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arXiv · 2512.18486

Uniqueness Theorem: With Normal Components Specified on External Spherical Surface

Rajavardhan Talashila
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Abstract

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.

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Rajavardhan Talashila. 2025-12-20. Uniqueness Theorem: With Normal Components Specified on External Spherical Surface. https://arxiv.org/abs/2512.18486

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