# Electric field in the dielectric of a transmission line

The study of transmission lines is based on the existence of electromagnetic waves that propagate through the dielectric between conductors. This question is to identify which is the electric field that composes these waves together with the magnetic field.

Variable currents cause excess charge in the conductors, which surface as a separate charge. In a line of two parallel wires the surface charge on one and the other conductor is of different sign, this charge separation generates an electric field with lines from one conductor to the other.

On the other hand, free charges (neutralized with positive nuclei) accelerate and decelerate in the variable currents, thus emitting spherical electromagnetic waves. The composition of many of them forms an electric field in the dielectric.

There are two clearly distinguishable electric fields, one is generated by separate charges with field lines from one charge to another, and the other is generated by neutralized charges and is composed of waves.

The question is, which of the two fields is part of the electromagnetic waves mentioned at the beginning, is it a composition of both, is one of them negligible compared to the other?

Any help would be appreciated.

For the configuration of two wires a distance $$\bf a$$ apart, with charge per unit length $$\lambda$$, the only electric field is $$$${\bf E}=\frac{2\lambda({\bf r_\perp-a}/2)}{|{\bf r_\perp-a}/2)|^2} +\frac{2\lambda({\bf r_\perp+a}/2)}{|{\bf r_\perp+a}/2)|^2}.$$$$ This field propagates with $$e^{i(kz-\omega t)}$$.