# Transient Electric: solved equations

## Introduction

In a Transient 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 Transient Electric application are the following:

- the study is time depend: d/dt ≠ 0

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.

## Equations and conditions

In the previously defined conditions of computation, the equations are summarized as follows:

Reminder about the differential operators:The curl divergence of a field is always null: [div rot (Field)] = 0.

## Solved equation

The equation solved by the finite elements method in Flux in case of a Transient Electric application is the following:

where:

**σ**is the tensor of the conductivity of the medium (in Siemens),**ε**is the tensor of the relative permittivity of dielectric materials_{r}**ε**is the vacuum permittivity; ε_{0}_{0}= 1/(36 π 10^{9}) (in F/m)**V**is the electric potential (in V)

## State variable

The state variable in a Transient Electric application is the electric potential V (written Ve in Flux 3D).

The uniqueness condition of the electric potential V requires that the value of this potential at least in a point of the computation domain be known.