经典电动力学中的补偿自由源与束缚源及非辐射条件
Compensated Free and Bound Sources and Nonradiating Conditions in Classical Electrodynamics
- Center for Magnetism and Magnetic Nanostructures, University of Colorado, Colorado Springs（科罗拉多大学科泉分校磁性及磁性纳米结构中心）
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中文总结 AI 辅助
本文研究经典电动力学中自由与束缚源补偿导致的非辐射条件，通过中和极化球体等例子，证明完整四电流相消是唯一永不辐射的紧支撑电流选择，并指出辅助场不能独立携带辐射。
中文摘要 AI 辅助
经典宏观电动力学允许自由源和束缚源作为分布相消，而辅助方程仍保留非零的自由源项。一个中和的均匀极化球体具有$\mathbf{E}=\mathbf{0}$和$\mathbf{D}=\mathbf{P}$，一个补偿的均匀磁化球体具有$\mathbf{B}=\mathbf{0}$和$\mathbf{H}=-\mathbf{M}$。这些辅助场由$\mathbf{P}$和$\mathbf{M}$确定，而非形成独立的自由度。时间依赖性将电荷相消与完整的四电流相消区分开来。仅相消电荷会留下一个无散的总电流，其壳上横向变换控制辐射。对于半径为$R$、由切向自由电流片维持的中和极化球体，外部场等于一个点电偶极子的场，其有效矩正比于球贝塞尔函数$j_2(kR)$，其中$k=\omega/c$。所有电荷多极子和普通磁偶极子都消失，但源在一般频率下辐射，且完整外部场在$j_2$的非零根处消失。完整的四电流相消移除所有延迟的源生成场。在保持相同电荷的紧支撑可分离电流中，它是唯一永不辐射的选择。在真空中，辅助场简化为$\mathbf{D}=\varepsilon_0\mathbf{E}$和$\mathbf{H}=\mathbf{B}/\mu_0$，因此$\mathbf{D}$和$\mathbf{H}$单独不能携带辐射。
英文摘要
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.
