Exact closed-form solution for the electrostatic interaction of two equal-sized charged conducting spheres

Electrostatics 2015

物理学;数学

Banerjee, Shubho^1 ; Levy, Mason^1

Physics Department, Rhodes College, Memphis

TN

38112, United States^1

关键词: Closed form solutions;    Conducting spheres;    Digamma functions;    Exact solution;    Infinite series;    Numerical calculation;    Q-analogues;    Surface separation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/646/1/012016/pdf
DOI  :  10.1088/1742-6596/646/1/012016

来源: IOP

【 摘 要 】

We provide an exact closed-form solution for the electrostatic interaction of two equal-sized conducting spheres. We calculate the capacitance coefficients for the spheres in terms of the q-analogue of the digamma function. In the near limit, when the two spheres are about to touch, the closed-form exact solutions allow for much faster numerical calculations than the well-known infinite series solutions. By analyzing the exact solution in the near limit, we provide Taylor series expressions for the capacitance coefficients in terms of the surface-to- surface separation of the two spheres.