So in our physics class today, we had a demonstration involving a charged rod and a neutral ball attached to a string (a physical pendulum). At first, when the rod was placed near the ball, the ball was attracted to the rod until the two objects "touched" and the neutral ball gained the same charge as the rod and was consequently repelled.
It is my understanding that from the perspective of atoms and electrons the objects never actually "touch." So something must happen at certain distance where electrons go from just repelling each other to actually being transferred.
So here are my questions: What exactly defines this threshold where charge is transferred between two objects? What forces and principles are at play that determine this? And finally, do we know any mathematical equations we know that can model or govern this?
Any help is appreciated, and if you could tailor your response to the understanding of someone who is about mid-way through high school AP Physics, I would be grateful.