  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
$\textit{increases}$ 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 maximised though
an optimal $\textit{lowering}$ of the voltage on the larger sphere at an
optimal sphere separation.
