My question concerns electromagnetic (EM) wave propagation.

[lost_in_space]

my question concerns electromagnetic (EM) wave propagation.

consider a two layer medium where the first layer has constant conductivity $\sigma_0$ and the second layer constant conductivity $\sigma_1$. If a EM wave propagates from the first medium into the second one boundary conditions have to be imposed at the interface.


Is it important to take this conditions into acount (i.e. can i ignore them) if i have a low frequency EM wave ?

 

[Born2bwire]

Yes, for the most part always. The change in material properties at the interface means that you will have reflection and refraction. In addition, the change in conductivity means that the attenuation will change between the two mediums. Even a modest conductivity greatly affects very low frequency waves. Wikipedia gives sea water as 4.8 mhos/m. That is a far cry from the conductivity of copper which is on the order of 10^8. But that is still enough that we needed to use ELF (~3-30 Hz) to communicate with submarines underwater. In fact, let's take the extreme of ELF, 30 Hz, and we find that the skin depth is around 40 m. So you have to go very very very low frequency and even then the skin depth is still of a very short distance (especially when you consider that the wavelength of 30 Hz is 10,000 km).

It still boils down to the electrical distances over which you are observing the wave, but as you can see with our salt water example the behavior can still change rapidly over a very small fraction of the wavelength. Now in terms of refraction and reflection, that may not be as significant depending upon the relative contrasts of the materials.

 

[lost_in_space]

Yes, for the most part always. The change in material properties at the interface means that you will have reflection and refraction. In addition, the change in conductivity means that the attenuation will change between the two mediums. Even a modest conductivity greatly affects very low frequency waves. Wikipedia gives sea water as 4.8 mhos/m. That is a far cry from the conductivity of copper which is on the order of 10^8. But that is still enough that we needed to use ELF (~3-30 Hz) to communicate with submarines underwater. In fact, let's take the extreme of ELF, 30 Hz, and we find that the skin depth is around 40 m. So you have to go very very very low frequency and even then the skin depth is still of a very short distance (especially when you consider that the wavelength of 30 Hz is 10,000 km).

It still boils down to the electrical distances over which you are observing the wave, but as you can see with our salt water example the behavior can still change rapidly over a very small fraction of the wavelength. Now in terms of refraction and reflection, that may not be as significant depending upon the relative contrasts of the materials.

thank you very much for the detailed answesr.

my question otginates from the field of medical imaging. To be more precise in MRI nuclei are excited (placed in static magnet field and then are influenced by another EM pulse) so that they will emit a radio frequency wave... this wave propagates outward and is detected ... i never saw that boundary conditions were imposed to describe the propagation of this RF wave when it leaves the body and travels through air until it reaches a measuring coil

on the other hand: in microwave imaging objects are placed inside a bolus (salt water that has nearly the same conductivity as the body), inside this bolus there are transmitting and receiving antennas. what i get from papers there is that they place the object inside this bolus in order to avoid distortions in microwave propagation. (bolus has the same role as the contact fluid in ultrasound imaging i guess)...

Radio frequency is lower than microwave frequency, so i thought the reason why boundary conditions are neglected in MRI is this lower frequency...