Question

Why does electric field of lines forms Smooth curves?

Answer 1

The Smooth curves are just the representation of the influence of the electric field. There are not only curved but straight too. Like in a uniform electric field,the field lines are straight.

Answer 2

By convention, electric field lines are said to start from a positive charge and end at a negative charge. As you can see in the above figure, the field lines come to an abrupt stop at the surface of the charge. When there isn't any charge, the electric field lines must be continuous. The only place where they can start or end is at a charge.