At the midpoint of the line joining two equal point charges, the field is zero, and the electric field lines on this line joining the charges each begin at a charge and kind of end at the midpoint. Does that violate the rule that electric field lines (atleast those of the coulomb force) can only start/end at charges/infinity? If not, why not?
A follow-up question – In light of the above case, how can we prove that a point of zero electric field (a null point) in an "arbitrary electrostatic field configuration" is necessarily a point of unstable equilibrium?
Best Answer
No. Although the electric fields of each of the two equal charges vectorially equal zero at the mid point between the charges, the electric field lines do not "end". The lines are diverted from that space but still wind up terminating at a charge. The following link shows examples.
https://www.physicsclassroom.com/class/estatics/Lesson-4/Electric-Field-Lines
The diagram below from the link demonstrates that the lines end at the charges.
Not quite sure what you mean by "prove", but clearly the field strength, which is proportional to the density of the field lines, is zero only at the mid point. A charge at any position not exactly at the mid point will experience a force and accelerate. Perhaps in that sense the situation of a charge at the mid point can be considered unstable.
Hope this helps.