Which role of a senator takes place only at the capitol?

I believe the answer is: serving on a committee

Within the committee,senators from each state have to form relationships with other senators that might have opposing view.

After that, they would debate their view in the chamber and eventually vote for the type of legislation that give the most positive benefit for the country.

classical republicanism, also known as civic humanism, is a form of republicanism  developed in the renaissance inspired by the governmental forms and writings of  classical  antiquity, especially such  classical  writers as aristotle, polybius, and cicero.