1. Model: Electric sensor

2. Introduction
By adding a voltage to a box containing different materials and measuring the surface charge density, we can see what shapes the materials have from the outside of the box.
This can be used as an electric sensor to check movements and shapes of elements inside a domain.

3. Geometry
The geometry of this model is a box containing two different shaped figures.
The objects, made by extruding 2D geometries, are surrounded by air.

4. Domain Equations
To solve an electrostatic problem we solve Gauss’ law.
The different materials have different values of the relative permittivity, e . For the surronding air the value is 1. The objects in the box have the value 2 and 3 respectivley. r

5. Boundary Conditions V=1 V=0
There is a potential variation in the box. Setting the condition on the bottom boundary to ground and on the top boundary to V=1. All the other boundaries are insulated.

6. Results
When plotting the surface density we can see a shadow of the figures on the surface of the box.
The plot also shows how the potential varies through the geometry.