Suppose we have two charges of +Q separated by some distance. Now, if we connect the particles along a line, and draw the field line along that line, then the field line will point away from the closer charge until we reach the midpoint in which case, the field line vanishes. This seems to violate the rule that field lines always begin on positive charges and end on negative charges.
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2$\begingroup$ This is a good reason not to think in terms of field lines. An electric or magnetic field is really a vector at each point in space, not a bunch of lines. The lines are just a sometimes-useful visualization of the field. $\endgroup$– G. SmithJun 26, 2019 at 0:45
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Field lines do not end at the midpoint between equal charges. As the electrostatic field approaches the midpoint, its direction bends sharply away, and near the midpoint, field lines turn, symmetrically on each side, and perpendicular to the line that joins the charges. The field is zero exactly at the midpoint, so field lines do not end there. Field line density is proportional to field strength, so they do not pass directly through the midpoint.
As G. Smith commented, field lines are a useful tool for vizualization, however, they have limits. In particular, field lines cannot easily be drawn correctly in regions where the field suddenly changes direction and vanishes.
answered Jun 26, 2019 at 1:30