitance Matrix Filename: File in which the capacitance matrix is being saved. It is only used if DataCalculate Capacitance Matrix is set to true.
• DataConstant Weights: If constant weighting for results is used.
• DataPotential Difference: Potential difference in Volt for which the capacitance is calculated. It is only used if DataCalculate 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.

## Constraint Information

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

### Note

Except for calculations in 2D, for electrostatic potential constraints it is important that they act on a face or body. Constraints for 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 DataCalculate * 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 ${\rm {J/m^{3}}}$ • Electric field in ${\rm {V/m}}$ • Electric flux in ${\rm {A\cdot s/m^{2}}}$ • Electric force density in ${\rm {N/m^{2}}}$ • Potential in ${\rm {V}}$ • Potential loads in ${\rm {C}}$   Electromagnetic equations Electricforce equation FEM 