Can there be a potential difference between two adjacent conductors carrying the same charge?

Consider two conducting spheres of radii R₁ and R₂ with R₁> R₂. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.

Do free electrons travel to region of higher potential or lower potential?

Can the potential function have a maximum or minimum in free space?

A test charge q is made to move in the electric field of a point charge Q along two different closed paths (Fig. 2.6). First path has sections along and perpendicular to lines of electric field. Second path is a rectangular loop of the same area as the first loop. How does the work do compare in the two cases?