两个带同性电荷导体球之间一直保持排斥力的条件

The condition for two conductor spheres with the same charge always keep repel

两个带同性电荷导体球之间的相互作用是大学物理教学中的重要问题.已有研究结果表明:在一般情况下两球之间会存在吸引力,但在两球电荷与半径比值相关的特殊条件下,两球之间会一直是排斥力.本文首先通过相互作用的定性讨论,推广了两球之间一直是排斥力的条件,拓展了两球之间一直是排斥力的参数区间.然后利用由系列电象法求出的两导体球的电容系数,用数值计算方法验证了定性分析的结论,发现两个带同性电荷的导体球确实可以在更宽泛的参数条件下一直保持排斥力.

When two conductor spheres are charged with the same charge, their interaction is an interesting problem for both research and teaching. Through the qualitative discussion and the numerical simulation, the condition for the two spheres with the same charge always keep repel is extended. Based on the relationship of the electric potential energy and the distance between two spheres, the general condition for two spheres are always repelling is given. It is found that the previous condition with exactly ratio of radius and charges is actually the sufficient condition. In more general conditions, two spheres with the same charges can keep repel all along.