  In this work we further advance theoretical investigation of radiation by the
electric dipole under the assumption that wavelength is much smaller than
charge separation distance of an electric dipole, which in turn is much smaller
than a distance up to the point of observation. The electric dipole considered
in this paper is the one with fixed charge positions, but oscillating charge
magnitudes. Specifically, two cases were considered. In the first case phase
delay between oscillations of the charge magnitudes was taken into account. In
the second case, opposite current wave travel direction was considered. These
results generalize the classical solution for electric dipole radiation, and
they show that under the above assumptions the electric dipole emits both
long-range longitudinal electric and transverse electromagnetic waves.
Longitudinal and transverse electric fields emitted by the electric dipole with
current wave traveling in both directions are displayed for specific values of
the dipole system parameters. It was shown that under the standard assumptions
that charge separation distance is much smaller than wavelength and non-zero
phase delay between charge oscillations: a) our solution reduces to classical
solution; b) transverse electromagnetic waves are dominant while longitudinal
electric waves are negligible; c) total radiated power is proportional to the
fourth degree of frequency and to the second degree of the charge separation
distance. In case wavelength is much smaller than charge separation distance:
a) the classical solution is invalid and it overestimates the total radiated
power; b) longitudinal electric waves are dominant and transverse
electromagnetic waves are negligible; c) total radiated power is proportional
to the third degree of frequency and to the charge separation distance. All
derived potential and force fields were summarized in the table.
