# TimeHarmonic¶

Type: | section |
---|---|

Appearance: | simple |

This section is used the describe an electromagnetic field problem in the frequency domain. This means that the electromagnetic field depends harmonically on time with an angular frequency . The relevant fields are replaced by complex phasors , , etc., related to the actual fields by

This allows to write Maxwell’s equations as

When splitting the electric current into the ohmic current and the impressed current , that is

the second equation reads as

with the complex permittivity tensor

In the context of time-harmonic problems the index ‘’ will be dropped and it should be kept in mind that the permittivity tensor is allowed to have complex-valued entries.

From this one obtains independent equations of second order for the electric and magnetic fields:

and