Why do equipotential curves have no direction associated with them?

Electric field lines illustrate the direction of the electric field, showing the path a positive test charge would take. Each line points away from positive charges and toward negative charges, creating a clear directional framework. In contrast, equipotential curves represent locations where the electric potential is the same. That means if a charge moves along an equipotential line, it does not gain or lose energy, regardless of its direction along that line.

The key difference is that electric field lines show how charges interact and move through the field, while equipotential curves focus solely on the energy state of a charge in that field. Because of this, equipotential surfaces are perpendicular to electric field lines, emphasizing that no work is done when moving along an equipotential curve. Thus, equipotential curves inherently lack any directional arrow, reflecting a state of energy equilibrium rather than a pathway of movement.

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