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

Magnetic field lines are

Magnetic lines form continuous closed loop. Why ?

Draw the magnetic field lines in uniform magnetic field.

(a) Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by (E_(2)-E_(1)).n = sigma/epsilon_(0) where hatn is a unit vector normal to the surface at a point and sigma is the surface charge density at that point. (The direction of hatn is from side 1 to side 2.) Hence, show that just outside a conductor, the electric field is sigma hatn //epsilon_(0) . (b) Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another. [Hint: For (a), use Gauss’s law. For, (b) use the fact that work done by electrostatic field on a closed loop is zero.]

What is the magnetic field lines outside of a solenoid?