{
  "abstract": "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29506",
  "author_total": 1,
  "authors": [
    {
      "name": "Natan Rentzber"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c0mwhr4bwx39r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29506",
  "fulltext_url": null,
  "id": "c0mwhr4bwx39r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29506",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.class-ph"
    ],
    [
      "openalex",
      "3107|Quantum and Classical Electrodynamics"
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  ],
  "openalex": "W7214324074",
  "pdf_url": "https://arxiv.org/pdf/2609.29506",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c0mwhr4bwx39r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.29506",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29506"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3107|Quantum and Classical Electrodynamics",
      "subfield": "amo"
    }
  ],
  "title": "Compensated Free and Bound Sources and Nonradiating Conditions in Classical Electrodynamics",
  "title_text": "Compensated Free and Bound Sources and Nonradiating Conditions in Classical Electrodynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/c0mwhr4bwx39r",
  "venue": "arXiv",
  "versions": []
}