Question

If electric field lines are mutually intersecting, then what is the meaning indicated?

Hint:

A field line's tangent gives the field direction; a crossing would demand two directions of E at one point.

Answer 1

Step 1: Meaning of a field line. The tangent drawn to an electric field line at any point gives the direction of the electric field \(\vec{E}\) at that point. So each point on a line is associated with one definite field direction.

Step 2: What intersection would imply. If two field lines crossed at a point, then two tangents could be drawn there, giving two different directions of the electric field at the same point. But at any point the electric field can have only one direction.

Step 3: Conclusion. Since a single point cannot have two field directions, electric field lines can never intersect. Intersecting field lines are physically impossible; if a diagram shows them crossing, it indicates two directions of \(\vec{E}\) at one point, which cannot exist.
\[\boxed{\text{Two field directions at one point} \Rightarrow \text{impossible; field lines never cross.}}\]