Generally, electromagnetic fields can be categorized into three groups: static fields, quasi-static fields and coupled electromagnetic fields. Only coupled electromagnetic fields require the full set of Maxwell's equations to be solved. In the case of static and quasi-static fields simplifications apply.
We can distinguish between electrostatic fields produced by non-moving charges and magnetostatic fields caused by steady currents. In the static case electric and magnetic fields are decoupled. Static field problems are therefore the least complex.
In the electrostatic case only electric fields exist. The magnetic fields are zero. The electric fields are caused by charges and can be described most efficiently by the scalar electric potential ϕ as seen in Section 2.1.1. Maxwell's coupled partial differential equations reduce to a second order differential equation (Poisson's equation).
Software tools for electrostatic problems usually look for solutions of Poisson's equation and calculate the electric field strength from the scalar electric potential by using the gradient operator (see Equation 2.8).
In the case of magnetostatic fields from steady currents we will first calculate the steady current density distribution in conductive media; that is, we solve the electric part of the problem. In the second step ...