Uniqueness Theorem: With Normal Components Specified on External Spherical Surface
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914212639408128 |
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| author | Talashila, Rajavardhan |
| author_facet | Talashila, Rajavardhan |
| contents | A uniqueness theorem for time-harmonic electromagnetic fields which requires the normal components of electromagnetic fields specified on a spherical surface is proposed and proved. The statement of the theorem is : "For a spherical volume $V$ that contains only perfect conductors and homogeneous lossless materials and for which the impressed currents $\mathbf{J}$ are specified, a time-harmonic solution to the Maxwell's equations within the volume, having outgoing waves alone, is uniquely specified by the values of the radial components of both $\mathbf{E}$ and $\mathbf{B}$ over the exterior spherical surface $V$ and the tangential components of either $\mathbf{E}$ or $\mathbf{B}$ on the interior surfaces." The proof of this theorem relies on the uniqueness of multipole expansion of electromagnetic fields outside the enclosing sphere. The conventional uniqueness theorem for the volume $V$ having loss-less materials is considered to be the case of lossy materials in the limit the dissipation approaching zero. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_18486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniqueness Theorem: With Normal Components Specified on External Spherical Surface Talashila, Rajavardhan Mathematical Physics A uniqueness theorem for time-harmonic electromagnetic fields which requires the normal components of electromagnetic fields specified on a spherical surface is proposed and proved. The statement of the theorem is : "For a spherical volume $V$ that contains only perfect conductors and homogeneous lossless materials and for which the impressed currents $\mathbf{J}$ are specified, a time-harmonic solution to the Maxwell's equations within the volume, having outgoing waves alone, is uniquely specified by the values of the radial components of both $\mathbf{E}$ and $\mathbf{B}$ over the exterior spherical surface $V$ and the tangential components of either $\mathbf{E}$ or $\mathbf{B}$ on the interior surfaces." The proof of this theorem relies on the uniqueness of multipole expansion of electromagnetic fields outside the enclosing sphere. The conventional uniqueness theorem for the volume $V$ having loss-less materials is considered to be the case of lossy materials in the limit the dissipation approaching zero. |
| title | Uniqueness Theorem: With Normal Components Specified on External Spherical Surface |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2512.18486 |