载流导体的表面电荷密度：任意形状无限细导线的精确解析解
Surface charge density of current-carrying conductors: An exact analytical solution for infinitely thin wires of arbitrary shape
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中文总结 AI 辅助
研究任意形状无限细导线载流时的表面电荷密度，通过推导精确渐近表达式，得出除导线末端边界层外电荷密度随弧长线性变化的结论，推广了早期结果，明晰了电路电荷积累物理图像。
中文摘要 AI 辅助
本文推导了与连接到电池的闭合回路或无限小横截面线段中的稳恒电流相关的表面电荷密度的精确渐近表达式。除了导线末端极薄的边界层外，无论导体形状如何，电荷密度随弧长线性变化，沿曲线的静电势也是如此。这种比例关系推广了早期结果，并为电路中的电荷积累提供了清晰的物理图像。
英文摘要
An exact asymptotic expression is derived for the surface charge density associated with a steady current in closed loops or wire segments of infinitesimal cross section connected to a battery. Except for vanishingly thin boundary layers at the ends of the wire, and irrespective of the conductor shape, the charge density varies linearly with arc length, as does the electrostatic potential along the curve. This proportionality generalizes earlier results and provides a clear physical picture of charge accumulation in electrical circuits.
