The exact solution to an electrostatic problem of finding the electric potential of point charges inside a dielectric prolate spheroid is discussed in this note by using the classical electrostatic theory, where the prolate spheroid is embedded in a dissimilar dielectric medium. Such a problem may find its application in hybrid solvent biomolecular simulations, in which biomolecules and a part of solvent molecules within a dielectric cavity are explicitly modeled while a surrounding dielectric continuum is used to model bulk effects of the solvent beyond the cavity. Numerical experiments have demonstrated the convergence of the proposed series solutions.

中文翻译：

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介电长球体内点电荷的静电势

在本笔记中，使用经典静电理论讨论了在电介质扁长球体内寻找点电荷电势的静电问题的精确解决方案，其中扁长球体嵌入不同的电介质中。这样的问题可能会在混合溶剂生物分子模拟中得到应用，其中介电腔内的生物分子和部分溶剂分子被明确建模，而周围的介电连续体用于建模腔外溶剂的整体效应。数值实验证明了所提出的系列解的收敛性。