Potential difference between two points is defined as the work done in moving a net positive charge from one point to the other. But, my question is, when the two points, that are potentially different, are connected using conducting wire having length more than the distance between the two points, charge flows through the conductor; and since the charge cannot move directly through air to the other point, it has to travel all the way through the length of the conductor, and that means it has to move a longer distance than the actual distance between the two points. Therefore, more amount of work would be required in order move that charge from one point to the other since the charge has to travel a longer distance. Thus, it would mean that the potential difference between the two points increases with the length of conductor.
Work done, as we all know depends on displacement not distance, but moving anything through a longer distance would require a greater amount of work. Where am I wrong?