Electro Static: solved equations
Introduction
In an Electro Static application the equations used for computation are:
- the corresponding Maxwell's equations for an electrical system, and
- the constitutive equations that characterize the dielectric materials
The conditions of computation of an Electro Static 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 D, E and of the magnetic fields B, H are decoupled.
- the fields are time independent (static): d/dt = 0
- the current density is null: J = 0
Equations and conditions
In the previously defined conditions of computation , the equations are summarized as follows:
| Equations | Description | |
|---|---|---|
|
|
E: electric field strength (in V/m) D: electric flux density (in C/m2) V: electric potential (in V) q: density of electric charges (in C/m3) |
|
 |
εr : relative
permittivity ε0 : vacuum permittivity (in F/m) |
Solved equation
The second order equation solved by the finite element method in Flux in case of an Electro Static application is the following:
where:
-
is the tensor of relative permittivity of
the medium - ε0 is the permittivity of the vacuum; ε0 = 1/(36π109) (in F/m)
- V is the electric potential (in V)
- q is the density of electric charges (in C/m3)
State variable
The state variable of the Electro Static application is the electric potential V (written Ve in Flux 3D).
The uniqueness condition of the scalar field of the electric potential V requires that the value of this potential be assigned to at least one point of the computation domain.