具有两个守恒电流的中性化极化球的电磁辐射（对应单一电荷历史）
Electromagnetic Radiation from a Neutralized Polarized Sphere with Two Conserved Currents for One Charge History
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中文总结 AI 辅助
研究总电荷密度为零的源能否辐射，以中性化极化球为对象，分析两种守恒电流的辐射特性，发现最小范数切向面电流可产生与j₂(kR)成正比的辐射，在长波长下功率受抑，在j₂正根处辐射为零，且与裸球辐射特性不同。
中文摘要 AI 辅助
当源的总电荷密度恒为零时，该源能否辐射？考虑一个均匀极化的球，其表面覆盖的自由面电荷在每一点、每一时刻都抵消了束缚面电荷，此时总电荷密度ρ_tot=0，因此所有电荷多极矩均为零。连续性方程仅能确定∇·J，这使得同一电荷历史可由不同的守恒电流支撑。补偿性的内部电流会使总电流J_tot=0，且在任意频率下均不产生电场E或磁场B。而最小范数切向面电流则会使总电流J_tot非零且无散，其辐射区场在kR处是精确的，且与球贝塞尔函数j₂(kR)成正比。在长波长极限下，辐射功率被因子(kR)⁴/100抑制，且在j₂的正根处精确为零。相同计算还给出了内部场和闭式能量平衡：驱动提供的平均功等于辐射功率，即便内部场依然存在，该平均功在这些根处仍会降至零。作为对比，裸球的对应因子为3j₁(kR)/(kR)，且在j₁的根处无辐射。
英文摘要
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 $j_1$.
