Maxwell Equations

The Maxwell Equations are a set of four fundamental equations that, along with the Lorentz Force Law, govern electric and magnetic fields:

\bnabla \cdot \vec{E} = \rho/\epsilon_0 \textrm{ or } \bnabla \cdot \vec{D} = \rho_f
\textrm{ (Gauss's Law)}

\bnabla \cdot \vec{B} = 0
\textrm{ (Gauss's Law for Magnetism)}

\bnabla \times \vec{E} = - \frac{\partial \vec{B}}{\partial t}
\textrm{ (Faraday's law of induction)}

\bnabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t} \textrm{ or }
\bnabla \times \vec{H} = \vec{J_f} + \frac{\partial \vec{D}}{\partial t}
\textrm{ (Amp\`{e}re's law)}

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.

See Also