Question

Why do electric field lines never cross each other?

Answer 1

Define electric field and electric field lines. Obtain the properties of electric field lines. The direction of the electric field lines at a particular point is given by the tangent drawn to the electric field line at that point. Again, the electric field lines also give the magnitude of the electric field at a point through which the field lines pass.

Complete step-by-step answer:
Electric field lines are imaginary lines propagating through empty space. The electric field lines always start at a positive charge and end at a negative charge. The intensity of electric field at a particular point is given by the closeness of the electric field lines at that point. If the electric field lines are close to each other, the electric field intensity is high and if the electric field lines are far apart from each other, the electric field intensity is low.
Electric field lines are the representation of electric fields due to a source. Each electric field line coming out of a source will give a specific magnetic and direction of the field at that point. If two electric field lines intersect at a point then at that point, we will have two different values of electric field at the same point, which is not possible. Again, we will have two different tangents to electric field lines at the same point which gives two different directions of electric field at the same point which is not possible. So, the electric field lines never intersect with each other.

Note: We also have some other properties of electric field lines. The field lines are always perpendicular to the surface charge. The number of field lines is directly proportional to the magnitude of charge. If we have a single positive charge, the field lines end at infinity and if we have a single negative charge, the field lines start at infinity.