<math> \mathbf{H(r)} = \frac{1}{\mu} \nabla \times \mathbf{A} (\mathbf{r})</math>
== Defining the Physical Structure in EM.Ferma ==Â The simplest static problems involve a charge source in the free space that produces an electric field, or a current source in the free space that produces a magnetic field. In such cases, the only applicable boundary conditions are defined at the computational domain boundary. As soon as you introduce a dielectric object next to a charge source or a magnetic (permeable) material next to a current source, you have to deal with a complex boundary value problem. In other words, you need to solve the electric or magnetic Poisson's equation subject to the domain boundary conditions as well as material interface boundary conditions. EM.Ferma used the Finite Difference technique for numerical solution of your static boundary value problem. Â === A Note on Material and Source Types in EM.Ferma ===
In [[EM.Cube]]'s other modules, material types are specified under the "Physical Structure" section of the Navigation Tree, and sources are organized under a separate "Sources" section. In those modules, the physical structure and its various material types typically represent all the CAD objects you draw in your project. Sources are virtual entities that might be associated with certain physical objects and provide the excitation of your boundary value problem.
In [[EM.Cube]]'s Static Module, materials and sources are all listed under the "Physical Structure" section of the Navigation Tree, and there is no separate "Sources" section. For example, you can define default zero-potential perfect electric conductors (PEC) in your project to model metal objects. You can also define fixed-potential PEC objects with a nonzero voltage, which can effectively act as a voltage source for your boundary value problem. In this case, you will solve the Lapalce equation subject to the specified nonzero potential boundary values. Both types of PEC objects are defined from the same PEC node of the Navigation Tree by assigning different voltage values. Charge and current sources are defined as CAD objects that you must draw in the project workspace.
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== Defining the Physical Structure in EM.Ferma ==
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The simplest static problems involve a charge source in the free space that produces an electric field, or a current source in the free space that produces a magnetic field. In such cases, the only applicable boundary conditions are defined at the computational domain boundary. As soon as you introduce a dielectric object next to a charge source or a magnetic (permeable) material next to a current source, you have to deal with a complex boundary value problem. In other words, you need to solve the electric or magnetic Poisson's equation subject to the domain boundary conditions as well as material interface boundary conditions. EM.Ferma used the Finite Difference technique for numerical solution of your static boundary value problem.
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For static analysis, the model can be excited with any number of Voltage Sources, Charge Sources, or Current Sources. For Quasistatic analysis, only Voltage Sources are of practical use.