Why cant two field lines intersect? The answer that i have often heard is that if they were to intersect, then there would be two different directions for force. But then two field lines can interesct in such a way that their tangetes at the point of intersection point in the same direction. ( Example: Consider the curves y = x^3 and y = -x^3. They intersect at (0,0) and the tangets are same ) I searched a bit on google and came across something called existance uniqueness theorem. Could someone explain in a little detail, maybe with some examples. Thanks.