• Why do electric lines of force never intersect each other?

The tangent to an electric field line denotes it direction, which is unique and singular at one point.

If electric field lines were to criss-cross each other this would lead to two tangents at a same point and thus two directions, which is impossible.

 

@Aarti, Thanks for the input, keep it going!

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  The electric field has a unique direction at any point in space. If two lines crossed, two directions would be indicated for at the point of intersection and the electric field would not be unique at that point.

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