Question

Electric field lines do not intersect. Why?

Hint:

If two lines crossed, the field would have two tangents (two directions) at one point, which is impossible.

Answer 1

Step 1 (Concept): The tangent drawn to an electric field line at any point gives the direction of the electric field \( \vec{E} \) at that point.

Step 2 (Assume they intersect): Suppose two field lines were to cross at a point P. Then at P we could draw two different tangents, one to each line.

Step 3 (The contradiction): Two tangents would mean two different directions of the electric field at the single point P. But at a given point the field can have only one definite direction. This is impossible.

Step 4 (Conclusion): Hence two electric field lines can never intersect.

\[\boxed{\text{At a crossing point the field would have two directions, which is not allowed.}}\]