# [Getdp] Eddy Current, how?

Patrick Dular Patrick.Dular at ulg.ac.be
Fri May 30 16:51:58 CEST 2008

```Dear Bernhard,

You are right, the electric field in the nonconducting region has other
components. Actually, the electric field in the nonconducting regions is
not obtained from the solution of an eddy current problem; this problem
does not contain enough information for that. If you need the electric
field in some non-conducting regions, you have to solve another problem
with the trace of the electric field (its tangential component) on the
boundary of each conductor as a boundary condition for the exterior
nonconducting region. The equations of this problem will be the Faraday
equation (curl e = -db/dt; with b known from the eddy current problem)
and the Gauss law (div d = ro), with d = eps e (eps is the electric
permittivity). This decoupling of magnetic and electric problem is only
correct for low frequencies. For higher frequencies, you have to iterate
between these problems or to work directly with the full Maxwell system.

Dual Finite Element Formulations for the Three-dimensional Modeling of
both Inductive and Capacitive Effects in Massive
Inductors,

P. Dular, P. Kuo-Peng,
IEEE Transactions on Magnetics, Vol.42, No.4, 2006, pp. 743-746.

Kind regards,

Patrick

Bernhard Kubicek wrote:

>Dear Group,
>I want to simulate some eddy current problem.
>
>The system is 2D and made from multiple conductors, e.g. two rectangles
>that are close together, in a big surrounding air region. In one
>rectangle, the current flows in one direction, in the other the same
>current returns.
>How would I simulate this?
>I mean, in a single conductor, one would probably use a scalar nodal
>value to have the electric field in the axial direction. And solve
>Laplace[E_z]=mu conductivity Dt[E_z] with a boundary condition of eg.
>setting Ez(centerpoint) to a fixed value.
>
>However, this is, if I understand it correctly, not valid in the
>surrounding air. Also, I get a big knot in my head thinking that the
>electric field would be in z-direction in the conductors, and outside
>not only in z-direction.
>
>So how would one simulate the interaction between the air-separated
>conductors ?
>using an h-based simulation in the conductors, and then using
>biot-savart from the current density to get the an new h on the boundary
>f the conductors?
>
>very nice greetings,
> bernhard
>
>
>
>
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>
>
>
>

--
Patrick Dular, Prof. Dr. Ir.,
Senior research associate (Maître de recherches) F.R.S.-FNRS
Department of Electrical Engineering and Computer Science
Unit of Applied and Computational Electromagnetics (ACE)
University of Liege - Montefiore Institute - B28 - Parking P32
B-4000 Liege - Belgium - Tel. +32-4 3663710 - Fax +32-4 3662910
E-mail: Patrick.Dular at ulg.ac.be

```