# EM field lines in non-isotropic media

1. Sep 15, 2010

### Bak

Electromagnetic field lines in non-isotropic media

Hello,

We are using time domain reflectometry (TDR) in soils to measure soil moisture.

I want to know how the electromagnetic fields are oriented when the soil is not isotropic, i.e some parts of the soil consist of moist or wetter parts, other parts in the soil matrix consist of dry air gaps.

TDR: 2 metal rods of 10cm are placed parallel in soil material at a distance of about 3 cm. An electrical step pulse is applied to the rods. The EM wave travels along the rods with a velocity that is dependent on the constitution of surrounding material. At the end of the rods the wave is reflected by an impedance change and travels back. The total traveltime of the wave is then measured and is a measure of the permittivity and thereby of the moisture content of the soil. But not all soils happen to be isotropic. So what happens in non-isotropic soils?

If I understand the article of Annan, A.P. 1977, Time-Domain Reflectometry - Air gap problem for parallel wire transmission lines well, he assumes that the direction of the electric field is not biased by the medium (at least it is not mentioned in the paper).

1. I do not know how he comes to the entire solution, because only the last part of the derivation is mentioned in the paper. Can anybody help? I would like to know the entire derivation to be able to calculate other situations. Electro magnetic fields are not my daily routine.
2. I know that EM field directions can be biased by a ferro-like material like in a transformer. Is in that case the bias caused by EM induction in the metal by which one side of it becomes more positive charged than the other and thus changes the direction of the EM field?
3. Can it than be possible that moist soil does the same job, whereas de EM field lines concentration is larger at moist soil positions compared to the concentration in dry air gaps?
4. And doesn't that change the net effect of air gaps in the travel time of the electromagnetic field in the rods of the TDR?
5. Furthermore I am struggeling with the fact that electrons move relatively slow in the rods when a voltage is applied. When placed in vacuum however the EM wave travels with the speed of light. How can that be possible since it travels along the rods and is induced by the potential change. Can I assume that the electrons don't move at all, only at the biginning of the step at the beginning of the rods?
6. Am I correct when I say: extra electrons are pumped into the rods but cannot move; the step causes an EM wave to occur. This wave travels along rods (why in this direction? When the electrons cannot move I assume that at the beginning of the rods there is an overkill of electrons causing it to be a point charge?), reach the end of the rods, meet a different permittivity (not the soil, but the end of the rods) and thus reflect back to the beginning of the rods.
7. If electrons do move though, how are they related to the speed of the EM wave?

Thank you.

Last edited: Sep 16, 2010