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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。
Sinusoidal current exists at both ends of the monopole charge, there is a singular point of charge density. In the sense of Riemann integral, we can not get the correct potential function by integrating the charge density distribution function. By introducing the charge distribution function, the Riemann integral is rewritten as Stieltjes integral. In the sense of Lebegue-Stieltjes integral, the corresponding Scalar potential and vector potential function, and get the correct expression of sinusoidal current unipolar near-field when considering the influence of terminal charge, which is the same as the previous one under the influence of the end-of-charge field.