## Electrokinetic (DC)

The electro-kinetic solution, also called 'DC Conduction Steady State', describes the distribution of static electric current in conductors.

## Features

• 2D, 3D or axisymmetric Solution, static
• Plot: Scalarpotential, Electric Fieldstrength, Current Density, Eddy Current Losses Density.
• Table: Ohm Resistance, Electrode Voltage, Electrode Current, Eddy Current Losses.
• Coupled Thermal: Temperature.

## Theory and Basics

### Formulations

The basis equations:
(1)        rot e = 0
(2)        div j = 0
(3)        j = σ e

Boundary conditions:
(4)        n x e  | Γ0e = 0
(5)        n * j  | Γ0j = 0

Electric scalar potential formulation for the conducting region:
(6)        div σ grad v = 0 with

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

### Basic Example: Ohm Resistance of Circular Plate

In this example we analyze for the ohm resistance in a circular plate. The simulated electric current density is shown in the following picture.

### Results

Analytic and numerical Results

Mesh:
Elements: 5406
Nodes: 11074

Analytic Result:
R = 1.08108e-5 Ohm

Numerical Result
R = 1.069698e-5 Ohm

Deviation: 0.089%

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