We compute the electric force between a dielectric sphere and a dielectric plane in the presence of an external electric field. Laplace’s equation is solved in bispherical coordinates and Maxwell’s stress tensor is used to calculate the force. The result is given as a series expansion that is evaluated numerically. Asymptotic expressions for the case of large and small distances are obtained and compared with well-known analytical solutions. We use COMSOL commercial software to validate the semi-analytical results.

中文翻译：

---

介电球和介电平面之间的电力

我们计算在存在外部电场的情况下介电球和介电平面之间的电力。拉普拉斯方程在双球坐标系中求解，麦克斯韦应力张量用于计算力。结果以数值计算的级数展开形式给出。获得了大距离和小距离情况的渐近表达式，并与众所周知的解析解进行了比较。我们使用 COMSOL 商业软件来验证半解析结果。