The Maxwell Equations are a set of four fundamental equations that, along with the Lorentz Force Law, govern electric and magnetic fields:
See also Wikipedia:Maxwell’s_equations for more details.
SIMION assumes that the time-varying terms (t) in these equations are negigible, which is acceptable for static or so-called low frequency fields–for details see Time-Dependent Field. Gauss’s Law forms the basis of the Laplace Equation and Poisson Equation used by SIMION Refine for E fields. They also apply to the treatment of Magnets.