Can two electric field lines merge into each other?

Question

Two electric field lines can never intersect because electric field at a point is unique but can the 2 vectors add up to give a single vector.Will both of them merge into a single field line?

What do you mean by "the 2 vectors add up"? And no, two field lines can't merge together - if there was a point where two field lines meet, which line would a charge follow if you placed it at that point? — Dawood ibn Kareem, Aug 19 '17 at 12:58
Related: Why can two (or more) electric field lines never cross? — The Photon, Aug 19 '17 at 16:29
Also related: Number of electric field lines and intensity of electric field --- If the density of field lines is proportional to the E field strength, then crossing lines would imply infinite field strength. — The Photon, Aug 19 '17 at 16:31

score 2 · Answer 1 · answered Aug 19 '17 at 12:59

No. Think of it this way. The electric field lines tell you the direction that a small positive test charge would feel a force at that point. If you had two field lines merging into one, at that junction point the a test change (or perhaps a negative test charge) would have two possibilities in terms of which direction it would experience an electric force. This doesn't model what actually happens.

score 2 · Answer 2 · answered Aug 19 '17 at 15:07

Yes, the field lines "merge" or rather they add vectorially. Anyone who says they do not may have misunderstood your question. The electric field is a vector that points in the direction of the electric force (as opposed to a magnetic field vector which points perpendicular to a "plane" or possible force directions) and each charge in the universe contributes to the electric field because each charge is a source of force on other charges. If the forces sum together then the field lines sum together.

The contribution of each charge will add with any other contribution, and the resulting vectors make up the electric field. This phebomenon can be termed "linear superposition" because of how the vectors are summed absolutely, no weighted values, when they are superimposed on one-another.

Interestingly enough, linear superposition is not proven to be correct at all scales, and there is still a debate about how valid linear superposition can be with extremely strong charges in close proximity. Different experiments have been carried out to attempt to prove or disprove that linear superposition always applies, but as anything in physics, we're never quite sure.

score 1 · Answer 3 · answered Aug 19 '17 at 14:26

Yeah, actually it does happen. In fact the electric field lines that we draw are the resultant lines. For example, if there are two protons a certain distance apart, then there will be a null point in the middle because a positive charge placed in the middle won't experience a force.

So in any charge distribution, the electric field lines don't intersect because they already represent the resultant of the electric fields due to all the charges and the resultant will always be a unique vector.

Can two electric field lines merge into each other?

3 Answers3