Physics: Electric Field Lines: Why They Never Cross

Electric fields are invisible, but electric field lines make them visible—mapping out the space around charges in a way that reveals both direction and strength. In this question, you’re looking at two point charges of equal magnitude but opposite sign, and the field lines that curve between them. The core idea here is that these lines are not just decorative: they encode the physical reality of the field at every single point. The key property that holds for any charge configuration is that field lines never cross. Why? Because the electric field at any point has one unique direction—it’s a vector field, and a vector can’t point two ways at once. The arrows on the lines show the direction of the force on a small positive test charge placed at that point, which is the conventional definition of field direction. The spacing between lines also matters: closer lines mean a stronger field. So when you see a diagram like this, you’re reading a story about force, direction, and magnitude—all tied together by the rule that no two lines can ever intersect.