Why are equipotential surfaces perpendicular to the field lines?
from the Earth, objects have a given amount of potential energy. Just as work must be done against
gravitational force to move an object to a new height, work must be done against an electric force to
move an object to a new equipotential surface. Therefore, it follows that electric field lines must run
perpendicular to equipotential lines just as gravitational field lines run perpendicular to heights of the
same potential energy.