Steady State AC Electric: solved equations
Introduction
In a Steady state AC Electric application the equations used for computation are:
 the corresponding Maxwell's equations for an electrical system, and
 the constitutive equation that characterizes the dielectric materials
The conditions of computation of a Steady state AC Electric application are the following:
 the computation concerns the D and E fields; the B and H fields are not computed. The equations of the electric fields E, D and of the magnetic fields B, H are decoupled.
 the fields are harmonic time dependent of the pulsation ω. In the complex form of the equations, the operator ∂/∂t is replaced by the multiplicator jω
Equations and conditions
In the previously defined conditions of computation, the equations in complex form are summarized as follows:
⇒ 

E : electric field strength (in V/m) D : electric flux density (C/m^{2}) V : electric potential (in V) J : current density (in A/m^{2}) 

⇒  σ : conductivity (in S) ε_{r} : relative permittivity ε_{0} : vacuum permittivity (in F/m) 
Reminder about the differential operators: The curl divergence of a field is always null: div [rot (Field)] = 0.
Solved equation
The second order equation solved by the finite elements method in Flux in case of a Steady state AC Electric application is the following:
where:
 [σ] is the tensor of the conductivity of the medium (in Siemens),
 [ε_{r}] is the tensor of the relative permittivity of dielectric materials
 ε_{0} is the vacuum permittivity; ε_{0} = 1/(36 π 10^{9}) (in F/m)
 V is the electric potential (in V)
State variable
The state variable in a Steady state AC Electric application is the electric potential V (written Ve in Flux 3D). It is a complex quantity.
The uniqueness condition of the scalar field of the complex electric potential V requires that the value of this potential at least in a point of the computation domain be known.
Complex permittivity
The permittivity ε is a complex quantity that takes account of the frequency:
[ε] = [ε'] j [ε'']
where:
 [ε'] stands for the real permittivity, and

[ε''] stands for the dielectric losses constant:
[ε''] = [ε'] tg δ_{h} (with δ_{h} angle of hysterezis losses)
The second order equation solved by the finite elements method in Flux in case of a Steady State AC Electric application is the following: