## Electrostatics

The electrostatic solution describes the distribution of electric fields due to static charges and / or levels of electric potential.

## Features

• 2D, 3D or axisymmetric Solution, static
• coupled with Thermal solution possible
• Outputs Plot:
• Electric Fluxdensity, Electric Fieldstrength, Electric Potential (phi-Pot)
• Outputs Table:
• Capacity, Electrode Voltage, Electrode Charge

## Theory and Basics

### Formulations

The basis equations:
(1)           rot e = 0
(2)           div d = ρ
(3)           d = ε e

Boundary conditions:
(4)        n x e  | Γ0e = 0
(5)        n * d  | Γ0d = 0

Electric scalar potential formulation:
(6)        div ε grad v = - ρ with

Electrostatic weak v-formulation:
for all v’ element of Ω

### Basic Example: Point and Cylinder

Given is a charge Qf that is applied to a cylindrical face. The face starts at the position (0,0,0) has an radius of R and a length of d. Further there is another charge Q being applied to a point, that is positioned on the axis of the cylinder and has a distance of a (a>d) from the origin. The hole space around has a constant permittivity of ε.

Goal is to analyze for the potential φ along the axis of the cylinder using the following parameters:
Q  =        1e-9 As
Qf=         1e-7 As
a =          0.35 m
d =          0.1 m
R =          0.1 m
ε =          8.85419e-12 F/m

### Result: Potential φ

The comparison gives good agreement between theory and numerical solution.

We use cookies on our website. Some of them are essential for the operation of the site, while others help us to improve this site and the user experience (tracking cookies). You can decide for yourself whether you want to allow cookies or not. Please note that if you reject them, you may not be able to use all the functionalities of the site.