  In systems with non-local potentials or other kinds of non-locality, the
Landauer-B\"uttiker formula of quantum transport leads to replace the usual
gauge-invariant current density $\textbf{J}$ with a current $\textbf{J}^{ext}$
which has a non-local part and coincides with the current of the extended
Aharonov-Bohm electrodynamics. It follows that the electromagnetic field
generated by this current can have some peculiar properties, and in particular
the electric field of an oscillating dipole can have a long-range longitudinal
component. The calculation is complex because it requires the evaluation of
double-retarded integrals. We report the outcome of some numerical integrations
with specific parameters for the source: dipole length $\sim 10^{-7}$ cm,
frequency 10 GHz. The resulting longitudinal field $E_L$ turns out to be of the
order of $10^2$ to $10^3$ times larger than the transverse component (only for
the non-local part of the current). Possible applications concern the radiation
field generated by Josephson tunnelling in thick SNS junctions in YBCO and by
current flow in molecular nano-devices.
