Exact and Approximate Capacitance and Force Expressions for the Electrostatic Interaction Between Two Equal-Sized Charged Conducting Spheres

We analyze the electrostatic interaction between two equal-sized charged conducting spheres. We obtain exact closed-form expressions for the capacitance coefficients and the electrostatic force in terms of the special q-digamma function. Additionally, we provide simpler-to-use approximate expressions for the capacitance coefficients and the force between the spheres, and then compare the approximations with the exact results.