A numerical method based on the Green＇s function (the potential theory) approach is adapted for computation of the electric fields in electrodynamic balances. The accuracy of the method is checked against analytical solutions for the case of a single torus and excellent agreement is found. Explicit numerical results for a typical double-ring balance are obtained. The method is an improvement over the existing ＇＇charge simulation technique＇＇ which, although often adequate, is not rigorously founded. Additionally, the equations of particle motion are solved using the numerically precise electric fields (rather than the linearized fields). Overall, the rigor of potential theory is combined with the computational/display power of Mathematica (R) to provide accurate descriptions of the electric fields and the particle motion. Use of Mathematica (R) also leads to the simple computation of particle stability diagrams.