Question

1. An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
2. Explain why two field lines never cross each other at any point?

Answer 1

1. 
   
   As, ${\displaystyle {\overrightarrow{F}}_{OA}={\overrightarrow{F}}_{OC}\text{or}{\overrightarrow{F}}_{OA}+{\overrightarrow{F}}_{OC}=0}$  ...(i)
   Therefore, at zero, the net force on the charge is + 1 µC.
   ${\displaystyle \overrightarrow{F}={\overrightarrow{F}}_{OA}+{\overrightarrow{F}}_{OC}+{\overrightarrow{F}}_{OB}+{\overrightarrow{F}}_{OD}\text{or}\overrightarrow{F}=0}$
   An electrostatic field line is a continuous curve because a charge experiences a continuous force when traced in an electrostatic field. The field line cannot have sudden breaks because the charge moves continuously and does not jump from one point to the other.
2. If two field lines cross each other at a point, then electric field intensity will show two directions at that point. This is not possible. Hence, two field lines never cross each other.