Simulate Charge Density in Matlab

[wusa]

Hey guys :)

How can I calculate the charge density with the PDE Toolbox, when I know the overall charge or the electrical potential of the areas? I want to know how the charges in two conducting spheres align when they are near to each other. I'm looking for a simple graphical way to play with this but I don't want to go deep into the physics or math behind it.

Can you help me? I just want to visualize electrostatic induction, but there's no preset in the toolbox for that...

Heres's a little image for you:

The red and the blue painting are the desired solution I want to create.

 

[Vailanor]

The best way to do this is by using the Finite Element Method (FEM). FEM is a numerical technique that allows you to solve complex equations, such as the Poisson equation, which governs the charge density in electrostatics. The PDE Toolbox provides functions for solving the Poisson equation. To use the PDE Toolbox, you need to define the geometry of your problem and then provide the boundary conditions. In your case, you need to specify the overall charge or electrical potential of the two conducting spheres. Then, the PDE Toolbox will compute the charge density in the regions around them.