Field Lines and Equipotential lines Why can't 2 field lines cross, and why can't 2 equipotential lines cross? I understand that equipotential lines are perpendicular to field lines. And I see that it'd be impossible to find an equipotential line if two field lines have crossed, since there cannot be two places on field lines where an equipotential line can be found. But I don't know the reasoning of why 2 field lines cannot cross. nor 2 equipotential lines. Am I correct in saying that field lines don't cross because a magnetic object placed at a point in the field moves only in 1 direction due to attraction or repulsion. If 2 lines crossed, it means the object can move in 2 directions, which is not the case.