The AC power electromagnetics problems are found when studying motors, transformers, and conductors carrying alternating currents. The Helmholtz's equation
describes the propagation of plane electromagnetic waves in imperfect dielectrics and good conductors (σ » ωε). Here, ω is the angular frequency, ε is the coefficient of dielectricity, µ is the magnetic permeability, and σ is the conductivity. Complex permittivity εc is εc = ε-jσ/ω. The conditions at material interfaces with abrupt changes of ε and µ are typical for the variational formulation and do not require special attention.
The boundary conditions associated with AC power electromagnetics are a Dirichlet boundary condition, specifying the value of the electric field Ec on the boundary, and a Neumann condition, specifying the normal derivative of Ec. This is equivalent to specifying the tangential component of the magnetic field .
For details, see AC Power Electromagnetics Equations.
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Equations used by the PDE Modeler app in the AC Power Electromagnetics mode.