Poynting Vector and Energy Density

We give the formula for the Poynting Vector and an example of how to use it in calculations, as well as discuss the energy density contained within a region that contains electromagnetic fields.

[@williamwalker39]

The Poynting vector has a problem in the nearfield of a dipole source. It can be shown that by setting the wave equation equal to a oscillating charge, that the transverse electric field component is generated outside the source at about 1/4 wavelength and launches waves both toward and away from the source, whereas the other components: longitudinal electric field and transverse magnetic field.are created at the source and propagate away from the source. The problem with using the Poynting vector in the nearfield is that it hides the fact that some of the energy is going back into the source and some is propagating away from the source, which cancel, creating no net energy flow in the nearfield, but energy flow in the farfield. Whereas in reality there is energy flow in the nearfield if one isolates each the individual field component terms, which can be done with a suitable dectector. Analyzing the individual field terms shows that the speed of the fields are instantaneous in the nearfield and reduces to about the speed of light in the farfield, at about 1 wavelength from the source. This corresponds to the phase speed, group speed, and information spees. Since the energy is proportional to the square of the field, then the energy is propagating at the group speed, which as I mentioned is instantaneous in the nearfield and reduces to about the speed of light in the farfield, at about 1/4 wavelength from the source. For more information see my paper: arxiv.org/abs/physics/0603240 The consequences of these results are discussed in my KZbin video presentation, and the paper it is based on: *KZbin presentation: kzbin.info/www/bejne/qZazlX1tq7iErLM *Based on this paper: vixra.org/abs/2309.0145 Here is our most recent paper which experimentally demonstrates an EM pulse propagates instantaneously in the nearfield: *Electromagnetic pulse experiment paper: www.techrxiv.org/doi/full/10.36227/techrxiv.170862178.82175798/v1