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

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

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

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?

Prove that a closed equipotential surface with no charge within itself must enclose an equipotential volume.