论文标题
圆形电容器电容的分析结果
Analytical results for the capacitance of a circular plate capacitor
论文作者
论文摘要
我们研究了圆形平行板电容器电容的经典问题。在板块之间的小分离处，基尔乔夫最初是在19世纪考虑的，他在电容中找到了领先和统一的术语。尽管对这个问题引起了极大的兴趣，但一个半世纪后，在分析中仅发现了第二个转向统称。利用有限支持的第二类弗雷德霍尔姆积分方程的渐近分析的最新进展，我们在这里研究了一个管理圆形电容器的一个，称为爱情方程。我们在小分离中分析了许多新的转向术语。我们还计算了大分离处的渐近扩展，因此提供了两个简单的表达式，这些表达式实际上描述了各个距离的电容。此处描述的方法可用于找到与大小分离方案中任意数量的术语电容的确切分析扩展。
We study the classic problem of the capacitance of a circular parallel plate capacitor. At small separations between the plates, it is initially considered in 19th century by Kirchhoff who found the leading and the subleading term in the capacitance. Despite a large interest in the problem, one and a half century later, analytically was found only the second subleading term. Using the recent advances in the asymptotic analysis of Fredholm integral equations of the second kind with finite support, here we study the one governing the circular capacitor, known as the Love equation. We found analytically many new subleading terms in the capacitance at small separations. We also calculated the asymptotic expansion at large separations, thus providing the two simple expressions which practically describe the capacitance at all distances. The approach described here could be used to find exact analytical expansions for the capacitance to an arbitrary number of terms in both regimes of small and large separations.
