正弦电流单极子近场公式的一点注解

A Note on Near-Zone Field Formulae of Sinusoidal Monopole

正弦电流单极子两端存在端电荷,电荷密度存在奇异点。论文针对Riemann积分意义下,无法对电荷密度分布函数积分获得正确的标势函数的问题,通过引入电荷分布函数,将Riemann积分改写为Stieltjes积分,在Lebegue-Stieltjes积分意义下,重新推导出相应的标量势和矢量势函数,并得到考虑端电荷影响时,正弦电流单极子近场的正确表达式,该计算式在忽略端电荷场影响下与已有结果相同。

The sinusoidal monopole has point charges at both ends and the charge desity has singularity. In the mean- ing of Riemann integral, one cann＇t get correct scalar potential function through integrating charge density function. This pa- per introducts charge distribution function, and rewrites the Reimann integral into Stieltjes integral. In the meaning of Lebe- gue-Stiehjes integral, the scalar potential and vector potential are derived and the exact formulae of near-zone field of sinu- soidal monopole are gained on considering the effect of endpoint charges. The formulae are in agreement with the known re- suits when neglecting the contribution from endpoint charges.