Question

I was wondering what the near-field expression of the Electric field for a cylindrical wave is. I know that in the case of a spherical wave, as shown in Jackson (9.18), the far field has a 1/r dependance, as expected for the energy to be conserved, and the near field has a 1/r³ dependance.

In the case of a cylindrical wave the Electric field in the far-field has a 1/sqrt(rho) dependance and I was wondering what the near-field dependance is.

I unsuccessfully attempted to reproduce Jackson's procedure for a cylindrical wave.

I then looked at a book by Roger Harrington considering an infinite fillament as a source. His fields are written in terms of the cylindrical Hankel functions of the first kind for both the infinite fillament case, as well as generally.

Based on his fields I get the Poynting vector from the corresponding Electric and Magnetic field expressions. By then considering the assymptotic form of the Hankel functions I get a 1/rho dependance, which is what one would expect for the far field (I get this dependance for both the assymptotic forms k * rho -->0 and k * rho-->infinity). It seems like by considering his procedure you cannot obtain the near-fields as I also followed and continued his case of a spherical wave and only got the 1/r far-field dependance.

While it seems like this should be a very simple problem I can't seem to find any literature mentioning it.

Answer 1

The near-field expression of the electric field for a cylindrical wave depends on the distance from the source and can be obtained by considering the electric field produced by an infinite filament as a source.

Step-by-step explanation:

The near-field expression of the electric field for a cylindrical wave depends on the distance from the source, but it does not have a simple 1/r^n dependence like in the far field. The near-field expression for a cylindrical wave can be obtained by considering the electric field produced by an infinite filament as a source. The fields can be written in terms of the cylindrical Hankel functions, and by considering the asymptotic form of these functions, you can obtain a 1/rho dependence for the electric field. This is similar to the far-field behavior, but it is important to note that the near field is not exactly the same as the far field.