EM Sandbox 2D is an interactive environment for exploring electrostatic potential distributions of a parallel plate capacitor in 2D. The project addresses the classical problem of finding steady-state scalar potential fields in heterogeneous media with prescribed boundary conditions. To solve this, the continuous domain is discretized on a uniform grid and the potential is computed using an iterative relaxation method: values at each grid point are updated repeatedly using weighted averages of neighboring cells that account for local dielectric contrasts. This Gauss-Seidel successive over-relaxation (SOR) converges robustly for typical configurations and is implemented in-place for memory efficiency. The solver supports fixed-potential boundaries and simple Neumann-like side treatments, while the application overlays a real-time visualization and controls for modifying geometries and material properties. The combination of a straightforward finite-difference discretization, an in-place iterative solver, and multiple relaxation steps per animation frame provides a responsive tool for teaching, rapid prototyping, and qualitative investigation of electrostatic phenomena in complex dielectric layouts.

An interactive playground is available here: em2d.mdshahriar.com. All the codes are available in GitHub.