# Long-Range Longitudinal Electric Wave in Vacuum Radiated by Electric Dipole: Part III

## TL;DR

This paper investigates the radiation emitted by an electric dipole under specific assumptions, revealing that it emits both long-range longitudinal electric and transverse electromagnetic waves, with detailed calculations for various system configurations.

## Contribution

It demonstrates that electric dipoles can emit both longitudinal and transverse waves, expanding understanding of dipole radiation beyond traditional electromagnetic wave emission.

## Key findings

- Electric dipoles emit long-range longitudinal electric waves.
- Both systems with and without charge oscillations produce these waves.
- Quantitative analysis of radiated power and radiation resistance.

## Abstract

In this paper, radiation due to standing wave currents are considered for the electric dipole. Assumptions that wavelength is much smaller than the dipole separation distance, which in turn is much smaller than the distance to the point of observation, were employed. Results indicate that the electric dipole, which now essentially is a linear antenna, emits both long range longitudinal electric and transverse electromagnetic waves. Two systems were considered: electric dipole with and without charge oscillations at its ends. Each system was further divided into two sub-systems: with even and odd number of half-wavelengths. For specific values of the system, longitudinal electric and transverse electromagnetic waves, total radiated power, longitudinal to transverse power ratio and radiation resistance were calculated and depicted.

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Source: https://tomesphere.com/paper/1901.09166