The electric potential near two plates with fixed potential.
The Laplace Equation model uses the relaxation method to find the potential V(x,y) in a charge-free region bounded by conductors. The method of solving for V(x,y) is based on Laplace's equation which can be expressed in Cartesian coordinates as
The problem is to find the function V(x,y) that satisfies the Laplace's equation and the specified boundary conditions. This type of problem is an example of a boundary value problem. Because analytical methods for regions of arbitrary shape do not exist, the only general approach is to use numerical methods. Laplace's equation is not a new law of physics, but can be derived from the definition of electric potential in regions of space where there is no charge.
The following EJS models are described in Chapter 10 of the EJS adaptation of An Introduction to Computer Simulation Methods.
Additional models to be written.
The Laplace Equation model was created by Wolfgang Christian using the Easy Java Simulations (EJS) modeling tool version 4.2. You can examine and modify the model for this simulation if you have EJS installed by right-clicking within the program and selecting "Open Ejs Model" from the pop-up menu.
Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.