Exact closed-form and asymptotic expressions for the electrostatic force between two conducting spheres

We present exact closed-form expressions and complete asymptotic expansions for the electrostatic force between two charged conducting spheres of arbitrary sizes. Using asymptotic expansions of the force, we confirm that even like-charged spheres attract each other at sufficiently small separation unless their voltages/charges are the same as they would be at contact. We show that for sufficiently large size asymmetries, the repulsion between two spheres increases when they separate from contact if their voltages or their charges are held constant. Additionally, we show that in the constant voltage case, this like-voltage repulsion can be further increased and maximized through an optimal lowering of the voltage on the larger sphere at an optimal sphere separation.

Optimization of the electric field calculation for a rod-shaped conductor in a uniform electric field

A rod-shaped conductor in a uniform electric field is analyzed based on finite difference method. Most induction charges distribute at the two hemisphere ends, which is similar with two connected conducting spheres in a uniform field. Therefore, the boundary potentials are calculated by multiple image method for the system with two connected conducting spheres. Comparing the results from our method with those from traditional method with constant boundary potentials, our method can improve calculation evidently. Results prove that this method is available and credible, and it can give electric field with high precision.