正弦电流单极子近场公式的一点注解

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。

A Note on Near Zone Field Formulae of Sinusoidal Monopole

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 Stieltjes integral, the scalar potential and vector potential are derived and the exact formulae of near zone field of sinusoidal monopole are gained on considering the effect of endpoint charges. The formulae are in agreement with the known re sults when neglecting the contribution from endpoint charges.