Q.If two lines of force intersect at one point, what does it mean?

[!TLDR] Two lines of force can never actually intersect -- an intersection would mean the field has two different directions at the same point, which is impossible. [!ANSWER] Two lines of force can never intersect; if they appeared to, …

By definition, the tangent to a line of force at any point gives the direction of the electric field at that exact point. If two DIFFERENT lines of force were to intersect at some common point, the tangents to the two different curves at that shared point would, in general, point in two DIFFERENT directions -- which would mean the electric field has two distinct directions simultaneously at one single point in space. But the electric field at any given point is a single, well-defined vector quantity (it is, after all, the vector sum -- by superposition -- of the fields due to every source charge, which always combines to one unique resultant vector at each point); it cannot have two different directions at once. Therefore, real electric lines of force, correctly drawn, NEVER intersect or cross one another anywhere -- if a diagram appears …

Reason from the basic tangent-definition of a line of force: an intersection would force the field to have two directions at one point, which contr …

Treating this as a purely geometric/drawing-convention rule to be memorised, rather than connecting it back to the underlying physi …