2022/01/20 by Nikita A. Nemkov, Nemkov, Nikita, V.A. Fedotov +1
Engineering · Physics and Astronomy · #Energy Harvesting in Wireless Networks #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Optics (physics.optics) #Radio Astronomy Observations and Technology #Underwater Vehicles and Communication Systems
paper · pdf · doi:10.48550/arxiv.2201.08333
openalex publication_date 2022/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The time derivative of the charge density is linked to the current density by the continuity equation. However, it features only the longitudinal part of a current density, which is known to produce no radiation. This fact usually remains unnoticed though it poses a seemingly serious paradox, suggesting that the temporal variation of a charge density should be also irrelevant for radiation. We resolve this paradox by showing that the effective longitudinal currents are not spatially confined even when the time-dependent charge density that generates them is. This enforces the co-existence of the complementary (i.e. transverse) part of the current density through the Helmholtz decomposition. We illustrate the mechanics of the underlying non-locality of the Helmholtz decomposition in the case of a dynamic electric dipole, discussing its practical implication for underwater antenna communications. More generally, we explain the role of the Helmholtz decomposition in shaping the structure of the conventional multipole expansion.