Sharing Charge Between Connected Conductors

Charge is free to move inside a conductor, so when two conductors touch, electrons rearrange until the electric field driving them stops. That happens exactly when both conductors sit at the same potential. If the potentials were different, free charge would keep flowing from the higher-potential conductor to the lower one, so equilibrium means V1 = V2, not Q1 = Q2.

For an isolated sphere, V = kQ/R. Setting V1 = V2 gives kQ1/R1 = kQ2/R2, so Q1/Q2 = R1/R2: the charge splits in direct proportion to radius. A bigger sphere has more surface area spread over a larger radius, so it can hold more charge while keeping the same potential as the smaller one. That is why touching a large charged sphere to a tiny neutral one dumps most of the charge onto the large sphere - the large sphere needs much more charge just to catch up to the same potential.

This sits right after the idea that conductors in equilibrium have constant potential throughout their volume and surface, and it feeds directly into field strength near curved surfaces. Once charge redistributes, the smaller sphere ends up with less charge but a tighter radius, so its surface field E = kQ/R² can still be large, or even larger than before connecting. That link between charge sharing and field concentration at sharp or small conductors sets up later reasoning about charge density and field strength on irregularly shaped conductors.