An electrostatic field line cannot be discontinsous. Why ?

An electrostatic field line cannot be discontinuous. Why?

Statement-1 Electrostatic field lines are discontinuous at the surface of a conductor Statement-2 Magnetic field lines produced by permanent magnets are never discontinuous

Statement-1 Electrostatic field lines are discontinuous at the surface of a conductor Statement-2 Magnetic field lines produced by permanent magnets are never discontinuous

An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?

An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?

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