arXiv subjects

Natan Rentzber

Publications and source records attributed to Natan Rentzber.

3 recordsLinked to original sources

arXiv2026

Compensated Free and Bound Sources and Nonradiating Conditions in Classical Electrodynamics

Classical macroscopic electrodynamics allows free and bound sources to cancel as distributions while the auxiliary equations retain nonzero free-source terms. A neutralized uniformly polarized sphere has $\mathbf{E}=\mathbf{0}$ and $\mathbf{D}=\mathbf{P}$, and a compensated uniformly magnetized sphere has $\mathbf{B}=\mathbf{0}$ and $\mathbf{H}=-\mathbf{M}$. These auxiliary fields are fixed by $\mathbf{P}$ and $\mathbf{M}$ rather than forming independent degrees of freedom. Time dependence separates charge cancellation from complete four-current cancellation. Canceling the charge alone leaves a divergence-free total current whose on-shell transverse transform controls radiation. For a neutralized polarized sphere of radius $R$ maintained by a tangential free-current sheet, the exterior field equals that of a point electric dipole whose effective moment is proportional to the spherical Bessel function $j_2(kR)$, where $k=ω/c$. Every charge multipole and the ordinary magnetic dipole vanish, yet the source radiates at generic frequencies, and the complete exterior field vanishes at nonzero roots of $j_2$. Complete four-current cancellation removes all retarded source-generated fields. Among the compactly supported separable currents that maintain the same charge, it is the only choice that never radiates. In vacuum the auxiliary fields reduce to $\mathbf{D}=\varepsilon_0\mathbf{E}$ and $\mathbf{H}=\mathbf{B}/μ_0$, so no radiation can be carried by $\mathbf{D}$ and $\mathbf{H}$ alone.

physics.class-ph↗

arXiv2026

Electromagnetic Radiation from a Neutralized Polarized Sphere with Two Conserved Currents for One Charge History

Can a source radiate when its total charge density vanishes identically? Consider a uniformly polarized sphere coated with free surface charge that cancels the bound surface charge at every point and time. Then $ρ_{\mathrm{tot}}=0$, so every electric charge multipole vanishes. Continuity determines only $\nabla\cdot\mathbf{J}$, which allows the same charge history to be supported by different conserved currents. A compensating interior current gives $\mathbf{J}_{\mathrm{tot}}=\mathbf{0}$ and produces no $\mathbf{E}$ or $\mathbf{B}$ at any frequency. The minimum-norm tangential sheet current instead leaves $\mathbf{J}_{\mathrm{tot}}$ nonzero and divergence-free. Its radiation-zone field is exact in $kR$ and proportional to $j_2(kR)$. At long wavelength the radiated power is suppressed by $(kR)^4/100$, and it vanishes exactly at the positive roots of $j_2$. The same calculation gives the interior field and a closed-form energy balance. The average work supplied by driving equals the radiated power and falls to zero at those roots even though interior fields remain. For comparison, the bare sphere has the factor $3j_1(kR)/(kR)$ and is silent at the roots of $j_1$.

physics.class-ph↗

arXiv2026

Scalar-Longitudinal Radiation in Extended Electrodynamics with Multipole Theory and a Compensated Source Model

Extended electrodynamics (EED) leaves the Lorenz gauge condition unimposed and treats the scalar combination $C=\nabla\cdot\mathbf{A}+c^{-2}\partialΦ/\partial t$ as a dynamical field. For a conserved source with no scalar initial field, $C=0$ and the theory reduces to classical electrodynamics. A source with a nonzero local continuity anomaly has no Maxwell solution, but EED remains well posed and can support a scalar-longitudinal sector. For each radiating frequency of a localized source, the far field separates into the usual transverse Maxwell channel and a scalar-longitudinal channel with a longitudinal electric field, no magnetic field of its own, and a co-propagating $C$ field. Under the field-only energy balance used here, the time-averaged fluxes add without interference. The scalar channel depends only on $Λ=\partialρ/\partial t+\nabla\cdot\mathbf{J}$ and radiates when its moments at $k=ω/c$ are nonzero. An all-orders multipole formula is derived for this flux. Bound polarization and magnetization sources conserve charge identically and cannot excite the scalar channel. A compensated polarized carrier with a globally neutral anomalous surface layer isolates the channel and gives its dipole flux in closed form. The connection between the adopted flux and a physical stress-energy tensor remains unresolved. These results are conditional predictions of EED and do not imply a failure of charge conservation in classical electrodynamics.

physics.class-ph↗